Linear Bivariate BMM with SAMBA toy models : switchcos mixing

2.3. Linear Bivariate BMM with SAMBA toy models : switchcos mixing#

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

This notebook try to reproduce the work by A. C. Semposki, R. J. Furnstahl, D. R. Phillips in Uncertainties here, there, and everywhere: interpolating between small- and large-g expansions using Bayesian Model Mixing using the Bayesian model mixing package Taweret.

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

Steps for Bayesian Model Mixing with Taweret

1. Define your models using BayesModel class in `Taweret.core.bayesmodel` (Only if you want to bring in your own models)
2. Choose a Mixing method (Avilable mixing methods can be found in Taweret/mix)
3. Find the posterior for the mixture weights (parameters in the mixture function) and/or model parameters by training the mixed model. 
4. Make predictions! 

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

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     # comment if already installed
import bilby

# For other operations
import numpy as np

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2.3.1. 1. Get toy models and the pseudo-experimental data#

# 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()

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)

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()

<matplotlib.legend.Legend at 0x7efca3ff8410>
../../_images/e6e69ad7a1f9f7ed7f00998125fbc94d5aa8d42fe85b2313476c2d8cfd77500a.png

2.3.2. 2. Choose a Mixing method#

# 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='switchcos') 

switchcos mixing function has 3                   free parameter(s)
Warning : Default prior is set to {'switchcos_0': Uniform(minimum=0, maximum=1, name='switchcos_0', latex_label='switchcos_0', unit=None, boundary=None), 'switchcos_1': Uniform(minimum=0, maximum=1, name='switchcos_1', latex_label='switchcos_1', unit=None, boundary=None), 'switchcos_2': Uniform(minimum=0, maximum=1, name='switchcos_2', latex_label='switchcos_2', unit=None, boundary=None)}
To change the prior use `set_prior` method

/home/runner/work/Taweret/Taweret/.tox/book/lib/python3.12/site-packages/bilby/core/likelihood.py:83: FutureWarning: <class 'Taweret.sampler.likelihood_wrappers.likelihood_wrapper_for_bilby'> log_likelihood or log_likelihood_ratio method does not accept 'parameters' as an argument. This is deprecated behaviour  and will be removed in Bilby version 3. See https://bilby-dev.github.io/bilby/parameters for more details.
  warnings.warn(

Need to speceify a constained prior for switchcos. g1 < g3 < g2

We follow Bilby documentation on how to specefy a prior with constraints https://lscsoft.docs.ligo.org/bilby/prior.html#prior-constraints

# from scipy import stats 

# def luniform(theta, a, b):

#     if theta > a and theta < b:
#         return 0.0
#     else:
#         return -np.inf

# def lpdf(params):
#     if len(params) == 3:
#         #g1 truncated between (0, 0.35) 
#         g1 = luniform(params[0], 0.01, 0.3) + stats.norm.logpdf(params[0], 0.1, 0.05)   #0.1 for 2 v 2, #0.1 for 5 v 5
#         #g3 truncated between (g1, 0.35)
#         g3 = luniform(params[2], params[0], 0.55) + stats.norm.logpdf(params[2], 0.4, 0.05)   #0.4 for 2 v 2, #0.25 for 5 v 5
#         #g2 truncated between (g3, 0.35)
#         g2 = luniform(params[1], params[2], 0.8) + stats.norm.logpdf(params[1], 0.6, 0.05)  #0.6 for 2 v 2, #0.4 for 5 v 5
#         return (g1 + g2 + g3)
#     else:
#         print(params)
#         raise ValueError('The number of parameters does not match any available switching function.')

from bilby.core.prior.joint import BaseJointPriorDist, JointPrior, JointPriorDistError
from Taweret.utils.priors import Priors as samba_P
samba_prior = samba_P()


class custom_prior_switchcos(BaseJointPriorDist):
    def __init__(self, names, bounds=None):
        '''
        A class defining prior for swithcos mixing method

