Linear Bivariate BMM with SAMBA toy models : step mixing
The best way to learn Taweret is to use it. You can run, modify and experiment with this notebook on GitHub Codespaces.
This notebook shows how to use the Bayesian model mixing package Taweret for a toy problem.
Author : Dan Liyanage
Date : 11/10/2022
More about SAMBA toy models can be found in Uncertainties here, there, and everywhere: interpolating between small- and large-g expansions using Bayesian Model Mixing
[1]:
import sys
import os
# You will have to change the following imports depending on where you have
# the packages installed
cwd = os.getcwd()
# Get the first part of this path and append to the sys.path
tw_path = cwd.split("Taweret/")[0] + "Taweret"
samba_path = tw_path + "/subpackages/SAMBA"
sys.path.append(tw_path)
sys.path.append(samba_path)
# For plotting
import matplotlib.pyplot as plt
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
1. Get toy models and the pseudo-experimental data
[2]:
# Toy models from SAMBA
from Taweret.models import samba_models as toy_models
m1 = toy_models.Loworder(2, 'uninformative')
m2 = toy_models.Highorder(2, 'uninformative')
truth = toy_models.TrueModel()
exp = toy_models.Data()
[3]:
g = np.linspace(0.1, 0.6, 10)
plot_g = np.linspace(0.01,1,100)
m1_prediction = m1.evaluate(plot_g)
m2_prediction = m2.evaluate(plot_g)
true_output = truth.evaluate(plot_g)
exp_data= exp.evaluate(g,error = 0.01)
/Users/dananjayaliyanage/temp2/Taweret/Taweret/models/samba_models.py:333: RuntimeWarning: invalid value encountered in reciprocal
* self.x**(-2.0*self.order - 2)
[4]:
fig, ax_f = plt.subplots(figsize=(10,10))
ax_f.plot(plot_g, m1_prediction[0].flatten(), label='low order')
ax_f.plot(plot_g, m2_prediction[0].flatten(), label='high order')
ax_f.plot(plot_g, true_output[0], label='truth')
ax_f.scatter(g,exp_data[0], marker='x', label='experimental data')
ax_f.set_ylim(1.2,3.2)
ax_f.legend()
[4]:
<matplotlib.legend.Legend at 0x7fc8db24ba50>
2. Choose a Mixing method
[5]:
from Taweret.core.base_model import BaseModel
isinstance(m1, BaseModel)
[5]:
True
[6]:
# Mixing method
from Taweret.mix.bivariate_linear import BivariateLinear as BL
models= {'low_order':m1,'high_order':m2}
mix_model = BL(models_dic=models, method='step')
step mixing function has 1 free parameter(s)
Warning : Default prior is set to {'step_0': Uniform(minimum=0, maximum=1, name='step_0', latex_label='step_0', unit=None, boundary=None)}
To change the prior use `set_prior` method
[ ]:
[7]:
#uncoment to change the prior from the default
#priors = bilby.core.prior.PriorDict()
#priors['step_0'] = bilby.core.prior.Uniform(0, 1, name="step_0")
#mix_model.set_prior(priors)
3. Train to find posterior
[9]:
y_exp = np.array(exp_data[0]).reshape(1,-1)
y_err = np.array(exp_data[1]).reshape(1,-1)
# The parameters are set to minimum values for computational ease.
# You should increase the ntemps, nwalkers and nsamples and see
# if your results are changing. If so keep increasing them
# until convergence of results.
kwargs_for_sampler = {'sampler': 'ptemcee',
'ntemps': 5,
'nwalkers': 50,
'Tmax': 100,
'burn_in_fixed_discard': 50,
'nsamples': 2000,
'threads': 6,
'printdt': 60}
result = mix_model.train(x_exp=g, y_exp=y_exp, y_err=y_err, outdir = 'outdir/samba_bivaraite', label='step_mix',
kwargs_for_sampler=kwargs_for_sampler)
15:29 bilby INFO : Running for label 'step_mix', output will be saved to 'outdir/samba_bivaraite'
15:29 bilby INFO : Search parameters:
15:29 bilby INFO : step_0 = Uniform(minimum=0, maximum=1, name='step_0', latex_label='step_0', unit=None, boundary=None)
The following settings were provided for sampler
{'sampler': 'ptemcee', 'ntemps': 5, 'nwalkers': 50, 'Tmax': 100, 'burn_in_fixed_discard': 50, 'nsamples': 2000, 'threads': 6, 'printdt': 60}
15:29 bilby INFO : Single likelihood evaluation took 1.493e-03 s
15:29 bilby WARNING : Supplied argument 'printdt' not an argument of 'Ptemcee', removing.
15:29 bilby INFO : Using sampler Ptemcee with kwargs {'ntemps': 5, 'nwalkers': 50, 'Tmax': 100, 'betas': None, 'a': 2.0, 'adaptation_lag': 10000, 'adaptation_time': 100, 'random': None, 'adapt': False, 'swap_ratios': False}
15:29 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=50, mean_logl_frac=0.01, thin_by_nact=0.5, nsamples=2000, ignore_keys_for_tau=None, min_tau=1, niterations_per_check=5)
15:29 bilby INFO : Generating pos0 samples
15:29 bilby INFO : Starting to sample
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15:31 bilby INFO : Finished sampling
15:31 bilby INFO : Writing checkpoint and diagnostics
15:31 bilby INFO : Finished writing checkpoint
15:31 bilby INFO : Walkers plot failed with exception cannot unpack non-iterable AxesSubplot object
15:31 bilby INFO : Sampling time: 0:02:10.442222
15:31 bilby INFO : Summary of results:
nsamples: 2100
ln_noise_evidence: nan
ln_evidence: 3.763 +/- 1.192
ln_bayes_factor: nan +/- 1.192
[10]:
# Posterior of the mixing parameters.
result.plot_corner()
[10]:
4. Predictions
[11]:
_,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])
(10000, 1)
using provided samples instead of posterior
[12]:
per5, per20, per80, per95 = CI
prior5, prior20, prior80, prior95 = CI_prior
[13]:
# Map value prediction for the step mixing function parameter
map_prediction = mix_model.evaluate(mix_model.map, plot_g)
[14]:
%matplotlib inline
sns.set_context('poster')
fig, ax = plt.subplots(figsize=(10,10))
ax.plot(plot_g, mean.flatten(), label='posterior mean')
ax.fill_between(plot_g,per5.flatten(),per95.flatten(),color=sns.color_palette()[4], alpha=0.2, label='90% C.I.')
ax.fill_between(plot_g,per20.flatten(),per80.flatten(), color=sns.color_palette()[4], alpha=0.3, label='60% C.I.')
ax.fill_between(plot_g,prior20.flatten(),prior80.flatten(),color=sns.color_palette()[2], alpha=0.2, label='60% C.I. Prior')
ax.scatter(g,exp_data[0], marker='x', label='experimental data')
ax.plot(plot_g, mean_prior.flatten(), label='prior mean')
ax.plot(plot_g, map_prediction.flatten(), label='MAP prediction')
ax.set_ybound(1,3)
ax.legend()
[14]:
<matplotlib.legend.Legend at 0x7fc8dcb72e10>
[ ]: