Consider a Gamma-Poisson Bayesian model for rate parameter \(\lambda\) with a Gamma(shape, rate) prior on \(\lambda\) and a Poisson likelihood for the data. Given information on the prior (shape and rate) and data (the sample size n and sum_y), this function summarizes the mean, mode, and variance of the prior and posterior Gamma models of \(\lambda\).
summarize_gamma_poisson(shape, rate, sum_y = NULL, n = NULL)positive shape parameter of the Gamma prior
positive rate parameter of the Gamma prior
sum of observed data values for the Poisson likelihood
number of observations for the Poisson likelihood
data frame
summarize_gamma_poisson(shape = 3, rate = 4, sum_y = 7, n = 12)
#> model shape rate mean mode var sd
#> 1 prior 3 4 0.750 0.5000 0.1875000 0.4330127
#> 2 posterior 10 16 0.625 0.5625 0.0390625 0.1976424