Taweret.mix.bivariate_linear

class Taweret.mix.bivariate_linear.BivariateLinear(models_dic: Dict[str, Type[BaseModel]], method: str = 'sigmoid', nargs_model_dic: Dict[str, int] | None = None, same_parameters: bool = False, full_cov: bool = False, BMMcor: bool = False, mean_mix: bool = False)

Bases: BaseMixer

Local linear Bayesian mixing of two models. This is a general class of mixing that offer both density (likelihood) and mean mixing methods. The default mixing method is linear mixing of two likelihoods.

Parameters:

models_dicdictionary {'name1'model1, 'name2'model2}

Two models to mix, each must be derived from the base_model.

methodstr

Mixing weight function form. This is a function of input parameters.

nargs_model_dicdictionary {'name1'N_model1, 'name2'N_model2}

Only used in calibration. Number of free parameters in each model

same_parametersbool

Only used in BMM with calibration. If set, two models are assumed to have same parameters.

full_covbool

This option is only used in BMMcor method. For BMMC full covariance is not needed and mean_mix must have full covariance.

BMMcorbool

If set use BMMcor method for Bayesian model mixing.

mean_mixbool

If set use mean mixing method for Bayesian model mixing.

evaluate(mixture_params: ndarray, x: ndarray, model_params: List[ndarray] | None = []) → ndarray

Evaluate the mixed model for given parameters at input values x

Parameters:

mixture_paramsnp.1darray

parameter values that fix the shape of mixing function

xnp.1daray

input parameter values array

model_params: list[model_1_params, mode_2_params]

list of model parameter values for each model

Returns:

evaluationnp.2darray

the evaluation of the mixed model at input values x Has the shape of len(x) x Number of observables in the model

evaluate_weights(mixture_params: ndarray, x: ndarray) → ndarray

return the mixing function values at the input parameter values x

Parameters:

mixture_paramsnp.1darray

parameter values that fix the shape of mixing function

xnp.1darray

input parameter values

Returns:

weightslist[np.1darray, np.1darray]

weights for model 1 and model 2 at input values x

property map

Stores the MAP values for the posterior distributions and is set during the self.train step

mix_loglikelihood(mixture_params: ndarray, model_param: ndarray, x_exp: ndarray, y_exp: ndarray, y_err: ndarray) → float

log likelihood of the mixed model given the mixing function parameters

Parameters:

mixture_paramsnp.1darray

parameter values that fix the shape of mixing function

model_params: list[model_1_params, mode_2_params]

list of model parameter values for each model

x_exp: np.1darray

Experimentally measured input values

y_exp: np.2darray

Experimentally measured observable values. Takes the shape len(x_exp) x number of observable types measured

y_err: np.2darray

Experimentally measured observable errors. Takes the shape len(x_exp) x number of observable types measured

property posterior

Stores the most recent posteriors from running self.train function

Returns:

_posteriornp.ndarray

posterior from learning the weights

predict(x: ndarray, CI: List = [5, 95], samples: ndarray | None = None, nthin: int = 1)

Evaluate posterior to make prediction at test points x.

Parameters:

xnp.1darray

input parameter values

CIlist

confidence intervals as percentages

samples: np.ndarray

If samples are given use that instead of posterior for predictions.

Returns:

evaluated_posteriornp.ndarray

array of posterior predictive distribution evaluated at provided test points

meannp.ndarray

average mixed model value at each provided test points

credible_intervalsnp.ndarray

intervals corresponding for 60%, 90% credible intervals

std_devnp.ndarray

sample standard deviation of mixed model output at provided test points

predict_weights(x: ndarray, CI: List = [5, 95], samples: ndarray | None = None)

Calculate posterior predictive distribution for first model weights

Parameters:

xnp.1darray

input parameter values

CIlist

confidence intervals

samples: np.ndarray

If samples are given use that instead of posterior for predictions.

Returns:

posterior_weightsnp.ndarray

array of posterior predictive distribution of weights

meannp.ndarray

average mixed model value at each provided test points

credible_intervalsnp.ndarray

intervals corresponding for 60%, 90% credible intervals

std_devnp.ndarray

sample standard deviation of mixed model output at provided test points

property prior

Dictionary of prior distributions. Format should be compatible with sampler.

Returns:

_priorDict[str, Any]

Underlying prior object(s)

Example:

Please consult BaseMixer.set_prior for an example

prior_predict(x: ndarray, CI: List = [5, 95], n_sample: int = 10000)

Evaluate prior to make prediction at test points x.

Parameters:

xnp.1darray

input parameter values

CIlist

confidence intervals

n_samplesint

number of samples to evaluate prior_prediction

Returns:

evaluated_priornp.ndarray

array of prior predictive distribution evaluated at provided test points

meannp.ndarray

average mixed model value at each provided test points

credible_intervalsnp.ndarray

intervals corresponding for 60%, 90% credible intervals

std_devnp.ndarray

sample standard deviation of mixed model output at provided test points

set_prior(bilby_prior_dic)

Set prior for the mixing function parameters. Prior for the model parameters should be defined in each model.

Parameters:

bilby_prior_dic (bilby.core.prior.PriorDict) --

The keys should be named as following :

'<mix_func_name>_1', '<mix_func_name>_2', ...

Returns:

• A full Bilby prior object for the mixed model.

• Including the mixing function parameters and model parameters.

• The Bilby prior dictionary has following keys. --

  Prior for mixture function parameter :

  '<mix_func_name>_1', '<mix_func_name>_2', ...

  Prior parameters for model 1 :

  '<name_of_the_model>_1', '<name_of_the_model>_2' , ...

  Prior parameters for model 2 :

  '<name_of_the_model>_1', '<name_of_the_model>_2' , ...

train(x_exp: ndarray, y_exp: ndarray, y_err: ndarray, label: str = 'bivariate_mix', outdir: str = 'outdir', kwargs_for_sampler: Dict[str, int] | None = None, load_previous: bool = False, plot: bool = False)

Run sampler to learn parameters. Method should also create class members that store the posterior and other diagnostic quantities important for plotting MAP values, and finds the MAP values for each parameter, and sets them equal to a class variable for easy access.

Parameters:

x_exp: np.1darray

Experimentally measured input values

y_exp: np.2darray

Experimentally measured observable values. Takes the shape len(x_exp) x number of observable types measured

y_err: np.2darray

Experimentally measured observable errors. Takes the shape len(x_exp) x number of observable types measured

label: str

Name of the chain to be stored after sampling

outdir: str

Where to save the MCMC chain and output of bilby samplers

kwargs_for_sampler: Dict

Optional arguments to be used instead of default Bibly sampler settings

load_previous: bool

If a previous training has been done, load that chain instead of retraining.

Returns:

resultbilby posterior object

object returned by the bilby sampler