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Nested sampling¶
In this example, we fit the same event with the same model as in the annual parallax example, except using dynamic nested sampling as implemented in dynesty instead of Hamiltonian Monte Carlo.
[2]:
import numpy as np
from matplotlib import pyplot as plt
import pymc3 as pm
import theano.tensor as T
import caustic as ca
import dynesty
from dynesty import utils as dyfunc
np.random.seed(42)
# Load event data
event_dir = "../../data/OB05086/"
event = ca.data.OGLEData(event_dir)
# Plot data
fig, ax = plt.subplots(figsize=(10, 5))
event.plot_standardized_data(ax);
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[108]:
# Initialize a SingleLensModel object
model = ca.models.SingleLensModel(event)
with model:
n_bands = len(event.light_curves)
# Initialize linear parameters
testval_ln_DeltaF = T.log(
ca.utils.estimate_peak_flux(event) - ca.utils.estimate_baseline_flux(event)
) # helper functions
ln_DeltaF = pm.Normal("ln_DeltaF", mu=4.0, sd=4, testval=testval_ln_DeltaF[0])
DeltaF = T.exp(ln_DeltaF)
ln_Fbase = pm.Normal(
"ln_Fbase", mu=2, sd=4, testval=T.log(ca.utils.estimate_baseline_flux(event)[0])
)
Fbase = T.exp(ln_Fbase)
# Initialize nonlinear parameters
t0 = pm.Uniform(
"t0",
model.t_min,
2 * model.t_max,
testval=ca.utils.estimate_t0(event),
transform=None,
)
ln_tE = pm.Normal("ln_tE", mu=3.0, sd=6, testval=2.0)
tE = pm.Deterministic("tE", T.exp(ln_tE))
# In the parallax model, u_0 can be negative
u0 = pm.Normal("u0", mu=0.0, sd=3, testval=-0.41)
# Initialize the two parallax parameters
piEE = pm.Normal("piEE", mu=0.0, sigma=1.0, testval=0.1)
piEN = pm.Normal("piEN", mu=0.0, sigma=1.0, testval=-0.3)
# Deterministic transformations
m_source, g = ca.compute_source_mag_and_blend_fraction(event, DeltaF, Fbase, u0)
pm.Deterministic("m_source", m_source)
pm.Deterministic("g", g)
pm.Deterministic("piE", T.sqrt(piEE ** 2 + piEN ** 2))
# Compute the trajectory including parallax
trajectory = ca.trajectory.Trajectory(event, t0, u0, tE, piEE=piEE, piEN=piEN)
u = trajectory.compute_trajectory(model.t)
# Compute the magnification
mag = model.compute_magnification(u, u0)
# Compute the mean model
mean = DeltaF * mag + Fbase
# We allow for rescaling of the error bars by a constant factor
ln_c = pm.Exponential("ln_c", 0.5, testval=0.8 * T.ones(n_bands), transform=None)
# Diagonal terms of the covariance matrix
var_F = (T.exp(ln_c) * model.sigF) ** 2
# Compute the Gaussian log_likelihood, add it as a potential term to the model
ll = model.compute_log_likelihood(model.F - mean, var_F)
pm.Potential("log_likelihood", ll)
# We'll need this later
pm.Deterministic("log_likelihood_", ll)
[109]:
print(model.vars)
[ln_DeltaF, ln_Fbase, t0, ln_tE, u0, piEE, piEN, ln_c]
To use dynamic nested sampling, we have to re write the priors in the form of a prior transfer function which maps i.i.d uniformly distributed parameters defined on a unit cube to our parameters of interest. The ppf function associated with probability distributions defined in scipy.stats does exactly that. To learn why this step is necessary, check out the dynesty docs.
[5]:
import scipy
def prior_transform(u):
"""
Transforms the uniform random variables `u ~ Unif[0., 1.)`
to the parameters of interest.
