Getting Started

This guide illustrates the basic functionality of the BayesBlendModel and Draws classes.

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BayesBlend provides an easy-to-use interface for combining predictions from multiple Bayesian models using techniques including (pseudo) Bayesian model averaging, stacking, and hierarchical stacking. The core functionality is divided into two classes:

• Draws
• BayesBlendModel

Draws

The Draws class is used to store and manipulate MCMC draws from the posterior distribution of an arbitrary Bayesian model. Specifically, Draws.log_lik and Draws.post_pred indicate the posterior log likelihood and posterior predictions for each datapoint in a model. Both attributes should be in the form of an np.ndarray with any shape (athough their shapes should match).

BayesBlendModel

The BayesBlendModel is an abstract base class that is subclassed into the following various Bayesian model averaging and Bayesian stacking models:

• MleStacking
• BayesStacking
• HierarchicalBayesStacking
• PseudoBma

Each of these models takes a dictionary of Draws objects as input (one for each underlying substantive model of interest). The core functionality of each BayesBlendModel is then housed in the .fit and .blend methods. The .fit method fits the associated averaging/stacking model given the Draws fit data, and the latter returns a new Draws object that blends together the posterior predictions across substantive models given the estimated averaging/stacking parameters.

Example

The below example expands on the cmdstanpy example, fitting a bernoulli model twice and then blending the results together.

bernoulli.stan

data {
    int<lower=0> N;
    array[N] int<lower=0, upper=1> y;
} 
parameters {
    real<lower=0, upper=1> theta;
}
model {
    theta ~ beta(1, 1);
    y ~ bernoulli(theta);
}
generated quantities {
    array[N] int post_pred;
    vector[N] log_lik;

    for (n in 1:N){
        log_lik[n] = bernoulli_lpmf(y[n] | theta);
        post_pred[n] = bernoulli_rng(theta);
    }
}

Fit and stack models

from cmdstanpy import CmdStanModel
from bayesblend import MleStacking

model = CmdStanModel(stan_file="bernoulli.stan")

stan_data = {
    "N": 10,
    "y": [0, 1, 0, 0, 0, 0, 0, 0, 0, 1],
}

# fit model to data (pretend these are different models!)
fit1 = model.sample(chains=4, data=stan_data, seed=1)
fit2 = model.sample(chains=4, data=stan_data, seed=2)

# fit the MleStacking model - fit() returns self
mle_stacking_fit = MleStacking.from_cmdstanpy(dict(fit1=fit1, fit2=fit2))
mle_stacking_fit.fit()

# generate blended predictions
mle_stacking_blend = mle_stacking_fit.predict()

The mle_stacking_blend object is a bayesblend.Draws object.

The particular weights estimated in the stacking model can be inspected using mle_stacking_fit.weights.

For models like hierarchical stacking with covariates, the weights during prediction might differ from the weights estimated in the stacking model because the weights have their own posterior predictive distribution. For this instance, setting return_weights=True in BayesBlendModel.predict will return a tuple of the blended predictions and a dictionary of weights used during prediction.