Hyperparameter draws from a nested-Laplace fit

The hyperparameter half of a draw from the outer-grid mixture: one row per draw, one column per outer-grid axis. A draw's coordinate on each axis is sampled from the within-cell density its cell carries under the fit's own within-cell read, so the columns are a continuous marginal rather than the handful of grid-node values fit$theta_grid[cells, ] returns.

An axis carrying a declared POINT MASS – the copy scale's alpha = 0, the "no coupling" model whose prior probability is stated rather than read off a node count – keeps it: draws in that cell are exactly the level, in the proportion the fit reports as fit$copy_atom$posterior_mass, and the continuum above it is continuized on its own partition. The level is a model and not a cell representative, so spreading it over a box would both put mass where the axis has none and leave none on the level itself.

Reading the node coordinate directly is what tulpa_posterior_draws() consumers used to do, and on a 5- to 15-node axis it makes every draw an atom: a truth between two nodes, or past the outermost one, has no draw that can land near it. The continuization is the cell-conditional of the SAME construction the fit reports its interval from (box_uniform by default, chord when the fit asked for it or its support does not admit the box read), so the draws reproduce the fit's own theta_ci_lo / theta_median / theta_ci_hi to Monte Carlo error.

Usage

tulpa_hyper_draws(fit, cells = NULL, n = 1000, within = NULL)

Arguments

fit

A nested-Laplace fit (tulpa_nested_laplace() or tulpa_nested_laplace_joint()).

cells

Integer vector of outer-grid cell indices, one per draw – the "cells" attribute of a tulpa_posterior_draws() matrix, so the hyperparameter row and the latent row of a draw come from the same cell. NULL (default) allocates n fresh draws across the cells by weight.

n

Number of draws when cells is NULL (default 1000); ignored otherwise.

within

Within-cell construction, "box_uniform", "log_quadratic" or "chord". Under "log_quadratic" a draw in a cell is the point its row's reconstructed CDF reaches inside the share of that CDF the cell's mass owns, so the draws in one cell stay around it. NULL (default) takes the one the fit was read with (fit$within_cell_requested).

Value

A numeric matrix [n x n_axes] with the outer grid's axis names as columns, or NULL when the fit carries no outer-grid axis. Carries attr(., "cells") – the cell each row's coordinates were drawn in – plus attr(., "within_cell") and attr(., "within_cell_declined"), the per-axis construction that ran and why a requested one did not, and attr(., "within_cell_copula"), the Gaussian-copula correlation matrix that ties the axes' within-cell draws together so the draws keep the grid's own correlation between axes (the identity where the grid's axes are uncorrelated). Each axis's marginal is the same whatever the copula.

See also

tulpa_posterior_draws(), tulpa_nested_laplace()

Examples

# \donttest{
set.seed(1)
S <- 30L                                   # spatial units in a chain
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))
th <- tulpa_hyper_draws(fit, n = 200)
quantile(th[, "tau"], c(0.025, 0.5, 0.975))
# }