"""
x = np.array(u) # copy u
# ln_DeltaF
x[0] = scipy.stats.norm.ppf(u[0], loc=5.0, scale=2.0)
# ln_Fbase
x[1] = scipy.stats.norm.ppf(u[1], loc=4.0, scale=3.0)
# t0
x[2] = scipy.stats.norm.ppf(u[2], model.t_min, model.t_max)
# ln_tE
x[3] = scipy.stats.norm.ppf(u[3], loc=3.0, scale=3.0)
# u0
x[4] = scipy.stats.norm.ppf(u[4], loc=0.0, scale=1.0)
# pi_EE
x[5] = scipy.stats.norm.ppf(u[5], loc=0.0, scale=0.5)
# pi_EN
x[6] = scipy.stats.norm.ppf(u[6], loc=0.0, scale=0.5)
# ln_c
x[7] = scipy.stats.expon.ppf(u[7], scale=1 / 0.5)
return x
[6]:
model.vars
[6]:
[ln_DeltaF, ln_Fbase, t0_interval__, ln_tE, u0, piEE, piEN, ln_c_log__]
Let’s run the sampling, this will take some time…
[7]:
# This will take a long time
with model:
loglike = ca.utils.get_log_likelihood_function(model.log_likelihood)
ndim = len(model.vars)
sampler = dynesty.DynamicNestedSampler(loglike, prior_transform, ndim, sample="rwalk")
sampler.run_nested(wt_kwargs={"pfrac": 1.0}, print_progress=True, nlive_init=500)
results = sampler.results
# Resample samples such that they have equal weight
samples_reweighted, weights = results.samples, np.exp(results.logwt - results.logz[-1])
new_samples = dyfunc.resample_equal(samples, weights)
8326it [05:28, 20.94it/s, batch: 0 | bound: 98 | nc: 25 | ncall: 185965 | eff(%): 4.465 | loglstar: -inf < -2803.630 < inf | logz: -2825.214 +/- 0.289 | dlogz: 540.543 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
8614it [05:41, 23.03it/s, batch: 0 | bound: 103 | nc: 25 | ncall: 193750 | eff(%): 4.434 | loglstar: -inf < -2739.238 < inf | logz: -2761.476 +/- 0.289 | dlogz: 479.079 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
8678it [05:46, 24.18it/s, batch: 0 | bound: 105 | nc: 25 | ncall: 197085 | eff(%): 4.392 | loglstar: -inf < -2720.852 < inf | logz: -2743.141 +/- 0.292 | dlogz: 1035.421 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
9136it [06:08, 23.49it/s, batch: 0 | bound: 113 | nc: 25 | ncall: 209666 | eff(%): 4.347 | loglstar: -inf < -2594.622 < inf | logz: -2617.939 +/- 0.298 | dlogz: 909.350 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
9216it [06:14, 22.47it/s, batch: 0 | bound: 115 | nc: 25 | ncall: 213030 | eff(%): 4.316 | loglstar: -inf < -2570.048 < inf | logz: -2593.692 +/- 0.302 | dlogz: 885.047 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
9333it [06:20, 22.62it/s, batch: 0 | bound: 117 | nc: 25 | ncall: 216607 | eff(%): 4.299 | loglstar: -inf < -2536.056 < inf | logz: -2559.149 +/- 0.296 | dlogz: 850.011 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
9576it [06:34, 18.72it/s, batch: 0 | bound: 121 | nc: 25 | ncall: 224116 | eff(%): 4.263 | loglstar: -inf < -2471.597 < inf | logz: -2495.273 +/- 0.301 | dlogz: 785.658 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
9808it [06:47, 18.92it/s, batch: 0 | bound: 125 | nc: 25 | ncall: 231134 | eff(%): 4.234 | loglstar: -inf < -2412.500 < inf | logz: -2437.441 +/- 0.307 | dlogz: 727.527 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
10040it [07:00, 23.52it/s, batch: 0 | bound: 130 | nc: 25 | ncall: 238304 | eff(%): 4.204 | loglstar: -inf < -2346.638 < inf | logz: -2371.297 +/- 0.310 | dlogz: 660.793 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
10273it [07:13, 21.26it/s, batch: 0 | bound: 134 | nc: 25 | ncall: 245563 | eff(%): 4.175 | loglstar: -inf < -2287.211 < inf | logz: -2312.558 +/- 0.312 | dlogz: 601.628 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
10422it [07:23, 22.65it/s, batch: 0 | bound: 137 | nc: 25 | ncall: 251019 | eff(%): 4.144 | loglstar: -inf < -2252.943 < inf | logz: -2278.015 +/- 0.313 | dlogz: 566.688 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
10548it [07:32, 24.06it/s, batch: 0 | bound: 140 | nc: 25 | ncall: 256371 | eff(%): 4.106 | loglstar: -inf < -2222.945 < inf | logz: -2248.501 +/- 0.313 | dlogz: 536.940 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
10773it [07:43, 24.98it/s, batch: 0 | bound: 144 | nc: 25 | ncall: 263040 | eff(%): 4.088 | loglstar: -inf < -2169.241 < inf | logz: -2194.941 +/- 0.314 | dlogz: 482.898 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
10818it [07:49, 22.13it/s, batch: 0 | bound: 146 | nc: 25 | ncall: 266025 | eff(%): 4.059 | loglstar: -inf < -2159.311 < inf | logz: -2185.547 +/- 0.317 | dlogz: 473.465 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
