The outer hyperparameter grid of a nested-Laplace fit

A nested-Laplace fit integrates its hyperparameters on an outer grid: each cell is one hyperparameter value, carries an integration weight, and holds the inner Laplace solve at that value. This returns that grid, cell by cell, so the integration can be inspected or reused (a discrete hyperparameter posterior for sbc_discrete(), a grid-marginalized latent field).

The per-cell latent modes average to the grid-marginalized posterior mean of any latent coordinate: colSums(g$weights * g$modes). Columns seq_len(g$n_fixed) are the fixed effects and the rest the latent field and random effects, in the order the fit's latent vector stores them.

Usage

tulpa_outer_grid(fit)

Arguments

fit

A nested-Laplace fit: tulpa_nested_laplace(), tulpa_nested_laplace_joint(), or a tulpa() fit routed to that tier.

Value

A list:

nodes

numeric matrix [n_cells x n_axes], the hyperparameter value of each cell, with the axis names as column names.

weights

the cells' integration weights, normalized to sum to one.

log_marginal

each cell's log marginal likelihood, hyperprior density included; with the cell's quadrature volume it gives the weight. NULL when the fit does not keep it.

support

named list of natural-scale c(lo, hi) intervals, the span each axis's outer measure integrates (including levels a refinement pass added); NULL when the fit records none.

modes

numeric matrix [n_cells x n_latent], each cell's inner Laplace mode, or NULL when the fit keeps none.

n_fixed

how many leading columns of modes are fixed effects.

See also

tulpa_hyper_draws() for continuous draws of the hyperparameters, tulpa_posterior_draws() for draws of the latent field, and summary(fit)$hyperparameters for their marginal summaries.

Examples

# \donttest{
set.seed(1)
S <- 30L
nb <- lapply(seq_len(S), function(s) setdiff(c(s - 1L, s + 1L), c(0L, S + 1L)))
nn <- lengths(nb)
field <- as.numeric(scale(cumsum(rnorm(S, 0, 0.4))))
idx <- rep(seq_len(S), each = 6L); n <- length(idx); x <- rnorm(n)
y <- rbinom(n, 1L, plogis(-0.2 + 0.6 * x + field[idx]))
prior <- list(type = "icar", n_spatial_units = S, spatial_idx = idx,
              adj_row_ptr = c(0L, cumsum(nn)), adj_col_idx = unlist(nb) - 1L,
              n_neighbors = nn, tau_grid = c(0.5, 1, 2, 4, 8))
fit <- tulpa_nested_laplace(y, rep(1L, n), cbind(1, x), prior = prior,
                            family = "binomial",
                            control = list(progress = FALSE))
g <- tulpa_outer_grid(fit)
cbind(g$nodes, weight = g$weights)
field_hat <- colSums(g$weights * g$modes)[-seq_len(g$n_fixed)]
# }