countSTAR (version 1.2.0)

blm_star_exact: Monte Carlo sampler for STAR linear regression with a g-prior

Description

Compute direct Monte Carlo samples from the posterior and predictive distributions of a STAR linear regression model with a g-prior.

Usage

blm_star_exact(
  y,
  X,
  X_test = X,
  transformation = "np",
  y_max = Inf,
  psi = length(y),
  nsave = 1000,
  compute_marg = FALSE
)

Value

a list with the following elements:

• coefficients: the posterior mean of the regression coefficients

• post.beta: nsave x p samples from the posterior distribution of the regression coefficients

• post.pred: draws from the posterior predictive distribution of y

• post.pred.test: nsave x n_test samples from the posterior predictive distribution at test points X_test (if given, otherwise NULL)

• sigma: The estimated latent data standard deviation

• marg.like: the marginal likelihood (if requested; otherwise NULL)

Arguments

y

n x 1 vector of observed counts

X

n x p matrix of predictors

X_test

n_test x p matrix of predictors for test data

transformation

transformation to use for the latent data; must be one of

• "identity" (identity transformation)

• "log" (log transformation)

• "sqrt" (square root transformation)

• "np" (nonparametric transformation estimated from empirical CDF)

• "pois" (transformation for moment-matched marginal Poisson CDF)

• "neg-bin" (transformation for moment-matched marginal Negative Binomial CDF)

y_max

a fixed and known upper bound for all observations; default is Inf

psi

prior variance (g-prior)

nsave

number of Monte Carlo simulations

compute_marg

logical; if TRUE, compute and return the marginal likelihood

Details

STAR defines a count-valued probability model by (1) specifying a Gaussian model for continuous *latent* data and (2) connecting the latent data to the observed data via a *transformation and rounding* operation. Here, the continuous latent data model is a linear regression.

There are several options for the transformation. First, the transformation can belong to the *Box-Cox* family, which includes the known transformations 'identity', 'log', and 'sqrt' Second, the transformation can be estimated (before model fitting) using the the data y. Options in this case include the empirical cumulative distribution function (ECDF), which is fully nonparametric ('np'), or the parametric alternatives based on Poisson ('pois') or Negative-Binomial ('neg-bin') distributions. For the parametric distributions, the parameters of the distribution are estimated using moments (means and variances) of y.

The Monte Carlo sampler produces direct, joint draws from the posterior predictive distribution under a g-prior.