mcmc_mra_vecchia: Bayesian Multi-resolution Spatial Regression
In jtipton25/BayesMRA: Bayesian Multi-Resolution Gaussian Process Approximations

mcmc_mra_vecchia

R Documentation

Bayesian Multi-resolution Spatial Regression

Description

this function runs Markov Chain Monte Carlo to estimate the Bayesian multi-resolution spatial regression model.

Usage

mcmc_mra_vecchia(
  y,
  locs,
  params,
  M = 3,
  n_neighbors = 68,
  n_coarse_grid = 10,
  n_padding = 5L,
  inits = NULL,
  normalize = TRUE,
  verbose = FALSE,
  config = NULL,
  constraint = "overall",
  n_chain = 1
)

Arguments

`y`	is a `n` vector of Gaussian data.
`locs`	is a `n \times 2` matrix of observation locations.
`params`	is a list of parameter settings. The list `params` must contain the following values: `n_adapt`: A positive integer number of adaptive MCMC iterations. `n_mcmc`: A positive integer number of total MCMC iterations post adaptation. `n_thin`: A positive integer number of MCMC iterations per saved sample. `n_message`: A positive integer number of frequency of iterations to output a progress message. For example, `n_message = 50` outputs progress messages every 50 iterations.
`M`	The number of resolutions.
`n_neighbors`	The expected number of neighbors for each interior basis function. This determines the basis radius parameter.
`n_coarse_grid`	The number of basis functions in one direction (e.g. `n_coarse_grid = 10` results in a `10 \times 10` course grid which is further extended by the number of additional padding basis functions given by `n_padding`.
`n_padding`	The number of additional boundary points to add on each boundary. For example, n_padding = 5 will add 5 boundary knots to the both the left and right side of the grid).
`inits`	is the list of initial values if the user wishes to specify initial values. If these values are not specified, then the initial values will be randomly sampled from the prior.
`normalize`	A logical value of whether to normalize the basis functions or not.
`verbose`	Should verbose output be printed? Typically this is only useful for troubleshooting.
`config`	is the list of configuration values if the user wishes to specify initial values. If these values are not specified, then default a configuration will be used.
`constraint`	What constraint should be applied to the spatial process? Options include no constraint (`constraint = "unconstrained"`), a constraint so the entire MRA process sums to 0 (`constraint = "overall"`), a constraint so that each of the M levels of the MRA process sum to 0 (`constraint = "resolution"`), or whether the predicted process must sum to 0 (`constraint = "predicted"`). Note: `constraint = "predicted"` is NOT currently supported.
`n_chain`	is the MCMC chain id. The default is 1.

Examples

set.seed(111)
## genereate the locations
locs <- matrix(runif(20), 10, 2)
## generate some covariates and regression coefficients
X <- cbind(1, matrix(rnorm(30), 10, 3))
beta <- rnorm(ncol(X))

## simulate the MRA process
M <- 2
MRA <- mra_wendland_2d(locs, M = M, n_coarse_grid = 4)
W <- MRA$W
n_dims <- MRA$n_dims
dims_idx <- MRA$dims_idx

## set up the process precision matrices
Q_alpha <- make_Q_alpha_2d(sqrt(n_dims), c(0.9, 0.8))
Q_alpha_tau2 <- make_Q_alpha_tau2(Q_alpha, tau2 = c(2, 4))

## add in constraints so each resolution has random effects that sum to 0
constraints <- make_constraint(MRA, constraint = "resolution", joint = TRUE)
A_constraint <- constraints$A_constraint
a_constraint <- constraints$a_constraint
alpha <- as.vector(spam::rmvnorm.prec.const(
    n = 1,
    mu = rep(0, nrow(W)),
    Q = Q_alpha_tau2,
    A = A_constraint,
    a = a_constraint))
## define the data
y <-  as.vector(X %*% beta + W %*% alpha + rnorm(10))

## define the params for MCMC fitting
params <- list(
    n_mcmc    = 5,
    n_adapt   = 5,
    n_thin    = 1,
    n_message = 5)

## define the model priors
priors <- list(
    alpha_tau2   = 1,
    beta_tau2    = 1,
    alpha_sigma2 = 1,
    beta_sigma2  = 1,
    mu_beta      = rep(0, ncol(X)),
    Sigma_beta   = 5 * diag(ncol(X)))

## Fit the MRA model using MCMC
# out     <- mcmc_mra_vecchia(
#     y             = y,
#     X             = X,
#     locs          = locs,
#     params        = params,
#     priors        = priors,
#     M             = 2,
#     n_coarse_grid = 4
# )

jtipton25/BayesMRA documentation built on Feb. 28, 2024, 1:27 p.m.