2.6. Comparative study of BMM method in bivariate linear module using Coleman toy models.

The best way to learn Taweret is to use it. You can run, modify and experiment with this notebook using GitHub Codespaces.

The models can be found in Coleman Thesis : https://go.exlibris.link/3fVZCfhl

This notebook shows how to use the Bayesian model mixing methods available in bivariate_linear mixing method of package Taweret for a toy problem.

Author : Dan Liyanage

Date : 08/14/2023

import sys
import os

# You will have to change the following imports depending on where you have 
# the packages installed

# ! pip install Taweret    # if using Colab, uncomment to install

# Setting Taweret path
cwd = os.getcwd()

# Get the first part of this path and append to the sys.path
tw_path = cwd.split("Taweret/")[0] + "Taweret"
sys.path.append(tw_path)

# For plotting
import matplotlib.pyplot as plt

! pip install seaborn    # comment if installed
! pip install ptemcee    # comment if installed

import seaborn as sns
sns.set_context('poster')
# To define priors. (uncoment if not using default priors)
# ! pip install bilby      # uncomment if not already installed
import bilby

# For other operations
import numpy as np

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# Import models with a predict method
from Taweret.models import coleman_models as toy_models

m1 = toy_models.coleman_model_1()
m2 = toy_models.coleman_model_2()
truth = toy_models.coleman_truth()

#!pwd

g = np.linspace(0,9,10)
plot_g = np.linspace(0,9,100)
true_output = truth.evaluate(plot_g)
exp_data = truth.evaluate(g)

2.6.1. 1. The models and the experimental data.

Truth

\(f(x) = 2-0.1(x-4)^2\), where \(x \in [-1, 9]\)

Model 1

\(f_1(x,\theta)= 0.5(x+\theta)-2\) , where \(\theta \in [1, 6]\)

Model 2

\(f_2(x,\theta)= -0.5(x-\theta) + 3.7\) , where \(\theta \in [-2, 3]\)

Experimental data

sampled from the Truth with a fixed standard deviation of 0.3

sns.set_context('notebook')
fig, axs = plt.subplots(1,2,figsize=(20,5))
prior_ranges = [(1,6), (-2,3)]
for i in range(0,2):
    ax = axs.flatten()[i]
    ax.plot(plot_g, true_output[0], label='truth', color='black')
    ax.errorbar(g,exp_data[0],exp_data[1], fmt='o', label='experimental data', color='r')
    ax.legend()
    ax.set_ylim(-2,4)
    for value in np.linspace(*prior_ranges[i],10):
        if i==0:
            predict_1 = m1.evaluate(plot_g, value, full_corr=False)
            ax.plot(plot_g, predict_1[0])
            ax.set_ylabel(r'$f_1(x)$')
        if i==1:
            predict_2 = m2.evaluate(plot_g, value, full_corr=False)
            ax.plot(plot_g, predict_2[0])      
            ax.set_ylabel(r'$f_2(x)$')    
    ax.set_xlabel('x') 
    

2.6.2. 2. Choose a Mixing method

# Mixing method
from Taweret.mix.bivariate_linear import BivariateLinear as BL

models= {'model1':m1,'model2':m2}

mix_model_BMMC_mix = BL(models_dic=models, method='addstepasym', nargs_model_dic={'model1':1, 'model2':1},
              same_parameters = False)

mix_model_BMMcor_mix = BL(models_dic=models, method='addstepasym', nargs_model_dic={'model1':1, 'model2':1},
              same_parameters = False, BMMcor=True)

mix_model_mean_mix = BL(models_dic=models, method='addstepasym', nargs_model_dic={'model1':1, 'model2':1},
              same_parameters = False, mean_mix=True)

mix_models = [mix_model_BMMC_mix, mix_model_BMMcor_mix, mix_model_mean_mix]