        Parameters
        ==========
        names: list
            A list of the parameter names in the prior
        '''
        super().__init__(names=names, bounds=bounds)
        self.names=names
    def ln_prob(self,value):
        try:
            n_sam = value.shape[1]
            return [samba_prior.lpdf(x) for x in value]
        except:
            return samba_prior.lpdf(value)

    def _sample(self, size, **kwargs):
        """
        Draw, and set, a sample for the switchcos parameter joint distribution

        Parameters
        ==========
        size: int
            number of samples to generate, defaults to 1
        """
        samps = np.zeros((size, len(self)))
        samps[:,0] = np.random.uniform(0.12, 0.18, size)
        samps[:,2] = np.random.uniform(0.19, 0.24, size)
        samps[:,1] = np.random.uniform(0.25, 0.30, size)

        return samps

class prior_switchcos(JointPrior):
    def __init__(self, dist, name=None, latex_label=None, unit=None):
        if not isinstance(dist, custom_prior_switchcos):
            raise JointPriorDistError("dist object must be instance of custom_prior_switchcos")
        super().__init__(dist=dist, name=name, latex_label=latex_label, unit=unit)

mvg = custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds=[[0.0,0.35],[0.0,0.35],[0.0,0.35]])
priors = bilby.core.prior.PriorDict()
priors['switchcos_0'] = prior_switchcos(mvg,'switchcos_0')
priors['switchcos_1'] = prior_switchcos(mvg,'switchcos_1')
priors['switchcos_2'] = prior_switchcos(mvg,'switchcos_2')

mix_model.set_prior(priors)

{'switchcos_0': __main__.prior_switchcos(dist=custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds={'switchcos_0': (0.0, 0.35), 'switchcos_1': (0.0, 0.35), 'switchcos_2': (0.0, 0.35)}), name='switchcos_0', latex_label='switchcos_0', unit=None),
 'switchcos_1': __main__.prior_switchcos(dist=custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds={'switchcos_0': (0.0, 0.35), 'switchcos_1': (0.0, 0.35), 'switchcos_2': (0.0, 0.35)}), name='switchcos_1', latex_label='switchcos_1', unit=None),
 'switchcos_2': __main__.prior_switchcos(dist=custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds={'switchcos_0': (0.0, 0.35), 'switchcos_1': (0.0, 0.35), 'switchcos_2': (0.0, 0.35)}), name='switchcos_2', latex_label='switchcos_2', unit=None)}

2.3.3. 3. Train to find posterior#

mix_model.prior

{'switchcos_0': __main__.prior_switchcos(dist=custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds={'switchcos_0': (0.0, 0.35), 'switchcos_1': (0.0, 0.35), 'switchcos_2': (0.0, 0.35)}), name='switchcos_0', latex_label='switchcos_0', unit=None),
 'switchcos_1': __main__.prior_switchcos(dist=custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds={'switchcos_0': (0.0, 0.35), 'switchcos_1': (0.0, 0.35), 'switchcos_2': (0.0, 0.35)}), name='switchcos_1', latex_label='switchcos_1', unit=None),
 'switchcos_2': __main__.prior_switchcos(dist=custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds={'switchcos_0': (0.0, 0.35), 'switchcos_1': (0.0, 0.35), 'switchcos_2': (0.0, 0.35)}), name='switchcos_2', latex_label='switchcos_2', unit=None)}

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,
                    'npool':1}
result = mix_model.train(x_exp=g, y_exp=y_exp, y_err=y_err,outdir = 'outdir/samba_bivariate_1', label='switchcos_mix', 
                         kwargs_for_sampler=kwargs_for_sampler)

/home/runner/work/Taweret/Taweret/.tox/book/lib/python3.12/site-packages/bilby/core/likelihood.py:127: FutureWarning: Setting non-trivial parameters for <class 'Taweret.sampler.likelihood_wrappers.likelihood_wrapper_for_bilby'>. This is deprecated behaviour  and will be removed in Bilby version 3. See https://bilby-dev.github.io/bilby/parameters for more details.
  warnings.warn(msg, FutureWarning)
20:04 bilby INFO    : Running for label 'switchcos_mix', output will be saved to 'outdir/samba_bivariate_1'

