fitdistrBayes

fitdistrBayes 0.2.0 fits common univariate distributions under registered objective Bayesian priors through a deliberately small interface:

fitdistrBayes(x, distr, prior)

For a built-in route, the package checks the sampling support and the known posterior-propriety condition before computation. It also records whether the posterior mean and variance of each parameter are mathematically certified to exist, so a finite chain is not used to justify a divergent moment.

Installation

Install the source archive supplied with this research release and load it:

install.packages("fitdistrBayes_0.2.0.tar.gz", repos = NULL,
                 type = "source")
library(fitdistrBayes)

Quick start

An exact-posterior example:

set.seed(10)
x <- rexp(40, rate = 2)
fit_exp <- fitdistrBayes(x, "exponential", "jeffreys", seed = 11)
fit_exp
confint(fit_exp)

An MCMC example with a parameter-specific reference prior:

set.seed(20)
x <- rgamma(50, shape = 2.5, rate = 1.3)
fit_gamma <- fitdistrBayes(
  x, "gamma", "reference-shape",
  iter = 6000, warmup = 1000, chains = 4, seed = 21
)
summary(fit_gamma)
plot(fit_gamma, type = "trace")
plot(fit_gamma, type = "acf")

fit$summary contains posterior medians, equal-tail intervals, R-hat, bulk and tail ESS, and MCSE when the relevant moments exist. Acceptance rates labelled overall use post-warmup iterations; warmup and all-iteration rates are stored separately.

Posterior prediction and pointwise log likelihood are computed on demand:

yrep <- predict(fit_gamma, draws = 500, size = length(x), seed = 22)
ll <- log_lik(fit_gamma, draws = 500, seed = 23)
dim(yrep)
dim(ll)

Supported routes

Version 0.2.0 has 50 enabled model--prior combinations for 19 distributions. The public machine-readable catalogue is the concise way to inspect them:

fitdistrBayes_routes()
fitdistrBayes_routes("gamma")
fitdistrBayes_routes("t")

The catalogue reports the estimated parameters, any required fixed parameter, the computational engine, and a concise propriety condition. The fitting function performs the authoritative sample-dependent check. In particular, the negative-binomial routes estimate mu with known positive size:

x <- rnbinom(40, size = 5, mu = 3)
fit_nb <- fitdistrBayes(
  x, "negative binomial", "reference", fixed = list(size = 5), seed = 30
)

Automatic initialization

When start = NULL and numerical initialization is required, the package uses classical estimators: ordinary moments where they exist, quantile matching for Cauchy and heavy-tailed Student-t cases, and closed-form L-moments for Weibull, Frechet, and Lomax. The Exponential-Logarithmic model uses a stable scalar moment equation. Exact independent posterior simulation does not require a starting point. The selected rule and center are stored in fit$initialization.

For the implemented Frechet parameterization, F(x) = exp(-scale * x^(-shape)); hence the argument named scale is the positive coefficient in the exponent, while the conventional quantile scale is scale^(1 / shape).

Custom densities

A custom density requires named starting values and a prior function. Log mode is inferred only from an explicit log argument; the presence of ... alone does not imply that log = TRUE is honored. The contract can be set explicitly with control$density_is_log and control$prior_is_log. Use control$prior_style = "scalar" or "vector" when automatic prior calling is ambiguous. Bounds are supplied through control$lower and control$upper; the package constructs the componentwise transform and Jacobian. A predictive RNG and its optional support validator can be supplied through control$rng and control$rng_validator.

Posterior propriety and posterior-moment existence remain the user's responsibility for every custom target.

Scope and limitations

The current package is for complete iid univariate samples. It does not implement censoring, truncation, observation weights, regression, hierarchical models, or automatic comparison among candidate distributions. It refuses routes known to be improper, including the Lomax independent Jeffreys/reference posterior and the Nakagami-m MDI posterior, and it does not substitute an approximation when full-model propriety has not been established. Numerical overflow or underflow stops with an explicit error; values are not silently clipped into the floating-point range.

Teaching example, citation, and support

A console-oriented walkthrough is installed at inst/examples/teaching.R. For the complete mathematical catalogue and computational validation, cite the accompanying manuscript, fitdistrBayes: Objective Bayesian Distribution Fitting in R. Until a public issue tracker is announced, reproducible problem reports can be sent to the maintainer address in DESCRIPTION.

This research version is licensed under GPL-3.