addstepasym mixing function has 3                   free parameter(s)
Warning : Default prior is set to {'addstepasym_0': Uniform(minimum=0, maximum=1, name='addstepasym_0', latex_label='addstepasym_0', unit=None, boundary=None), 'addstepasym_1': Uniform(minimum=0, maximum=1, name='addstepasym_1', latex_label='addstepasym_1', unit=None, boundary=None), 'addstepasym_2': Uniform(minimum=0, maximum=1, name='addstepasym_2', latex_label='addstepasym_2', unit=None, boundary=None)}
To change the prior use `set_prior` method
Using default priors for model 1
{'model1_0': Uniform(minimum=1, maximum=6, name='model1_0', latex_label='model1_0', unit=None, boundary=None)}
Using default priors for model 2
{'model2_0': Uniform(minimum=-2, maximum=3, name='model2_0', latex_label='model2_0', unit=None, boundary=None)}
addstepasym mixing function has 3                   free parameter(s)
Warning : Default prior is set to {'addstepasym_0': Uniform(minimum=0, maximum=1, name='addstepasym_0', latex_label='addstepasym_0', unit=None, boundary=None), 'addstepasym_1': Uniform(minimum=0, maximum=1, name='addstepasym_1', latex_label='addstepasym_1', unit=None, boundary=None), 'addstepasym_2': Uniform(minimum=0, maximum=1, name='addstepasym_2', latex_label='addstepasym_2', unit=None, boundary=None)}
To change the prior use `set_prior` method
addstepasym mixing function has 3                   free parameter(s)
Warning : Default prior is set to {'addstepasym_0': Uniform(minimum=0, maximum=1, name='addstepasym_0', latex_label='addstepasym_0', unit=None, boundary=None), 'addstepasym_1': Uniform(minimum=0, maximum=1, name='addstepasym_1', latex_label='addstepasym_1', unit=None, boundary=None), 'addstepasym_2': Uniform(minimum=0, maximum=1, name='addstepasym_2', latex_label='addstepasym_2', unit=None, boundary=None)}
To change the prior use `set_prior` method

## uncoment to change the prior from the default
priors = bilby.core.prior.PriorDict()
priors['addstepasym_0'] = bilby.core.prior.Uniform(0, 9, name="addstepasym_0")
priors['addstepasym_1'] = bilby.core.prior.Uniform(0, 9, name="addstepasym_1")
priors['addstepasym_2'] = bilby.core.prior.Uniform(0, 1, name="addstepasym_2")
for mix_model in mix_models:
    mix_model.set_prior(priors)

for mix__model in mix_models:
    print(mix_model.prior)

{'addstepasym_0': Uniform(minimum=0, maximum=9, name='addstepasym_0', latex_label='addstepasym_0', unit=None, boundary=None), 'addstepasym_1': Uniform(minimum=0, maximum=9, name='addstepasym_1', latex_label='addstepasym_1', unit=None, boundary=None), 'addstepasym_2': Uniform(minimum=0, maximum=1, name='addstepasym_2', latex_label='addstepasym_2', unit=None, boundary=None), 'model1_0': Uniform(minimum=1, maximum=6, name='model1_0', latex_label='model1_0', unit=None, boundary=None), 'model2_0': Uniform(minimum=-2, maximum=3, name='model2_0', latex_label='model2_0', unit=None, boundary=None)}
{'addstepasym_0': Uniform(minimum=0, maximum=9, name='addstepasym_0', latex_label='addstepasym_0', unit=None, boundary=None), 'addstepasym_1': Uniform(minimum=0, maximum=9, name='addstepasym_1', latex_label='addstepasym_1', unit=None, boundary=None), 'addstepasym_2': Uniform(minimum=0, maximum=1, name='addstepasym_2', latex_label='addstepasym_2', unit=None, boundary=None), 'model1_0': Uniform(minimum=1, maximum=6, name='model1_0', latex_label='model1_0', unit=None, boundary=None), 'model2_0': Uniform(minimum=-2, maximum=3, name='model2_0', latex_label='model2_0', unit=None, boundary=None)}
{'addstepasym_0': Uniform(minimum=0, maximum=9, name='addstepasym_0', latex_label='addstepasym_0', unit=None, boundary=None), 'addstepasym_1': Uniform(minimum=0, maximum=9, name='addstepasym_1', latex_label='addstepasym_1', unit=None, boundary=None), 'addstepasym_2': Uniform(minimum=0, maximum=1, name='addstepasym_2', latex_label='addstepasym_2', unit=None, boundary=None), 'model1_0': Uniform(minimum=1, maximum=6, name='model1_0', latex_label='model1_0', unit=None, boundary=None), 'model2_0': Uniform(minimum=-2, maximum=3, name='model2_0', latex_label='model2_0', unit=None, boundary=None)}

2.6.3. 3. Train to find posterior

g.shape

(10,)

#from Taweret.utils.utils import normed_mvn_loglike

kwargs_for_sampler = {'sampler':'ptemcee',
                'ntemps':5,
                'nwalkers':40,
                'Tmax':100,
                'burn_in_fixed_discard':500,
                'nsamples':3000,
                'threads':6}
                #'safety':2,
                #'autocorr_tol':5}

import os
import shutil
outdirs = ['outdir/mix_model_1', 'outdir/mix_model_2', 'outdir/mix_model_3']
labels = ['BMMC','BMMcor','BMMmean']
results = []

for i in range(0,3):
    mix_model = mix_models[i]
    label = labels[i]
    outdir = outdirs[i]
    if os.path.isdir(outdir):
        print('removing '+outdir)
        shutil.rmtree(outdir)
    else:
        print('file does not exist '+outdir)
    result = mix_model.train(x_exp=g.reshape(-1,1), y_exp=exp_data[0].reshape(-1,1), y_err=exp_data[1].reshape(-1,1)
                         ,kwargs_for_sampler=kwargs_for_sampler, label=label, outdir=outdir)
    results.append(result)