The following settings were                     provided for sampler 
{'sampler': 'ptemcee', 'ntemps': 5, 'nwalkers': 50, 'Tmax': 100, 'burn_in_fixed_discard': 50, 'nsamples': 2000, 'npool': 1}

/home/runner/work/Taweret/Taweret/.tox/book/lib/python3.12/site-packages/bilby/core/sampler/ptemcee.py:134: FutureWarning: The ptemcee sampler interface in bilby is deprecated and will be removed in Bilby version 3. Please use the `ptemcee-bilby`sampler plugin instead: https://github.com/bilby-dev/ptemcee-bilby.
  warnings.warn(msg, FutureWarning)
20:04 bilby INFO    : Analysis priors:

20:04 bilby INFO    : switchcos_0=__main__.prior_switchcos(dist=custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds={'switchcos_0': (0.0, 0.35), 'switchcos_1': (0.0, 0.35), 'switchcos_2': (0.0, 0.35)}), name='switchcos_0', latex_label='switchcos_0', unit=None)

20:04 bilby INFO    : switchcos_1=__main__.prior_switchcos(dist=custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds={'switchcos_0': (0.0, 0.35), 'switchcos_1': (0.0, 0.35), 'switchcos_2': (0.0, 0.35)}), name='switchcos_1', latex_label='switchcos_1', unit=None)

20:04 bilby INFO    : switchcos_2=__main__.prior_switchcos(dist=custom_prior_switchcos(names=['switchcos_0', 'switchcos_1', 'switchcos_2'], bounds={'switchcos_0': (0.0, 0.35), 'switchcos_1': (0.0, 0.35), 'switchcos_2': (0.0, 0.35)}), name='switchcos_2', latex_label='switchcos_2', unit=None)

20:04 bilby INFO    : Analysis likelihood class: <class 'Taweret.sampler.likelihood_wrappers.likelihood_wrapper_for_bilby'>

20:04 bilby INFO    : Analysis likelihood noise evidence: nan

/home/runner/work/Taweret/Taweret/.tox/book/lib/python3.12/site-packages/bilby/core/likelihood.py:64: DeprecationWarning: Using parameters as state for likelihood_wrapper_for_bilby. This is deprecated behaviour  and will be removed in Bilby version 3. See https://bilby-dev.github.io/bilby/parameters for more details.
  warnings.warn(
/home/runner/work/Taweret/Taweret/.tox/book/lib/python3.12/site-packages/bilby/core/likelihood.py:113: FutureWarning: Parameter attribute queried for <class 'Taweret.sampler.likelihood_wrappers.likelihood_wrapper_for_bilby'>. This is deprecated behaviour  and will be removed in Bilby version 3. See https://bilby-dev.github.io/bilby/parameters for more details.
  warnings.warn(msg, FutureWarning)
20:04 bilby INFO    : Single likelihood evaluation took 4.159e-04 s

20:04 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}

20:04 bilby INFO    : Global meta data was removed from the result object for compatibility. Use the `BILBY_INCLUDE_GLOBAL_METADATA` environment variable to include it. This behaviour will be removed in a future release. For more details see: https://bilby-dev.github.io/bilby/faq.html#global-meta-data

20:04 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)

20:04 bilby INFO    : Generating pos0 samples

20:04 bilby INFO    : Starting to sample

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263|0:03:58|nc:3.3e+05|a0:0.61-0.66|swp:0.86-0.99|n:900<2000|t!1(+0.03,+0.30)|q:1.00|0.74ms/ev

264|0:03:59|nc:3.3e+05|a0:0.61-0.66|swp:0.86-0.99|n:950<2000|t=1(+0.02,+0.08)|q:1.00|0.74ms/ev

265|0:04:00|nc:3.3e+05|a0:0.61-0.66|swp:0.86-0.99|n:1000<2000|t!1(+0.02,+0.21)|q:1.00|0.75ms/ev

