tulpa_laplace_beta: Fit a beta-regression model via Laplace, estimating the...

In tulpa: Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

Fit a beta-regression model via Laplace, estimating the precision

Description

Thin wrapper around tulpa_laplace() for family = "beta". The Laplace engine treats phi as fixed per fit (same contract as gamma and neg_binomial_2); this wrapper does an outer 1-D optimisation of the Laplace-approximated log-marginal over phi, then refits at the optimum to return betas and Hessian.

The mean-precision parameterisation is y ~ Beta(mu * phi, (1 - mu) * phi) with default logit link; y must be strictly in ⁠(0, 1)⁠.

Usage

tulpa_laplace_beta(
  y,
  X,
  re_list = list(),
  spatial = NULL,
  weights = NULL,
  offset = NULL,
  max_iter = 100L,
  tol = 1e-06,
  n_threads = 1L,
  beta_prior = NULL,
  phi_init = NULL,
  phi_bounds = c(0.1, 10000),
  outer_tol = 1e-04,
  mode = c("laplace", "nuts"),
  control = list()
)

Arguments

y	Response in ⁠(0, 1)⁠.
X	Fixed-effects design matrix.
re_list, spatial, weights, offset, max_iter, tol, n_threads, beta_prior	Passed to tulpa_laplace() verbatim. beta_prior places a Gaussian penalty on the fixed effects (a list with sd, optional mean; see tulpa_laplace()). It is included in the Laplace log-marginal that the precision phi is optimised against, so the penalised model is fit consistently across the outer phi search. Not supported with spatial (the spatial solver carries its own prior).
phi_init	Optional starting value for the precision. If NULL, a method-of-moments warm start is used.
phi_bounds	Numeric length-2 vector with lower/upper bounds on phi for the outer optimisation. Default c(0.1, 1e4).
outer_tol	Tolerance for the outer optimisation. Default 1e-4.
mode	Inference method (the method is an argument, not a parallel verb): "laplace" (default) is the Laplace + Brent-over-phi point fit documented here; "nuts" delegates to tulpa_nuts_beta(), which samples phi jointly with the coefficients via NUTS. In "nuts" mode the Laplace-only arguments (re_list, spatial, weights, offset, phi_init, phi_bounds, outer_tol) are not used, and NUTS knobs are passed via control (see tulpa_nuts_beta()).
control	Passed to tulpa_nuts_beta() when mode = "nuts" (ignored for mode = "laplace").

Value

For mode = "laplace", the list returned by tulpa_laplace() at the optimum, augmented with phi (the optimised precision), phi_trace (the optimisation trace: a matrix with one row per objective evaluation and columns phi and log_marginal) and phi_converged (TRUE when the Brent search reported convergence). For mode = "nuts", the draws object returned by tulpa_nuts_beta().

Examples

set.seed(1)
n <- 200L
X <- cbind(1, rnorm(n))
mu <- plogis(X %*% c(0.2, 0.7)); phi <- 8
y <- rbeta(n, mu * phi, (1 - mu) * phi)
fit <- tulpa_laplace_beta(y, X)
fit$mode

tulpa documentation built on Oct. 19, 2026, 5:09 p.m.