14:59 bilby INFO    : Running for label 'BMMC', output will be saved to 'outdir/mix_model_1'

file does not exist outdir/mix_model_1
The following settings were                     provided for sampler 
{'sampler': 'ptemcee', 'ntemps': 5, 'nwalkers': 40, 'Tmax': 100, 'burn_in_fixed_discard': 500, 'nsamples': 3000, 'threads': 6}

14:59 bilby INFO    : Analysis priors:

14:59 bilby INFO    : addstepasym_0=Uniform(minimum=0, maximum=9, name='addstepasym_0', latex_label='addstepasym_0', unit=None, boundary=None)

14:59 bilby INFO    : addstepasym_1=Uniform(minimum=0, maximum=9, name='addstepasym_1', latex_label='addstepasym_1', unit=None, boundary=None)

14:59 bilby INFO    : addstepasym_2=Uniform(minimum=0, maximum=1, name='addstepasym_2', latex_label='addstepasym_2', unit=None, boundary=None)

14:59 bilby INFO    : model1_0=Uniform(minimum=1, maximum=6, name='model1_0', latex_label='model1_0', unit=None, boundary=None)

14:59 bilby INFO    : model2_0=Uniform(minimum=-2, maximum=3, name='model2_0', latex_label='model2_0', unit=None, boundary=None)

14:59 bilby INFO    : Analysis likelihood class: <class 'Taweret.sampler.likelihood_wrappers.likelihood_wrapper_for_bilby'>

14:59 bilby INFO    : Analysis likelihood noise evidence: nan

14:59 bilby INFO    : Single likelihood evaluation took nan s

14:59 bilby INFO    : Using sampler Ptemcee with kwargs {'ntemps': 5, 'nwalkers': 40, 'Tmax': 100, 'betas': None, 'a': 2.0, 'adaptation_lag': 10000, 'adaptation_time': 100, 'random': None, 'adapt': False, 'swap_ratios': False}

14:59 bilby INFO    : Using convergence inputs: ConvergenceInputs(autocorr_c=5, autocorr_tol=50, autocorr_tau=1, gradient_tau=0.1, gradient_mean_log_posterior=0.1, Q_tol=1.02, safety=1, burn_in_nact=50, burn_in_fixed_discard=500, mean_logl_frac=0.01, thin_by_nact=0.5, nsamples=3000, ignore_keys_for_tau=None, min_tau=1, niterations_per_check=5)

14:59 bilby INFO    : Generating pos0 samples

14:59 bilby INFO    : Starting to sample

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657|0:01:22|nc:6.6e+05|a0:0.36-0.41|swp:0.26-0.70|n:2280<3000|t=2(+0.01,+0.10)|q:1.00|0.14ms/ev

658|0:01:22|nc:6.6e+05|a0:0.36-0.41|swp:0.26-0.70|n:2320<3000|t=2(+0.01,+0.08)|q:1.00|0.14ms/ev

659|0:01:22|nc:6.6e+05|a0:0.36-0.41|swp:0.26-0.70|n:2360<3000|t!2(+0.01,+0.12)|q:1.00|0.14ms/ev

660|0:01:22|nc:6.6e+05|a0:0.36-0.41|swp:0.26-0.70|n:2400<3000|t!2(+0.01,+0.20)|q:1.00|0.14ms/ev

661|0:01:22|nc:6.6e+05|a0:0.36-0.41|swp:0.26-0.70|n:2440<3000|t!2(+0.02,+0.18)|q:1.00|0.14ms/ev

662|0:01:23|nc:6.6e+05|a0:0.36-0.41|swp:0.26-0.70|n:2480<3000|t!2(+0.02,+0.21)|q:1.00|0.15ms/ev

663|0:01:23|nc:6.6e+05|a0:0.36-0.41|swp:0.26-0.70|n:2520<3000|t=2(+0.02,+0.08)|q:1.00|0.15ms/ev

664|0:01:23|nc:6.6e+05|a0:0.36-0.41|swp:0.26-0.70|n:2560<3000|t!2(+0.01,+0.17)|q:1.00|0.15ms/ev

665|0:01:23|nc:6.6e+05|a0:0.36-0.41|swp:0.26-0.70|n:2600<3000|t!2(+0.01,+0.11)|q:1.00|0.14ms/ev

666|0:01:23|nc:6.7e+05|a0:0.36-0.41|swp:0.26-0.70|n:2640<3000|t!2(+0.01,+0.19)|q:1.00|0.14ms/ev

667|0:01:23|nc:6.7e+05|a0:0.36-0.41|swp:0.26-0.70|n:2680<3000|t=2(+0.02,+0.06)|q:1.00|0.14ms/ev