10891it [07:56, 18.43it/s, batch: 0 | bound: 148 | nc: 25 | ncall: 269738 | eff(%): 4.030 | loglstar: -inf < -2141.075 < inf | logz: -2167.937 +/- 0.322 | dlogz: 455.882 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
10973it [08:02, 22.86it/s, batch: 0 | bound: 150 | nc: 25 | ncall: 273017 | eff(%): 4.012 | loglstar: -inf < -2126.601 < inf | logz: -2152.689 +/- 0.318 | dlogz: 440.248 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
11023it [08:07, 22.32it/s, batch: 0 | bound: 152 | nc: 25 | ncall: 276064 | eff(%): 3.986 | loglstar: -inf < -2116.989 < inf | logz: -2143.454 +/- 0.320 | dlogz: 430.953 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11149it [08:16, 25.35it/s, batch: 0 | bound: 155 | nc: 25 | ncall: 281288 | eff(%): 3.957 | loglstar: -inf < -2087.030 < inf | logz: -2113.932 +/- 0.323 | dlogz: 401.211 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11163it [08:20, 8.26it/s, batch: 0 | bound: 157 | nc: 25 | ncall: 283685 | eff(%): 3.928 | loglstar: -inf < -2085.485 < inf | logz: -2111.881 +/- 0.320 | dlogz: 399.042 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11231it [08:26, 25.37it/s, batch: 0 | bound: 159 | nc: 25 | ncall: 287403 | eff(%): 3.901 | loglstar: -inf < -2070.011 < inf | logz: -2097.570 +/- 0.324 | dlogz: 424.983 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11305it [08:32, 25.26it/s, batch: 0 | bound: 161 | nc: 25 | ncall: 291374 | eff(%): 3.873 | loglstar: -inf < -2056.366 < inf | logz: -2083.412 +/- 0.322 | dlogz: 410.517 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11484it [08:43, 25.13it/s, batch: 0 | bound: 165 | nc: 25 | ncall: 298013 | eff(%): 3.847 | loglstar: -inf < -2025.305 < inf | logz: -2052.875 +/- 0.326 | dlogz: 379.683 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11526it [08:48, 23.41it/s, batch: 0 | bound: 167 | nc: 25 | ncall: 301342 | eff(%): 3.819 | loglstar: -inf < -2016.288 < inf | logz: -2043.787 +/- 0.326 | dlogz: 370.484 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11633it [08:57, 25.48it/s, batch: 0 | bound: 170 | nc: 25 | ncall: 306965 | eff(%): 3.784 | loglstar: -inf < -1991.410 < inf | logz: -2019.011 +/- 0.327 | dlogz: 414.051 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11785it [09:06, 25.42it/s, batch: 0 | bound: 173 | nc: 25 | ncall: 312666 | eff(%): 3.763 | loglstar: -inf < -1959.125 < inf | logz: -1987.101 +/- 0.330 | dlogz: 414.703 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11845it [09:11, 25.19it/s, batch: 0 | bound: 175 | nc: 25 | ncall: 316053 | eff(%): 3.742 | loglstar: -inf < -1948.243 < inf | logz: -1976.123 +/- 0.328 | dlogz: 403.561 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
11947it [09:19, 25.21it/s, batch: 0 | bound: 178 | nc: 25 | ncall: 320801 | eff(%): 3.718 | loglstar: -inf < -1928.468 < inf | logz: -1956.437 +/- 0.330 | dlogz: 383.665 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
12084it [09:28, 25.30it/s, batch: 0 | bound: 181 | nc: 25 | ncall: 326149 | eff(%): 3.699 | loglstar: -inf < -1905.117 < inf | logz: -1933.745 +/- 0.332 | dlogz: 360.745 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
12269it [09:39, 22.81it/s, batch: 0 | bound: 185 | nc: 25 | ncall: 332859 | eff(%): 3.680 | loglstar: -inf < -1872.784 < inf | logz: -1901.585 +/- 0.333 | dlogz: 347.622 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
12332it [09:45, 24.80it/s, batch: 0 | bound: 187 | nc: 25 | ncall: 336356 | eff(%): 3.661 | loglstar: -inf < -1864.281 < inf | logz: -1893.106 +/- 0.333 | dlogz: 338.978 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
12445it [09:54, 24.68it/s, batch: 0 | bound: 190 | nc: 25 | ncall: 341757 | eff(%): 3.636 | loglstar: -inf < -1848.175 < inf | logz: -1877.318 +/- 0.336 | dlogz: 322.999 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
12495it [10:00, 24.13it/s, batch: 0 | bound: 192 | nc: 25 | ncall: 345270 | eff(%): 3.614 | loglstar: -inf < -1839.911 < inf | logz: -1869.443 +/- 0.336 | dlogz: 315.046 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
12527it [10:05, 17.29it/s, batch: 0 | bound: 194 | nc: 25 | ncall: 348664 | eff(%): 3.588 | loglstar: -inf < -1833.489 < inf | logz: -1863.274 +/- 0.339 | dlogz: 308.871 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
