genMCMC_star_ispline: MCMC sampler for STAR with a monotone spline model for the...

In countSTAR: Flexible Modeling of Count Data

MCMC sampler for STAR with a monotone spline model for the transformation

Description

Run the MCMC algorithm for STAR given

1. a function to initialize model parameters; and

2. a function to sample (i.e., update) model parameters.

The transformation is modeled as an unknown, monotone function using I-splines. The Robust Adaptive Metropolis (RAM) sampler is used for drawing the parameter of the transformation function.

Usage

genMCMC_star_ispline(
  y,
  sample_params,
  init_params,
  lambda_prior = 1/2,
  y_max = Inf,
  nsave = 5000,
  nburn = 5000,
  nskip = 0,
  save_y_hat = FALSE,
  target_acc_rate = 0.3,
  adapt_rate = 0.75,
  stop_adapt_perc = 0.5,
  verbose = TRUE
)

Arguments

y	n x 1 vector of observed counts
sample_params	a function that inputs data y and a named list params containing at least mu: vector of conditional means (fitted values) sigma: the conditional standard deviation coefficients: a named list of parameters that determine mu and optionally a fourth element mu_test which contains the vector of conditional means at test points. The output is an updated list params of samples from the full conditional posterior distribution of coefficients and sigma (along with updates of mu and mu_test if applicable)
init_params	an initializing function that inputs data y and initializes the named list params of mu, sigma, coefficients and mu_test (if desired)
lambda_prior	the prior mean for the transformation g() is the Box-Cox function with parameter lambda_prior
y_max	a fixed and known upper bound for all observations; default is Inf
nsave	number of MCMC iterations to save
nburn	number of MCMC iterations to discard
nskip	number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
save_y_hat	logical; if TRUE, compute and save the posterior draws of the expected counts, E(y), which may be slow to compute
target_acc_rate	target acceptance rate (between zero and one)
adapt_rate	rate of adaptation in RAM sampler (between zero and one)
stop_adapt_perc	stop adapting at the proposal covariance at stop_adapt_perc*nburn
verbose	logical; if TRUE, print time remaining

Details

If the coefficients list from init_params and sample_params contains a named element beta, e.g. for linear regression, then the function output contains

• coefficients: the posterior mean of the beta coefficients

• post.beta: draws from the posterior distribution of beta

• post.othercoefs: draws from the posterior distribution of any other sampled coefficients, e.g. variance terms

If no beta exists in the parameter coefficients, then the output list just contains

• coefficients: the posterior mean of all coefficients

• post.beta: draws from the posterior distribution of all coefficients

Additionally, if init_params and sample_params have output mu_test, then the sampler will output post.predtest, which contains draws from the posterior predictive distribution at test points.

Value

A list with at least the following elements:

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

• post.sigma: draws from the posterior distribution of sigma

• post.log.like.point: draws of the log-likelihood for each of the n observations

• WAIC: Widely-Applicable/Watanabe-Akaike Information Criterion

• p_waic: Effective number of parameters based on WAIC

• post.g: draws from the posterior distribution of the transformation g

• post.sigma.gamma: draws from the posterior distribution of sigma.gamma, the prior standard deviation of the transformation g() coefficients

• fitted.values: the posterior mean of the conditional expectation of the counts y (NULL if save_y_hat=FALSE)

• post.fitted.values: posterior draws of the conditional mean of the counts y (NULL if save_y_hat=FALSE)

along with other elements depending on the nature of the initialization and sampling functions. See details for more info.

countSTAR documentation built on July 9, 2023, 5:12 p.m.