668|0:01:23|nc:6.7e+05|a0:0.36-0.41|swp:0.26-0.70|n:2720<3000|t!2(+0.02,+0.20)|q:1.00|0.14ms/ev

669|0:01:24|nc:6.7e+05|a0:0.36-0.41|swp:0.26-0.70|n:2760<3000|t!2(+0.02,+0.20)|q:1.00|0.14ms/ev

670|0:01:24|nc:6.7e+05|a0:0.36-0.41|swp:0.26-0.70|n:2800<3000|t!2(+0.02,+0.17)|q:1.00|0.14ms/ev

671|0:01:24|nc:6.7e+05|a0:0.36-0.41|swp:0.26-0.70|n:2840<3000|t!2(+0.01,+0.27)|q:1.00|0.14ms/ev

672|0:01:24|nc:6.7e+05|a0:0.36-0.41|swp:0.26-0.70|n:2880<3000|t!2(+0.01,+0.15)|q:1.00|0.14ms/ev

673|0:01:24|nc:6.7e+05|a0:0.36-0.41|swp:0.26-0.70|n:2920<3000|t=2(+0.02,+0.07)|q:1.00|0.14ms/ev

674|0:01:24|nc:6.7e+05|a0:0.36-0.41|swp:0.26-0.70|n:2960<3000|t!2(+0.02,+0.34)|q:1.00|0.14ms/ev

675|0:01:24|nc:6.8e+05|a0:0.36-0.41|swp:0.26-0.70|n:3000<3000|t!2(+0.02,+0.28)|q:1.00|0.14ms/ev

676|0:01:25|nc:6.8e+05|a0:0.36-0.41|swp:0.26-0.70|n:3040<3000|t=2(+0.02,+0.07)|q:1.00|0.14ms/ev

15:00 bilby INFO    : Finished sampling

15:00 bilby INFO    : Writing checkpoint and diagnostics

15:00 bilby INFO    : Finished writing checkpoint

15:00 bilby INFO    : Sampling time: 0:01:25.046926

15:00 bilby INFO    : Summary of results:
nsamples: 3040
ln_noise_evidence:    nan
ln_evidence: -7.558 +/-  2.809
ln_bayes_factor:    nan +/-  2.809

15:00 bilby INFO    : Running for label 'BMMcor', output will be saved to 'outdir/mix_model_2'

file does not exist outdir/mix_model_2
The following settings were                     provided for sampler 
{'sampler': 'ptemcee', 'ntemps': 5, 'nwalkers': 40, 'Tmax': 100, 'burn_in_fixed_discard': 500, 'nsamples': 3000, 'threads': 6}

15:00 bilby INFO    : Analysis priors:

15:00 bilby INFO    : addstepasym_0=Uniform(minimum=0, maximum=9, name='addstepasym_0', latex_label='addstepasym_0', unit=None, boundary=None)

15:00 bilby INFO    : addstepasym_1=Uniform(minimum=0, maximum=9, name='addstepasym_1', latex_label='addstepasym_1', unit=None, boundary=None)

15:00 bilby INFO    : addstepasym_2=Uniform(minimum=0, maximum=1, name='addstepasym_2', latex_label='addstepasym_2', unit=None, boundary=None)

15:00 bilby INFO    : model1_0=Uniform(minimum=1, maximum=6, name='model1_0', latex_label='model1_0', unit=None, boundary=None)

15:00 bilby INFO    : model2_0=Uniform(minimum=-2, maximum=3, name='model2_0', latex_label='model2_0', unit=None, boundary=None)

15:00 bilby INFO    : Analysis likelihood class: <class 'Taweret.sampler.likelihood_wrappers.likelihood_wrapper_for_bilby'>

15:00 bilby INFO    : Analysis likelihood noise evidence: nan

15:00 bilby INFO    : Single likelihood evaluation took nan s

15:00 bilby INFO    : Using sampler Ptemcee with kwargs {'ntemps': 5, 'nwalkers': 40, 'Tmax': 100, 'betas': None, 'a': 2.0, 'adaptation_lag': 10000, 'adaptation_time': 100, 'random': None, 'adapt': False, 'swap_ratios': False}

15:00 bilby INFO    : Using convergence inputs: ConvergenceInputs(autocorr_c=5, autocorr_tol=50, autocorr_tau=1, gradient_tau=0.1, gradient_mean_log_posterior=0.1, Q_tol=1.02, safety=1, burn_in_nact=50, burn_in_fixed_discard=500, mean_logl_frac=0.01, thin_by_nact=0.5, nsamples=3000, ignore_keys_for_tau=None, min_tau=1, niterations_per_check=5)

