Laplace_sampling_MCMC: Laplace Sampling Markov Chain Monte Carlo (MCMC) for...

In RiskMap: Geo-Statistical Modeling of Spatially Referenced Data

Laplace Sampling Markov Chain Monte Carlo (MCMC) for Generalized Linear Gaussian Process Models

Description

Performs MCMC sampling using Laplace approximation for Generalized Linear Gaussian Process Models (GLGPMs).

Usage

Laplace_sampling_MCMC(
  y,
  units_m,
  mu,
  Sigma,
  ID_coords,
  ID_re = NULL,
  sigma2_re = NULL,
  family,
  control_mcmc,
  Sigma_pd = NULL,
  mean_pd = NULL,
  messages = TRUE
)

Arguments

y	Response variable vector.
units_m	Units of measurement for the response variable.
mu	Mean vector of the response variable.
Sigma	Covariance matrix of the spatial process.
ID_coords	Indices mapping response to locations.
ID_re	Indices mapping response to unstructured random effects.
sigma2_re	Variance of the unstructured random effects.
family	Distribution family for the response variable. Must be one of 'gaussian', 'binomial', or 'poisson'.
control_mcmc	List with control parameters for the MCMC algorithm: n_sim Number of MCMC iterations. burnin Number of burn-in iterations. thin Thinning parameter for saving samples. h Step size for proposal distribution. Defaults to 1.65/(n_tot^(1/6)). c1.h, c2.h Parameters for adaptive step size tuning.
Sigma_pd	Precision matrix (optional) for Laplace approximation.
mean_pd	Mean vector (optional) for Laplace approximation.
messages	Logical; if TRUE, print progress messages.

Details

This function implements a Laplace sampling MCMC approach for GLGPMs. It maximizes the integrand using 'maxim.integrand' function for Laplace approximation if 'Sigma_pd' and 'mean_pd' are not provided.

The MCMC procedure involves adaptive step size adjustment based on the acceptance probability ('acc_prob') and uses a Gaussian proposal distribution centered on the current mean ('mean_curr') with variance 'h'.

Value

An object of class "mcmc.RiskMap" containing:

samples$S

Samples of the spatial process.

samples$<re_names[i]>

Samples of each unstructured random effect, named according to columns of ID_re if provided.

tuning_par

Vector of step size (h) values used during MCMC iterations.

acceptance_prob

Vector of acceptance probabilities across MCMC iterations.

Author(s)

Emanuele Giorgi [e-mail]

Claudio Fronterre [e-mail]

RiskMap documentation built on June 25, 2024, 5:08 p.m.