Laplace Sampling Markov Chain Monte Carlo (MCMC) for Generalized Linear Gaussian Process Models
Laplace_sampling_MCMC.RdPerforms 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.
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.
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`.