15:00 bilby INFO    : Generating pos0 samples

15:00 bilby INFO    : Starting to sample

1|0:00:00|nc:1.0e+03|a0:0.00-0.80|swp:0.26-0.47|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

2|0:00:00|nc:2.0e+03|a0:0.10-0.90|swp:0.15-0.36|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

3|0:00:00|nc:3.0e+03|a0:0.13-0.87|swp:0.11-0.33|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

4|0:00:00|nc:4.0e+03|a0:0.10-0.85|swp:0.09-0.33|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

5|0:00:00|nc:5.0e+03|a0:0.16-0.84|swp:0.07-0.33|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

6|0:00:01|nc:6.0e+03|a0:0.13-0.83|swp:0.06-0.32|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

7|0:00:01|nc:7.0e+03|a0:0.17-0.71|swp:0.05-0.33|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

8|0:00:01|nc:8.0e+03|a0:0.23-0.70|swp:0.05-0.33|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

9|0:00:01|nc:9.0e+03|a0:0.27-0.67|swp:0.05-0.33|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

10|0:00:01|nc:1.0e+04|a0:0.28-0.64|swp:0.06-0.33|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

11|0:00:01|nc:1.1e+04|a0:0.29-0.64|swp:0.06-0.34|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

12|0:00:01|nc:1.2e+04|a0:0.32-0.65|swp:0.07-0.34|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

13|0:00:02|nc:1.3e+04|a0:0.31-0.63|swp:0.08-0.35|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

14|0:00:02|nc:1.4e+04|a0:0.30-0.60|swp:0.08-0.35|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

15|0:00:02|nc:1.5e+04|a0:0.31-0.59|swp:0.09-0.36|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

16|0:00:02|nc:1.6e+04|a0:0.31-0.60|swp:0.10-0.37|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

17|0:00:02|nc:1.7e+04|a0:0.31-0.60|swp:0.11-0.38|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

18|0:00:02|nc:1.8e+04|a0:0.30-0.60|swp:0.11-0.39|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

19|0:00:03|nc:1.9e+04|a0:0.29-0.59|swp:0.12-0.39|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

20|0:00:03|nc:2.0e+04|a0:0.31-0.59|swp:0.13-0.40|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

21|0:00:03|nc:2.1e+04|a0:0.31-0.56|swp:0.14-0.40|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

22|0:00:03|nc:2.2e+04|a0:0.34-0.56|swp:0.14-0.41|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

23|0:00:03|nc:2.3e+04|a0:0.33-0.57|swp:0.15-0.41|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

24|0:00:03|nc:2.4e+04|a0:0.33-0.55|swp:0.15-0.41|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

25|0:00:04|nc:2.5e+04|a0:0.33-0.55|swp:0.16-0.41|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

26|0:00:04|nc:2.6e+04|a0:0.32-0.55|swp:0.17-0.41|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

27|0:00:04|nc:2.7e+04|a0:0.33-0.54|swp:0.17-0.42|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

28|0:00:04|nc:2.8e+04|a0:0.34-0.54|swp:0.17-0.43|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

29|0:00:04|nc:2.9e+04|a0:0.34-0.54|swp:0.18-0.44|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

30|0:00:04|nc:3.0e+04|a0:0.35-0.53|swp:0.18-0.44|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

31|0:00:05|nc:3.1e+04|a0:0.35-0.52|swp:0.18-0.45|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

32|0:00:05|nc:3.2e+04|a0:0.36-0.51|swp:0.19-0.45|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

33|0:00:05|nc:3.3e+04|a0:0.36-0.50|swp:0.19-0.45|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

34|0:00:05|nc:3.4e+04|a0:0.35-0.50|swp:0.19-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

35|0:00:05|nc:3.5e+04|a0:0.36-0.50|swp:0.20-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

36|0:00:05|nc:3.6e+04|a0:0.35-0.49|swp:0.20-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

37|0:00:06|nc:3.7e+04|a0:0.35-0.49|swp:0.20-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

38|0:00:06|nc:3.8e+04|a0:0.34-0.49|swp:0.20-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

39|0:00:06|nc:3.9e+04|a0:0.34-0.49|swp:0.21-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

40|0:00:06|nc:4.0e+04|a0:0.35-0.49|swp:0.21-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

41|0:00:06|nc:4.1e+04|a0:0.35-0.49|swp:0.21-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

42|0:00:06|nc:4.2e+04|a0:0.34-0.49|swp:0.21-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

43|0:00:07|nc:4.3e+04|a0:0.34-0.50|swp:0.22-0.46|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

44|0:00:07|nc:4.4e+04|a0:0.34-0.50|swp:0.22-0.47|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

45|0:00:07|nc:4.5e+04|a0:0.33-0.49|swp:0.22-0.47|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

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47|0:00:07|nc:4.7e+04|a0:0.34-0.49|swp:0.22-0.47|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

