Bayesian estimate of a mean (conjugate Normal-Normal or Stan)

For a numeric sample, returns the analytic Normal-Normal conjugate posterior for the mean: a normal prior N(prior_mean, prior_sd^2) combined with a normal likelihood of known scale sigma gives a normal posterior in closed form (a flat prior, prior_sd = Inf, reproduces the sampling posterior N(mean(y), sigma^2/n)). For a model formula the estimation is delegated to rstanarm/brms when installed, and errors informatively otherwise – the analytic numeric-vector path always runs.

Usage

bayesEstimate(
  y,
  data = NULL,
  prior_mean = 0,
  prior_sd = Inf,
  sigma = NULL,
  level = 0.95,
  seed = NULL
)

Arguments

y: A numeric vector (analytic path) or a model formula (Stan path).
data: Data frame for the formula path.
prior_mean, prior_sd: Normal prior mean and SD (default 0 and Inf, a flat prior).
sigma: Known likelihood SD; NULL uses the sample SD of y.
level: Credible level (default 0.95).
seed: Optional integer random seed recorded in the provenance.

Value

An AnalysisResult (from PhysioCore) with type = "bayes" whose result holds posterior_mean, posterior_sd, ci_lower, ci_upper, the level/method, plus a provenance log with the seed.

References

Gelman, A. et al. (2013). Bayesian Data Analysis, 3rd ed.

Examples

set.seed(1)
bayesEstimate(rnorm(30, mean = 5), prior_mean = 0, prior_sd = 10)
#> <AnalysisResult> bayes 
#>   fields: posterior_mean, posterior_sd, ci_lower, ci_upper, level, method 
#>   provenance: 1 entr(ies)