12565it [10:11, 21.68it/s, batch: 0 | bound: 196 | nc: 25 | ncall: 352049 | eff(%): 3.564 | loglstar: -inf < -1828.126 < inf | logz: -1857.795 +/- 0.337 | dlogz: 303.283 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
13213it [10:41, 22.84it/s, batch: 0 | bound: 206 | nc: 25 | ncall: 370446 | eff(%): 3.562 | loglstar: -inf < -1740.085 < inf | logz: -1770.517 +/- 0.344 | dlogz: 295.464 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
13645it [11:05, 23.61it/s, batch: 0 | bound: 213 | nc: 25 | ncall: 383892 | eff(%): 3.550 | loglstar: -inf < -1685.760 < inf | logz: -1717.301 +/- 0.350 | dlogz: 274.508 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
13721it [11:12, 23.22it/s, batch: 0 | bound: 215 | nc: 25 | ncall: 388207 | eff(%): 3.530 | loglstar: -inf < -1675.537 < inf | logz: -1706.968 +/- 0.349 | dlogz: 263.988 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
13793it [11:21, 23.90it/s, batch: 0 | bound: 217 | nc: 25 | ncall: 393562 | eff(%): 3.500 | loglstar: -inf < -1664.688 < inf | logz: -1696.466 +/- 0.351 | dlogz: 253.364 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
14075it [11:37, 24.16it/s, batch: 0 | bound: 222 | nc: 25 | ncall: 402985 | eff(%): 3.488 | loglstar: -inf < -1636.187 < inf | logz: -1667.939 +/- 0.351 | dlogz: 224.211 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
14260it [11:49, 23.57it/s, batch: 0 | bound: 226 | nc: 25 | ncall: 410368 | eff(%): 3.471 | loglstar: -inf < -1617.827 < inf | logz: -1649.975 +/- 0.354 | dlogz: 205.881 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
14304it [11:55, 22.40it/s, batch: 0 | bound: 228 | nc: 25 | ncall: 414262 | eff(%): 3.449 | loglstar: -inf < -1613.074 < inf | logz: -1645.571 +/- 0.355 | dlogz: 201.408 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
14352it [12:02, 22.91it/s, batch: 0 | bound: 230 | nc: 25 | ncall: 418546 | eff(%): 3.425 | loglstar: -inf < -1607.839 < inf | logz: -1640.426 +/- 0.356 | dlogz: 196.167 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
14477it [12:14, 21.62it/s, batch: 0 | bound: 233 | nc: 25 | ncall: 425274 | eff(%): 3.400 | loglstar: -inf < -1597.685 < inf | logz: -1630.034 +/- 0.355 | dlogz: 185.490 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
14828it [12:33, 21.73it/s, batch: 0 | bound: 239 | nc: 25 | ncall: 436861 | eff(%): 3.390 | loglstar: -inf < -1568.507 < inf | logz: -1601.551 +/- 0.359 | dlogz: 156.305 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
14915it [12:42, 16.75it/s, batch: 0 | bound: 242 | nc: 25 | ncall: 441129 | eff(%): 3.377 | loglstar: -inf < -1561.715 < inf | logz: -1595.044 +/- 0.360 | dlogz: 149.631 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
14952it [12:54, 18.04it/s, batch: 0 | bound: 244 | nc: 25 | ncall: 447085 | eff(%): 3.341 | loglstar: -inf < -1559.418 < inf | logz: -1592.702 +/- 0.359 | dlogz: 147.205 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
15228it [13:13, 16.33it/s, batch: 0 | bound: 249 | nc: 31 | ncall: 456778 | eff(%): 3.330 | loglstar: -inf < -1539.628 < inf | logz: -1574.136 +/- 0.365 | dlogz: 128.153 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
15351it [13:27, 24.74it/s, batch: 0 | bound: 252 | nc: 25 | ncall: 464155 | eff(%): 3.304 | loglstar: -inf < -1529.597 < inf | logz: -1563.496 +/- 0.364 | dlogz: 117.194 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
15398it [13:39, 20.33it/s, batch: 0 | bound: 254 | nc: 25 | ncall: 470996 | eff(%): 3.266 | loglstar: -inf < -1527.021 < inf | logz: -1561.079 +/- 0.363 | dlogz: 114.683 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
15863it [14:11, 23.64it/s, batch: 0 | bound: 262 | nc: 25 | ncall: 487352 | eff(%): 3.252 | loglstar: -inf < -1499.376 < inf | logz: -1534.186 +/- 0.368 | dlogz: 99.780 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
