Laplace_sampling_MCMC {RiskMap}

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]