Data engineering and BI courses are free!
Compute MCMC samples from the posterior and predictive distributions of a STAR linear regression model with a g-prior and BNP transformation.
blm_star_bnpgibbs(
y,
X,
X_test = X,
y_max = Inf,
psi = NULL,
approx_Fz = FALSE,
approx_Fy = FALSE,
nsave = 1000,
nburn = 1000,
nskip = 0,
verbose = TRUE
)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_ytilde: nsave x n0 samples
from the posterior predictive distribution at test points X_test
post_g: nsave posterior samples of the transformation
evaluated at the unique y values (only applies for 'bnp' transformations)
n x 1 vector of observed counts
n x p matrix of predictors
n0 x p matrix of predictors for test data;
default is the observed covariates X
a fixed and known upper bound for all observations; default is Inf
prior variance (g-prior)
logical; in BNP transformation, apply a (fast and stable) normal approximation for the marginal CDF of the latent data
logical; in BNP transformation, approximate
the marginal CDF of y using the empirical CDF
number of MCMC iterations to save
number of MCMC iterations to discard
number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
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 empirical distribution of the
data y. Options in this case include the empirical cumulative
distribution function (CDF), 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 distribution-based
transformations approximately preserve the mean and variance of the count data y
on the latent data scale, which lends interpretability to the model parameters.
Lastly, the transformation can be modeled using the Bayesian bootstrap ('bnp'),
which is a Bayesian nonparametric model and incorporates the uncertainty
about the transformation into posterior and predictive inference.