266|0:04:01|nc:3.3e+05|a0:0.61-0.66|swp:0.86-0.99|n:1050<2000|t!1(+0.03,+0.36)|q:1.00|0.75ms/ev

267|0:04:02|nc:3.3e+05|a0:0.61-0.66|swp:0.86-0.99|n:1100<2000|t!1(+0.04,+0.15)|q:1.00|0.74ms/ev

268|0:04:03|nc:3.4e+05|a0:0.61-0.66|swp:0.86-0.99|n:1150<2000|t!1(+0.03,+0.19)|q:1.00|0.73ms/ev

269|0:04:03|nc:3.4e+05|a0:0.61-0.66|swp:0.86-0.99|n:1200<2000|t!1(+0.02,+0.18)|q:1.00|0.74ms/ev

270|0:04:04|nc:3.4e+05|a0:0.61-0.66|swp:0.86-0.99|n:1250<2000|t!1(+0.02,+0.26)|q:1.00|0.74ms/ev

271|0:04:05|nc:3.4e+05|a0:0.61-0.66|swp:0.86-0.99|n:1300<2000|t!1(+0.04,+0.31)|q:1.00|0.73ms/ev

272|0:04:06|nc:3.4e+05|a0:0.61-0.66|swp:0.86-0.99|n:1350<2000|t!1(+0.05,+0.17)|q:1.00|0.74ms/ev

273|0:04:07|nc:3.4e+05|a0:0.61-0.66|swp:0.86-0.99|n:1400<2000|t!1(+0.05,+0.42)|q:1.00|0.74ms/ev

274|0:04:08|nc:3.4e+05|a0:0.61-0.66|swp:0.86-0.99|n:1450<2000|t!1(+0.04,+0.24)|q:1.00|0.75ms/ev

275|0:04:09|nc:3.4e+05|a0:0.60-0.66|swp:0.86-0.99|n:1500<2000|t!1(+0.03,+0.30)|q:1.00|0.75ms/ev

276|0:04:10|nc:3.4e+05|a0:0.60-0.66|swp:0.86-0.99|n:1550<2000|t!1(+0.03,+0.25)|q:1.00|0.75ms/ev

277|0:04:11|nc:3.5e+05|a0:0.60-0.66|swp:0.86-0.99|n:-900<2000|t!2(+0.03,+0.23)|q:1.00|0.76ms/ev

278|0:04:12|nc:3.5e+05|a0:0.60-0.66|swp:0.86-0.99|n:1650<2000|t!1(+0.04,+0.18)|q:1.00|0.75ms/ev

279|0:04:13|nc:3.5e+05|a0:0.60-0.66|swp:0.86-0.99|n:1700<2000|t!1(+0.04,+0.21)|q:1.00|0.75ms/ev

280|0:04:14|nc:3.5e+05|a0:0.60-0.66|swp:0.86-0.99|n:1750<2000|t!1(+0.06,+0.20)|q:1.00|0.74ms/ev

281|0:04:15|nc:3.5e+05|a0:0.60-0.66|swp:0.86-0.99|n:-700<2000|t!2(+0.03,+0.46)|q:1.00|0.73ms/ev

282|0:04:16|nc:3.5e+05|a0:0.60-0.66|swp:0.86-0.99|n:-650<2000|t!2(+0.02,+0.29)|q:1.00|0.74ms/ev

283|0:04:17|nc:3.5e+05|a0:0.60-0.65|swp:0.86-0.99|n:-600<2000|t!2(+0.02,+0.19)|q:1.00|0.76ms/ev

284|0:04:17|nc:3.6e+05|a0:0.60-0.66|swp:0.86-0.99|n:-550<2000|t!2(+0.01,+0.18)|q:1.00|0.77ms/ev

285|0:04:18|nc:3.6e+05|a0:0.60-0.66|swp:0.86-0.99|n:-500<2000|t!2(+0.02,+0.27)|q:1.00|0.78ms/ev