48|0:00:07|nc:4.8e+04|a0:0.33-0.48|swp:0.22-0.48|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.17ms/ev

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50|0:00:08|nc:5.0e+04|a0:0.33-0.48|swp:0.23-0.48|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

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67|0:00:11|nc:6.7e+04|a0:0.35-0.48|swp:0.24-0.50|n:nan<3000|t!nan(+nan,+nan)|q:inf|0.16ms/ev

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15:02 bilby INFO    : Finished sampling

15:02 bilby INFO    : Writing checkpoint and diagnostics

15:02 bilby INFO    : Finished writing checkpoint

15:02 bilby INFO    : Sampling time: 0:01:53.551721

15:02 bilby INFO    : Summary of results:
nsamples: 3160
ln_noise_evidence:    nan
ln_evidence:  7.107 +/-  5.256
ln_bayes_factor:    nan +/-  5.256

15:02 bilby INFO    : Running for label 'BMMmean', output will be saved to 'outdir/mix_model_3'

file does not exist outdir/mix_model_3
The following settings were                     provided for sampler 
{'sampler': 'ptemcee', 'ntemps': 5, 'nwalkers': 40, 'Tmax': 100, 'burn_in_fixed_discard': 500, 'nsamples': 3000, 'threads': 6}

15:02 bilby INFO    : Analysis priors:

15:02 bilby INFO    : addstepasym_0=Uniform(minimum=0, maximum=9, name='addstepasym_0', latex_label='addstepasym_0', unit=None, boundary=None)

15:02 bilby INFO    : addstepasym_1=Uniform(minimum=0, maximum=9, name='addstepasym_1', latex_label='addstepasym_1', unit=None, boundary=None)

15:02 bilby INFO    : addstepasym_2=Uniform(minimum=0, maximum=1, name='addstepasym_2', latex_label='addstepasym_2', unit=None, boundary=None)

15:02 bilby INFO    : model1_0=Uniform(minimum=1, maximum=6, name='model1_0', latex_label='model1_0', unit=None, boundary=None)

15:02 bilby INFO    : model2_0=Uniform(minimum=-2, maximum=3, name='model2_0', latex_label='model2_0', unit=None, boundary=None)

15:02 bilby INFO    : Analysis likelihood class: <class 'Taweret.sampler.likelihood_wrappers.likelihood_wrapper_for_bilby'>

15:02 bilby INFO    : Analysis likelihood noise evidence: nan

15:02 bilby INFO    : Single likelihood evaluation took nan s

15:02 bilby INFO    : Using sampler Ptemcee with kwargs {'ntemps': 5, 'nwalkers': 40, 'Tmax': 100, 'betas': None, 'a': 2.0, 'adaptation_lag': 10000, 'adaptation_time': 100, 'random': None, 'adapt': False, 'swap_ratios': False}

15:02 bilby INFO    : Using convergence inputs: ConvergenceInputs(autocorr_c=5, autocorr_tol=50, autocorr_tau=1, gradient_tau=0.1, gradient_mean_log_posterior=0.1, Q_tol=1.02, safety=1, burn_in_nact=50, burn_in_fixed_discard=500, mean_logl_frac=0.01, thin_by_nact=0.5, nsamples=3000, ignore_keys_for_tau=None, min_tau=1, niterations_per_check=5)

15:02 bilby INFO    : Generating pos0 samples

15:02 bilby INFO    : Starting to sample

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959|0:02:11|nc:9.6e+05|a0:0.41-0.45|swp:0.26-0.62|n:2200<3000|t!2(+0.01,+0.21)|q:1.00|0.15ms/ev

960|0:02:11|nc:9.6e+05|a0:0.41-0.45|swp:0.26-0.62|n:2240<3000|t!2(+0.01,+0.14)|q:1.00|0.15ms/ev

961|0:02:11|nc:9.6e+05|a0:0.41-0.45|swp:0.26-0.62|n:2280<3000|t!2(+0.02,+0.12)|q:1.00|0.15ms/ev

962|0:02:11|nc:9.6e+05|a0:0.41-0.45|swp:0.26-0.62|n:2320<3000|t!2(+0.02,+0.15)|q:1.00|0.15ms/ev

963|0:02:11|nc:9.6e+05|a0:0.41-0.45|swp:0.26-0.62|n:2360<3000|t!2(+0.01,+0.16)|q:1.00|0.15ms/ev

964|0:02:11|nc:9.6e+05|a0:0.41-0.45|swp:0.26-0.62|n:2400<3000|t!2(+0.01,+0.23)|q:1.00|0.15ms/ev

965|0:02:12|nc:9.6e+05|a0:0.41-0.45|swp:0.26-0.62|n:2440<3000|t!2(+0.02,+0.33)|q:1.00|0.15ms/ev