15910it [14:23, 20.86it/s, batch: 0 | bound: 264 | nc: 25 | ncall: 494539 | eff(%): 3.214 | loglstar: -inf < -1496.685 < inf | logz: -1531.758 +/- 0.369 | dlogz: 97.268 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16031it [14:38, 20.19it/s, batch: 0 | bound: 267 | nc: 25 | ncall: 503214 | eff(%): 3.183 | loglstar: -inf < -1491.200 < inf | logz: -1526.558 +/- 0.369 | dlogz: 96.441 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16165it [14:54, 20.66it/s, batch: 0 | bound: 270 | nc: 25 | ncall: 510575 | eff(%): 3.163 | loglstar: -inf < -1483.832 < inf | logz: -1519.501 +/- 0.372 | dlogz: 89.112 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16228it [15:11, 17.00it/s, batch: 0 | bound: 272 | nc: 25 | ncall: 519484 | eff(%): 3.121 | loglstar: -inf < -1480.915 < inf | logz: -1516.491 +/- 0.372 | dlogz: 85.968 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16340it [15:27, 22.02it/s, batch: 0 | bound: 275 | nc: 25 | ncall: 527204 | eff(%): 3.096 | loglstar: -inf < -1474.269 < inf | logz: -1510.039 +/- 0.374 | dlogz: 79.294 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16352it [15:37, 3.42it/s, batch: 0 | bound: 277 | nc: 25 | ncall: 532563 | eff(%): 3.068 | loglstar: -inf < -1473.707 < inf | logz: -1509.475 +/- 0.373 | dlogz: 78.703 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16620it [16:02, 16.29it/s, batch: 0 | bound: 282 | nc: 54 | ncall: 546125 | eff(%): 3.040 | loglstar: -inf < -1461.363 < inf | logz: -1497.415 +/- 0.375 | dlogz: 66.099 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16740it [16:17, 13.96it/s, batch: 0 | bound: 285 | nc: 25 | ncall: 554799 | eff(%): 3.015 | loglstar: -inf < -1456.152 < inf | logz: -1492.782 +/- 0.377 | dlogz: 61.239 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16787it [16:33, 17.20it/s, batch: 0 | bound: 287 | nc: 25 | ncall: 562483 | eff(%): 2.982 | loglstar: -inf < -1454.330 < inf | logz: -1490.795 +/- 0.377 | dlogz: 59.145 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16857it [16:50, 23.89it/s, batch: 0 | bound: 289 | nc: 25 | ncall: 571209 | eff(%): 2.949 | loglstar: -inf < -1451.263 < inf | logz: -1488.038 +/- 0.378 | dlogz: 62.579 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
16970it [17:06, 25.27it/s, batch: 0 | bound: 292 | nc: 25 | ncall: 581030 | eff(%): 2.918 | loglstar: -inf < -1447.013 < inf | logz: -1483.933 +/- 0.378 | dlogz: 58.245 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
17143it [17:27, 22.63it/s, batch: 0 | bound: 296 | nc: 25 | ncall: 592881 | eff(%): 2.889 | loglstar: -inf < -1441.043 < inf | logz: -1478.027 +/- 0.379 | dlogz: 52.179 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
17326it [17:45, 22.36it/s, batch: 0 | bound: 300 | nc: 25 | ncall: 603781 | eff(%): 2.867 | loglstar: -inf < -1435.216 < inf | logz: -1472.638 +/- 0.381 | dlogz: 46.429 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
17429it [18:00, 23.07it/s, batch: 0 | bound: 303 | nc: 25 | ncall: 613186 | eff(%): 2.840 | loglstar: -inf < -1432.553 < inf | logz: -1469.834 +/- 0.381 | dlogz: 53.428 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
17471it [18:16, 14.19it/s, batch: 0 | bound: 305 | nc: 25 | ncall: 622491 | eff(%): 2.804 | loglstar: -inf < -1431.089 < inf | logz: -1468.716 +/- 0.382 | dlogz: 52.233 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
17534it [18:32, 22.57it/s, batch: 0 | bound: 307 | nc: 25 | ncall: 631753 | eff(%): 2.773 | loglstar: -inf < -1429.144 < inf | logz: -1466.942 +/- 0.382 | dlogz: 50.335 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
17590it [18:46, 21.34it/s, batch: 0 | bound: 309 | nc: 25 | ncall: 640017 | eff(%): 2.746 | loglstar: -inf < -1427.348 < inf | logz: -1465.062 +/- 0.384 | dlogz: 48.337 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
17725it [19:03, 20.91it/s, batch: 0 | bound: 312 | nc: 25 | ncall: 649993 | eff(%): 2.725 | loglstar: -inf < -1423.815 < inf | logz: -1461.671 +/- 0.384 | dlogz: 47.782 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
17926it [19:24, 23.82it/s, batch: 0 | bound: 316 | nc: 25 | ncall: 661026 | eff(%): 2.710 | loglstar: -inf < -1418.987 < inf | logz: -1457.262 +/- 0.385 | dlogz: 42.972 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
18040it [19:42, 22.72it/s, batch: 0 | bound: 319 | nc: 25 | ncall: 672172 | eff(%): 2.682 | loglstar: -inf < -1416.372 < inf | logz: -1454.791 +/- 0.386 | dlogz: 40.272 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
18286it [20:06, 25.32it/s, batch: 0 | bound: 324 | nc: 25 | ncall: 687717 | eff(%): 2.657 | loglstar: -inf < -1411.323 < inf | logz: -1450.154 +/- 0.388 | dlogz: 35.142 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
18615it [20:31, 22.00it/s, batch: 0 | bound: 330 | nc: 58 | ncall: 703242 | eff(%): 2.645 | loglstar: -inf < -1406.180 < inf | logz: -1445.228 +/- 0.389 | dlogz: 29.551 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
18775it [20:53, 22.33it/s, batch: 0 | bound: 334 | nc: 25 | ncall: 717118 | eff(%): 2.616 | loglstar: -inf < -1403.483 < inf | logz: -1443.011 +/- 0.391 | dlogz: 27.017 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
19257it [21:29, 23.72it/s, batch: 0 | bound: 342 | nc: 25 | ncall: 738929 | eff(%): 2.604 | loglstar: -inf < -1397.706 < inf | logz: -1437.682 +/- 0.394 | dlogz: 21.526 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
19387it [21:50, 25.05it/s, batch: 0 | bound: 345 | nc: 25 | ncall: 751752 | eff(%): 2.577 | loglstar: -inf < -1396.453 < inf | logz: -1436.574 +/- 0.395 | dlogz: 20.157 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
19450it [22:05, 23.57it/s, batch: 0 | bound: 347 | nc: 25 | ncall: 760833 | eff(%): 2.555 | loglstar: -inf < -1395.732 < inf | logz: -1436.061 +/- 0.395 | dlogz: 19.518 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
19568it [22:29, 24.16it/s, batch: 0 | bound: 350 | nc: 25 | ncall: 776895 | eff(%): 2.517 | loglstar: -inf < -1394.515 < inf | logz: -1435.045 +/- 0.396 | dlogz: 18.266 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
19688it [22:46, 24.89it/s, batch: 0 | bound: 353 | nc: 25 | ncall: 787350 | eff(%): 2.499 | loglstar: -inf < -1393.280 < inf | logz: -1434.101 +/- 0.397 | dlogz: 17.717 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
19880it [23:06, 25.67it/s, batch: 0 | bound: 357 | nc: 25 | ncall: 800224 | eff(%): 2.483 | loglstar: -inf < -1391.569 < inf | logz: -1432.582 +/- 0.399 | dlogz: 15.813 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
20026it [23:22, 25.40it/s, batch: 0 | bound: 360 | nc: 25 | ncall: 810724 | eff(%): 2.469 | loglstar: -inf < -1390.255 < inf | logz: -1431.559 +/- 0.400 | dlogz: 14.498 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
20131it [23:36, 24.92it/s, batch: 0 | bound: 363 | nc: 25 | ncall: 819674 | eff(%): 2.454 | loglstar: -inf < -1389.378 < inf | logz: -1430.823 +/- 0.401 | dlogz: 13.553 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
20255it [23:59, 25.46it/s, batch: 0 | bound: 366 | nc: 25 | ncall: 835042 | eff(%): 2.424 | loglstar: -inf < -1388.380 < inf | logz: -1430.008 +/- 0.402 | dlogz: 12.489 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
20309it [24:14, 23.73it/s, batch: 0 | bound: 368 | nc: 25 | ncall: 844714 | eff(%): 2.403 | loglstar: -inf < -1387.984 < inf | logz: -1429.666 +/- 0.402 | dlogz: 12.039 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
20489it [24:32, 25.43it/s, batch: 0 | bound: 372 | nc: 25 | ncall: 856455 | eff(%): 2.391 | loglstar: -inf < -1386.715 < inf | logz: -1428.634 +/- 0.403 | dlogz: 10.646 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
20573it [24:52, 24.05it/s, batch: 0 | bound: 375 | nc: 25 | ncall: 870552 | eff(%): 2.362 | loglstar: -inf < -1386.214 < inf | logz: -1428.202 +/- 0.404 | dlogz: 10.374 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
20706it [25:11, 25.38it/s, batch: 0 | bound: 378 | nc: 25 | ncall: 883231 | eff(%): 2.343 | loglstar: -inf < -1385.394 < inf | logz: -1427.589 +/- 0.404 | dlogz: 9.494 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
20801it [25:29, 22.05it/s, batch: 0 | bound: 381 | nc: 25 | ncall: 893393 | eff(%): 2.327 | loglstar: -inf < -1384.861 < inf | logz: -1427.173 +/- 0.405 | dlogz: 8.888 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
20927it [25:55, 23.37it/s, batch: 0 | bound: 384 | nc: 25 | ncall: 909976 | eff(%): 2.298 | loglstar: -inf < -1384.141 < inf | logz: -1426.650 +/- 0.406 | dlogz: 8.114 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
21029it [26:24, 23.65it/s, batch: 0 | bound: 387 | nc: 25 | ncall: 927793 | eff(%): 2.265 | loglstar: -inf < -1383.662 < inf | logz: -1426.259 +/- 0.406 | dlogz: 7.519 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
21213it [26:50, 23.50it/s, batch: 0 | bound: 391 | nc: 25 | ncall: 943984 | eff(%): 2.246 | loglstar: -inf < -1382.797 < inf | logz: -1425.635 +/- 0.407 | dlogz: 7.652 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
21337it [27:17, 24.03it/s, batch: 0 | bound: 394 | nc: 25 | ncall: 961654 | eff(%): 2.218 | loglstar: -inf < -1382.276 < inf | logz: -1425.268 +/- 0.408 | dlogz: 7.037 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