286|0:04:19|nc:3.6e+05|a0:0.60-0.65|swp:0.86-0.99|n:-450<2000|t!2(+0.01,+0.18)|q:1.00|0.77ms/ev

287|0:04:20|nc:3.6e+05|a0:0.60-0.65|swp:0.86-0.99|n:-400<2000|t!2(+0.02,+0.36)|q:1.00|0.77ms/ev

288|0:04:21|nc:3.6e+05|a0:0.60-0.65|swp:0.86-0.99|n:-350<2000|t!2(+0.02,+0.51)|q:1.00|0.74ms/ev

289|0:04:22|nc:3.6e+05|a0:0.60-0.65|swp:0.86-0.99|n:-300<2000|t!2(+0.02,+0.19)|q:1.00|0.75ms/ev

290|0:04:23|nc:3.6e+05|a0:0.60-0.66|swp:0.86-0.99|n:-250<2000|t!2(+0.02,+0.32)|q:1.00|0.74ms/ev

291|0:04:24|nc:3.6e+05|a0:0.60-0.66|swp:0.86-0.99|n:-200<2000|t!2(+0.01,+0.26)|q:1.00|0.73ms/ev

292|0:04:25|nc:3.6e+05|a0:0.60-0.66|swp:0.86-0.99|n:-150<2000|t!2(+0.02,+0.18)|q:1.00|0.71ms/ev

293|0:04:26|nc:3.7e+05|a0:0.60-0.66|swp:0.86-0.99|n:-100<2000|t!2(+0.02,+0.08)|q:1.00|0.71ms/ev

294|0:04:27|nc:3.7e+05|a0:0.60-0.66|swp:0.86-0.99|n:-50<2000|t!2(+0.01,+0.22)|q:1.00|0.73ms/ev

295|0:04:28|nc:3.7e+05|a0:0.60-0.66|swp:0.86-0.99|n:0<2000|t!2(+0.03,+0.18)|q:1.00|0.73ms/ev

296|0:04:29|nc:3.7e+05|a0:0.60-0.66|swp:0.86-0.99|n:50<2000|t!2(+0.01,+0.30)|q:1.00|0.73ms/ev

297|0:04:29|nc:3.7e+05|a0:0.60-0.66|swp:0.86-0.99|n:100<2000|t!2(+0.01,+0.36)|q:1.00|0.73ms/ev

298|0:04:30|nc:3.7e+05|a0:0.60-0.66|swp:0.86-0.99|n:150<2000|t!2(+0.01,+0.21)|q:1.00|0.74ms/ev

299|0:04:31|nc:3.7e+05|a0:0.60-0.65|swp:0.86-0.99|n:200<2000|t!2(+0.01,+0.12)|q:1.00|0.74ms/ev

300|0:04:32|nc:3.8e+05|a0:0.60-0.65|swp:0.86-0.99|n:250<2000|t!2(+0.01,+0.12)|q:1.00|0.74ms/ev

301|0:04:33|nc:3.8e+05|a0:0.60-0.66|swp:0.86-0.99|n:300<2000|t!2(+0.02,+0.22)|q:1.00|0.74ms/ev

302|0:04:34|nc:3.8e+05|a0:0.60-0.65|swp:0.86-0.99|n:350<2000|t!2(+0.01,+0.47)|q:1.00|0.73ms/ev

303|0:04:35|nc:3.8e+05|a0:0.60-0.65|swp:0.86-0.99|n:400<2000|t!2(+0.01,+0.29)|q:1.00|0.73ms/ev

304|0:04:36|nc:3.8e+05|a0:0.60-0.65|swp:0.86-0.99|n:450<2000|t!2(+0.01,+0.29)|q:1.00|0.73ms/ev

305|0:04:37|nc:3.8e+05|a0:0.60-0.65|swp:0.86-0.99|n:500<2000|t!2(+0.01,+0.21)|q:1.00|0.74ms/ev

306|0:04:38|nc:3.8e+05|a0:0.60-0.65|swp:0.86-0.99|n:3050<2000|t=1(+0.01,+0.09)|q:1.00|0.75ms/ev

20:08 bilby INFO    : Finished sampling

20:08 bilby INFO    : Writing checkpoint and diagnostics

20:08 bilby INFO    : Finished writing checkpoint

20:08 bilby INFO    : Sampling time: 0:04:38.259784

20:08 bilby WARNING : Result.save_to_file called with extension=True. This will default to json, and ignore the extension from the filename. This behaviour is deprecated and will be removed. 