966|0:02:12|nc:9.7e+05|a0:0.41-0.45|swp:0.26-0.62|n:2480<3000|t!2(+0.02,+0.26)|q:1.00|0.15ms/ev

967|0:02:12|nc:9.7e+05|a0:0.41-0.45|swp:0.26-0.62|n:2520<3000|t!2(+0.02,+0.41)|q:1.00|0.15ms/ev

968|0:02:12|nc:9.7e+05|a0:0.41-0.45|swp:0.26-0.62|n:2560<3000|t!2(+0.04,+0.21)|q:1.00|0.15ms/ev

969|0:02:12|nc:9.7e+05|a0:0.41-0.45|swp:0.26-0.62|n:2600<3000|t!2(+0.03,+0.11)|q:1.00|0.15ms/ev

970|0:02:12|nc:9.7e+05|a0:0.41-0.45|swp:0.26-0.62|n:2640<3000|t=2(+0.02,+0.10)|q:1.00|0.15ms/ev

971|0:02:12|nc:9.7e+05|a0:0.41-0.45|swp:0.26-0.62|n:2680<3000|t!2(+0.01,+0.11)|q:1.00|0.15ms/ev

972|0:02:13|nc:9.7e+05|a0:0.41-0.45|swp:0.26-0.62|n:2720<3000|t!2(+0.01,+0.21)|q:1.00|0.15ms/ev

973|0:02:13|nc:9.7e+05|a0:0.41-0.45|swp:0.26-0.62|n:2760<3000|t!2(+0.02,+0.28)|q:1.00|0.15ms/ev

974|0:02:13|nc:9.7e+05|a0:0.41-0.45|swp:0.26-0.62|n:2800<3000|t!2(+0.01,+0.14)|q:1.00|0.15ms/ev

975|0:02:13|nc:9.8e+05|a0:0.41-0.45|swp:0.26-0.62|n:2840<3000|t!2(+0.01,+0.16)|q:1.00|0.15ms/ev

976|0:02:13|nc:9.8e+05|a0:0.41-0.45|swp:0.26-0.62|n:2880<3000|t!2(+0.02,+0.34)|q:1.00|0.15ms/ev

977|0:02:13|nc:9.8e+05|a0:0.41-0.45|swp:0.26-0.62|n:2920<3000|t!2(+0.02,+0.33)|q:1.00|0.15ms/ev

978|0:02:14|nc:9.8e+05|a0:0.41-0.45|swp:0.26-0.62|n:2960<3000|t!2(+0.03,+0.10)|q:1.00|0.15ms/ev

979|0:02:14|nc:9.8e+05|a0:0.41-0.45|swp:0.26-0.62|n:3000<3000|t!2(+0.03,+0.15)|q:1.00|0.15ms/ev

980|0:02:14|nc:9.8e+05|a0:0.41-0.45|swp:0.26-0.62|n:3040<3000|t=2(+0.02,+0.08)|q:1.00|0.15ms/ev

15:05 bilby INFO    : Finished sampling

15:05 bilby INFO    : Writing checkpoint and diagnostics

15:05 bilby INFO    : Finished writing checkpoint

15:05 bilby INFO    : Sampling time: 0:02:14.329333

15:05 bilby INFO    : Summary of results:
nsamples: 3040
ln_noise_evidence:    nan
ln_evidence: -1.753 +/-  4.220
ln_bayes_factor:    nan +/-  4.220

posteriors = [0,0,0]
for i in range(0,3):
    result = results[i]
    label = labels[i]
    result = result.posterior.iloc[:,0:-2]
    result['model'] = label
    posteriors[i]=result

/tmp/ipykernel_3471/3955572814.py:6: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  result['model'] = label
/tmp/ipykernel_3471/3955572814.py:6: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  result['model'] = label
/tmp/ipykernel_3471/3955572814.py:6: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  result['model'] = label

import pandas as pd

df = pd.concat(posteriors, ignore_index=True, sort=False)

df.head(-10)

	addstepasym_0	addstepasym_1	addstepasym_2	model1_0	model2_0	model
0	3.577443	4.365066	0.991233	5.614310	1.546296	BMMC
1	3.360323	7.870432	0.899973	5.298600	1.475326	BMMC
2	6.788237	6.001776	0.878605	4.362493	1.080984	BMMC
3	3.814027	6.995905	0.834819	5.530295	1.225247	BMMC
4	3.898735	6.755405	0.810004	5.619542	1.224350	BMMC
...	...	...	...	...	...	...
9225	3.763418	5.933109	0.966352	4.769874	0.740553	BMMmean
9226	3.114620	0.545556	0.982246	4.677854	1.585482	BMMmean
9227	4.131844	4.417148	0.937221	4.464089	1.137183	BMMmean
9228	4.131844	4.417148	0.937221	4.464089	1.137183	BMMmean
9229	4.259244	4.936786	0.941790	4.391083	1.194091	BMMmean

