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Fit a Bayesian GLM by NUTS

bayes_glm_fit.Rd

Samples the posterior of a GLM with nuts-rs, the Rust core of nutpie. The design is R's model.matrix(), as for glm_fit(). Coefficients have normal priors with mean 0: standard deviation intercept_sd for the intercept and prior_sd for the rest (on the link scale; standardize covariates). For the Gaussian, gamma and inverse Gaussian the dispersion is sampled with a half-normal prior of scale dispersion_scale, unless dispersion fixes it. Chains run in parallel, start near the maximum-likelihood fit, and replay exactly from seed. Posterior means and standard deviations match exact grid integration (validation/scripts/bayes_glm_grid.py).

Usage

bayes_glm_fit(
  formula,
  data,
  family = "poisson",
  link = NULL,
  offset = NULL,
  weights = NULL,
  prior_sd = 2.5,
  intercept_sd = 10,
  dispersion = NULL,
  dispersion_scale = 10,
  chains = 4,
  tune = 1000,
  draws = 1000,
  seed = 0,
  target_accept = 0.8,
  max_depth = 10,
  theta = NULL,
  power = NULL,
  link_power = NULL
)

Arguments

formula

A model formula; offset(...) terms are honoured.

data

A data frame.

family

"gaussian", "poisson", "gamma", "inverse_gaussian", "binomial" (response a proportion, weights the trials), "negative_binomial" (needs theta) or "tweedie" (needs power).

"identity", "log", "logit", "probit", "cloglog", "inverse", "inverse_squared" or "power" (needs link_power); NULL for the family's canonical link.

offset

Optional offset added to any offset() terms.

weights

Optional prior weights.

prior_sd, intercept_sd

Prior standard deviations of the slopes and the intercept.

dispersion

A fixed dispersion, or NULL for the family's default.

dispersion_scale

Scale of the half-normal prior on a sampled dispersion.

chains, tune, draws

Chains, warm-up draws and kept draws per chain.

seed

Seed, a whole number.

target_accept

Target acceptance rate for step-size adaptation.

max_depth

Largest tree depth.

theta

Negative binomial theta (variance mu + mu^2 / theta).

power

Tweedie power in (1, 2).

Exponent of the power link.

Value

A bayes_glm_model with properties coefficients (posterior means), summary (a data frame of mean, sd, quantiles, R-hat and ESS per parameter), draws (a matrix, one row per draw), dispersion_draws and divergences. Use stats::coef(), stats::predict(), predict_distribution() and bayes_loo().

Examples

d <- data.frame(claims = rep(c(1, 2, 3, 5), 10), x = rep(c(-1.5, -0.5, 0.5, 1.5), 10))
m <- bayes_glm_fit(claims ~ x, d, family = "poisson", chains = 2, tune = 300, draws = 300)
m@summary
#>     parameter      mean         sd       q05       q50       q95      rhat
#> 1 (Intercept) 0.8462963 0.11569769 0.6453650 0.8531218 1.0243032 1.0013364
#> 2           x 0.5078291 0.09628648 0.3417002 0.5136568 0.6601851 0.9983802
#>   ess_bulk ess_tail
#> 1 367.4871 327.0323
#> 2 402.9908 457.0260