21376it [27:35, 15.43it/s, batch: 0 | bound: 396 | nc: 25 | ncall: 972829 | eff(%): 2.196 | loglstar: -inf < -1382.116 < inf | logz: -1425.158 +/- 0.408 | dlogz: 6.849 > 0.010]/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
21570it [28:05, 24.69it/s, batch: 0 | bound: 400 | nc: 25 | ncall: 991440 | eff(%): 2.175 | loglstar: -inf < -1381.421 < inf | logz: -1424.667 +/- 0.409 | dlogz: 5.972 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
21686it [28:30, 24.60it/s, batch: 0 | bound: 403 | nc: 25 | ncall: 1008231 | eff(%): 2.150 | loglstar: -inf < -1381.021 < inf | logz: -1424.405 +/- 0.410 | dlogz: 5.479 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
21813it [28:55, 24.52it/s, batch: 0 | bound: 406 | nc: 25 | ncall: 1025080 | eff(%): 2.127 | loglstar: -inf < -1380.689 < inf | logz: -1424.160 +/- 0.410 | dlogz: 4.983 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
22471it [29:47, 18.08it/s, batch: 0 | bound: 418 | nc: 69 | ncall: 1056870 | eff(%): 2.125 | loglstar: -inf < -1379.001 < inf | logz: -1423.239 +/- 0.412 | dlogz: 3.382 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
22728it [30:04, 23.98it/s, batch: 0 | bound: 423 | nc: 25 | ncall: 1066965 | eff(%): 2.129 | loglstar: -inf < -1378.370 < inf | logz: -1422.993 +/- 0.413 | dlogz: 2.660 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
22796it [30:29, 22.73it/s, batch: 0 | bound: 425 | nc: 25 | ncall: 1083677 | eff(%): 2.103 | loglstar: -inf < -1378.245 < inf | logz: -1422.933 +/- 0.414 | dlogz: 2.479 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
22942it [30:53, 21.58it/s, batch: 0 | bound: 428 | nc: 25 | ncall: 1098493 | eff(%): 2.088 | loglstar: -inf < -1377.982 < inf | logz: -1422.818 +/- 0.414 | dlogz: 2.114 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
23052it [31:16, 24.25it/s, batch: 0 | bound: 431 | nc: 25 | ncall: 1112871 | eff(%): 2.070 | loglstar: -inf < -1377.781 < inf | logz: -1422.741 +/- 0.414 | dlogz: 1.932 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
23087it [31:36, 12.81it/s, batch: 0 | bound: 433 | nc: 25 | ncall: 1126602 | eff(%): 2.048 | loglstar: -inf < -1377.725 < inf | logz: -1422.718 +/- 0.415 | dlogz: 1.853 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
23171it [32:04, 23.62it/s, batch: 0 | bound: 436 | nc: 25 | ncall: 1145709 | eff(%): 2.022 | loglstar: -inf < -1377.571 < inf | logz: -1422.666 +/- 0.415 | dlogz: 1.671 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
23235it [32:23, 23.63it/s, batch: 0 | bound: 438 | nc: 25 | ncall: 1158947 | eff(%): 2.004 | loglstar: -inf < -1377.448 < inf | logz: -1422.628 +/- 0.415 | dlogz: 1.539 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
23410it [32:48, 24.42it/s, batch: 0 | bound: 442 | nc: 25 | ncall: 1175165 | eff(%): 1.991 | loglstar: -inf < -1377.157 < inf | logz: -1422.534 +/- 0.415 | dlogz: 1.209 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
23768it [33:24, 24.99it/s, batch: 0 | bound: 448 | nc: 25 | ncall: 1199272 | eff(%): 1.981 | loglstar: -inf < -1376.733 < inf | logz: -1422.392 +/- 0.416 | dlogz: 0.691 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
23879it [33:51, 24.71it/s, batch: 0 | bound: 451 | nc: 25 | ncall: 1217219 | eff(%): 1.961 | loglstar: -inf < -1376.614 < inf | logz: -1422.359 +/- 0.417 | dlogz: 0.579 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
23947it [34:15, 24.19it/s, batch: 0 | bound: 453 | nc: 25 | ncall: 1233629 | eff(%): 1.940 | loglstar: -inf < -1376.541 < inf | logz: -1422.340 +/- 0.417 | dlogz: 0.648 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
24006it [34:38, 23.53it/s, batch: 0 | bound: 455 | nc: 25 | ncall: 1249237 | eff(%): 1.921 | loglstar: -inf < -1376.486 < inf | logz: -1422.326 +/- 0.417 | dlogz: 0.587 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
24136it [35:07, 24.41it/s, batch: 0 | bound: 458 | nc: 25 | ncall: 1269553 | eff(%): 1.900 | loglstar: -inf < -1376.338 < inf | logz: -1422.297 +/- 0.417 | dlogz: 0.469 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
25263it [36:13, 24.67it/s, batch: 0 | bound: 474 | nc: 25 | ncall: 1311584 | eff(%): 1.925 | loglstar: -inf < -1375.445 < inf | logz: -1422.172 +/- 0.418 | dlogz: 0.060 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