9230 rows × 6 columns

df_renamed=df.rename(columns={'addstepasym_0':r'$\beta_0$', 'addstepasym_1':r'$\beta_1$', 
                              'addstepasym_2':r'$\alpha$', 'model1_0':r'$\theta_1$', 
                              'model2_0':r'$\theta_2$', 'model':'method'})

#g.savefig('temp_save')

import seaborn as sns
sns.set_context('paper', font_scale=1.5)
gg = sns.PairGrid(df_renamed, hue="method", diag_sharey=False, hue_kws={'alpha':0.5}, corner=True,
                palette={'BMMC':sns.color_palette()[2],'BMMcor':sns.color_palette()[3], 'BMMmean':sns.color_palette()[-1]})
gg.map_lower(sns.kdeplot, fill=True)
gg.map_diag(sns.kdeplot, linewidth=2, fill=True)
gg.add_legend(loc='upper center')
plt.tight_layout()
plt.savefig('comparative_posterior', dpi=100)

2.6.3.1. 4. Predictions

sns.set_context('paper', font_scale=1.9)
fig, axs = plt.subplots(1,2,figsize=(20,10))
ax, ax2 = axs.flatten()
#fig2, ax2 = plt.subplots(figsize=(10,10))
colors = {'BMMC':sns.color_palette()[2],'BMMcor':sns.color_palette()[3], 'BMMmean':sns.color_palette()[-1]}
for i, mix_model in enumerate(mix_models):
    _,mean_prior,CI_prior, _ = mix_model.prior_predict(plot_g, CI=[5,20,80,95])
    _,mean,CI, _ = mix_model.predict(plot_g, CI=[5,20,80,95])
    per5, per20, per80, per95 = CI
    prior5, prior20, prior80, prior95 = CI_prior
    # Map value prediction for the step mixing function parameter

    model_params = [np.array(mix_model.map[3]), np.array(mix_model.map[4])]
    map_prediction = mix_model.evaluate(mix_model.map[0:3], plot_g, model_params=model_params)
    print(mix_model.map)
    
    _,_,CI_weights,_=mix_model.predict_weights(plot_g, CI=[5,20, 80, 95])
    perw_5, perw_20, perw_80, perw_95 = CI_weights
    
    
    #ax.fill_between(plot_g,perw_5,perw_95,color=colors[labels[i]], alpha=0.2, label='90% C.I.')
    ax.fill_between(plot_g,perw_20,perw_80, color=colors[labels[i]], alpha=0.3, label=labels[i])
    
    if i==0:
        ax2.fill_between(plot_g,prior20.flatten(),prior80.flatten(),color=sns.color_palette()[7], alpha=0.2, label='60% C.I. Prior')
        ax2.errorbar(g,exp_data[0],yerr=exp_data[1], marker='x', label='experimental data', color='red', fmt='.')
        ax2.plot(plot_g, mean_prior.flatten(), label='prior mean')
    #ax2.plot(plot_g, mean.flatten(), label=labels[i])
    #ax2.fill_between(plot_g,per5.flatten(),per95.flatten(),color=sns.color_palette()[4], alpha=0.2, label='90% C.I.')
    ax2.fill_between(plot_g,per20.flatten(),per80.flatten(), color=colors[labels[i]], alpha=0.3, label=labels[i])

    ax2.plot(plot_g, map_prediction.flatten(), color=colors[labels[i]], linestyle='dashed')

    
ax.legend()
ax.set_xlabel('x')
ax.set_ylabel('Model weight (w)')


ax2.set_ybound(-1,4)
ax2.legend(loc='upper center')
ax2.set_xlabel('x')
ax2.set_ylabel('Model output')

ax.set_title('(a)')
ax2.set_title('(b)')

plt.tight_layout()
fig.savefig('comparative_posterior_prditcions', dpi=100)
#fig2.savefig('comparative_posterior_predict', dpi=100)

(10000, 5)
using provided samples instead of posterior

[3.8831695  1.17361241 0.99989426 4.98453429 1.17704711]
(3040, 100)
(10000, 5)
using provided samples instead of posterior

/tmp/ipykernel_3471/1972745161.py:26: UserWarning: marker is redundantly defined by the 'marker' keyword argument and the fmt string "." (-> marker='.'). The keyword argument will take precedence.
  ax2.errorbar(g,exp_data[0],yerr=exp_data[1], marker='x', label='experimental data', color='red', fmt='.')

[3.62615461 2.47041345 0.99711489 5.04025008 1.28542767]
(3160, 100)
(10000, 5)
using provided samples instead of posterior

[3.1877353  4.52904161 0.99220364 5.02412432 1.21360602]
(3040, 100)