20:08 bilby WARNING : Result.save_to_file called with extension=True. This will default to json, and ignore the extension from the filename. This behaviour is deprecated and will be removed. 

20:08 bilby INFO    : Summary of results:
nsamples: 3050
ln_noise_evidence:    nan
ln_evidence:  4.488 +/-  0.008
ln_bayes_factor:    nan +/-  0.008

# Posterior of the mixing parameters.
result.plot_corner()
../../_images/e606c89eea45dab77ffa0540e3fd6cc012015fa85cae0b05b265e1b5d781d245.png 
#corner plots
import corner
fig, axs = plt.subplots(3,3, figsize=(10,10), dpi=100)
corner.corner(mix_model.posterior,labels=['switchcos_0','switchcos_1', 'switchcos_2'],quantiles=[0.16, 0.5, 0.84],fig=fig)
plt.show()
../../_images/baba857ec4b20bd768be888bbb7a6ed67647086fd5451ae9df5b61a947322585.png

2.3.4. 4. Predictions#

_,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, 3)
using provided samples instead of posterior

per5, per20, per80, per95 = CI
prior5, prior20, prior80, prior95 = CI_prior

# Map value prediction for the step mixing function parameter
map_prediction = mix_model.evaluate(mix_model.map, plot_g)

_,_,CI_weights,_=mix_model.predict_weights(plot_g, CI=[5,20, 80, 95])
perw_5, perw_20, perw_80, perw_95 = CI_weights

(3050, 100)

prior_sample = np.array(list(priors.sample(5000).values())).T
_,_,CI_prior_weights,_=mix_model.predict_weights(plot_g, CI=[5,20, 80, 95], samples=prior_sample)
priorw_5, priorw_20, priorw_80, priorw_95 = CI_prior_weights

using provided samples instead of posterior

(5000, 100)

%matplotlib inline
fig, ax = plt.subplots(figsize=(10,10))
ax.fill_between(plot_g,perw_5,perw_95,color=sns.color_palette()[4], alpha=0.2, label='90% C.I.')
ax.fill_between(plot_g,perw_20,perw_80, color=sns.color_palette()[4], alpha=0.3, label='60% C.I.')

ax.fill_between(plot_g,priorw_5,priorw_95,color=sns.color_palette()[2], alpha=0.2, label='90% C.I.Prior')
ax.fill_between(plot_g,priorw_20,priorw_80, color=sns.color_palette()[2], alpha=0.3, label='60% C.I. Prior')


w,_= mix_model.evaluate_weights(mix_model.map,plot_g)
ax.vlines(mix_model.map[0],0,1, linestyle='--', color=sns.color_palette()[1], label='swithcos_0')
ax.vlines(mix_model.map[1],0,1, linestyle='--', color=sns.color_palette()[2], label='swithcos_1')
ax.vlines(mix_model.map[2],0,1, linestyle='--', color=sns.color_palette()[3], label='swithcos_2')
ax.plot(plot_g, w, label='MAP')
ax.legend()
ax.set_title('The Mixing Function')
ax.set_xlabel('g')
ax.set_ylabel('w')

Text(0, 0.5, 'w')
../../_images/6fa13bc6f101f9daa4406bafd8dc3254c93d775bad3e13b7a03eb5397db9f6a3.png 
%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()
ax.set_xlabel('g')

Text(0.5, 0, 'g')
../../_images/d4243e4f08a1da1fcc757a4f3517bef418eb806574f9e3210b354612e1baad5e.png