26058it [36:52, 25.13it/s, batch: 0 | bound: 486 | nc: 25 | ncall: 1335000 | eff(%): 1.951 | loglstar: -inf < -1375.010 < inf | logz: -1422.150 +/- 0.418 | dlogz: 0.013 > 0.010] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:219: UserWarning: Random number generation appears to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random number generation appears to be "
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
26689it [38:21, 23.07it/s, batch: 1 | bound: 490 | nc: 25 | ncall: 1367760 | eff(%): 1.951 | loglstar: -1379.778 < -1379.614 < -1377.077 | logz: -1422.141 +/- 0.419 | stop: 1.981] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
29443it [41:07, 15.67it/s, batch: 3 | bound: 521 | nc: 73 | ncall: 1441692 | eff(%): 2.025 | loglstar: -1381.267 < -1381.060 < -1380.538 | logz: -1422.171 +/- 0.415 | stop: 1.473] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
30499it [42:19, 19.65it/s, batch: 4 | bound: 531 | nc: 25 | ncall: 1471015 | eff(%): 2.056 | loglstar: -1381.760 < -1380.466 < -1377.905 | logz: -1422.139 +/- 0.414 | stop: 1.368] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
37124it [48:36, 18.81it/s, batch: 7 | bound: 615 | nc: 25 | ncall: 1649792 | eff(%): 2.233 | loglstar: -1383.099 < -1380.703 < -1376.653 | logz: -1422.139 +/- 0.411 | stop: 1.114] /Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/sampling.py:241: UserWarning: Random walk proposals appear to be extremely inefficient. Adjusting the scale-factor accordingly.
warnings.warn("Random walk proposals appear to be "
39707it [50:48, 13.03it/s, batch: 7 | bound: 648 | nc: 25 | ncall: 1721672 | eff(%): 2.306 | loglstar: -1383.099 < -1374.693 < -1376.653 | logz: -1422.139 +/- 0.411 | stop: 0.888]
The sampling appears to have converged according to internal criteria specified in dynesty with a total of ~2M likelihood calls, let’s plot the diagnostics plots.
[49]:
from dynesty import plotting as dyplot
# Plot a summary of the run.
fig = plt.subplots(4, 1, figsize=(10, 8))
rfig, raxes = dyplot.runplot(results, fig=fig)
# Plot traces and 1-D marginalized posteriors.
tfig, taxes = dyplot.traceplot(
results,
labels=["ln_DeltaF", "ln_Fbase", "t0", "ln_tE", "u0", "piEE", "piEN", "ln_c"],
)
/Users/fb90/anaconda3/envs/pymc3/lib/python3.7/site-packages/dynesty/plotting.py:245: UserWarning: Attempting to set identical bottom == top == 0.0 results in singular transformations; automatically expanding.
axes[i].set_ylim([ymin, ymax])
Let’s plot the posterior over the \(u_0\) parameter, which we expect to be multi-modal
[50]:
# Plot posterior for u0
fig, ax = plt.subplots()
ax.hist(samples_reweighted[:, 4], bins=50, density=True)
ax.grid()
ax.set_xlabel("$u_0$")
[50]:
Text(0.5, 0, '$u_0$')
Looks like dynesty not only managed to discover both significant modes in the posterior, but also the relative height between the two modes matches what we’ve oberved in the annual parallax example.
Let’s plot the model to check that it makes sense, and plot the posterior trajectories from the multi-modal pdf.
[115]:
with model:
# Create dense grid
t_dense = np.tile(np.linspace(model.t_min, model.t_max, 1000), (n_bands, 1))
t_dense_tensor = T.as_tensor_variable(t_dense)
# Evaluate trajectory components on dense grid
u, un, ue = trajectory.compute_trajectory(t_dense_tensor, return_components=True)
# Compute the magnification
mag_dense = model.compute_magnification(T.sqrt(un ** 2 + ue ** 2), u0)
# Compute the mean model
mean_dense = DeltaF * mag_dense + Fbase
[131]:
# To plot the model, we need to transform the transformed parameters
def get_samples_from_array(array, size=1):
for i in range(size):
sample_idx = np.random.randint(len(array))
yield model.bijection.rmap(array[sample_idx][::-1])
# Plot model
fig, ax = plt.subplots(
2, 1, gridspec_kw={"height_ratios": [3, 1]}, figsize=(10, 6), sharex=True
)
samples = list(get_samples_from_array(samples_reweighted, size=50))
with model:
ca.utils.plot_model_and_residuals(ax, event, samples, t_dense_tensor, mean_dense)
[138]:
# Plot trajectory
fig, ax = plt.subplots(figsize=(8, 8))
with model:
ca.utils.plot_trajectory_from_samples(
ax, samples, t_dense_tensor, un, ue, color="C0"
)
Looks good. Whereas in the parallax example with HMC we had to manually discover the different modes and had no idea about their relative importance, dynesty properly sampled the full pdf.