hyperbootstrap {plpoisson}

Bootstrap Methods to Estimate Hyperparameters for a Gamma Prior

Description

The function provides three bootstrap implementations to estimate the hyperparameters of a gamma prior distribution. The method of moments, maximum likelihood and chi-square approximation are implemented for studying the uncertainties associated with the choice of the hyperparameters a (shape) and b (rate).

Usage

hyperbootstrap(xvec, B = 1000L, 
               method = c("moments", "likelihood", "chisq"))

Arguments

xvec

a numeric vector of data with the observed occurrencies (assumed to be Poisson distributed).

B

a numeric value representing the total number of bootstrap iterations.

method

a character string (or strings) with the name/s of the method/s chosen to obtain hyperparameter estiamtes.

Details

The function performs a choosen number of iterations using either the method of momemnts (method = "moments"), the maximum likelihood (method = "likelihood"), or the chi-square approximation (method = "chisq").

Value

A list containing the following components:

a

A matrix of values for the shape hyperparameter of the gamma distribution. The results of each method are organized by column.

b

A matrix of values for the rate hyperparameter of the gamma distribution. The results of each method are organized by column.

Author(s)

Valbona Bejleri, Luca Sartore and Balgobin Nandram

References

Bejleri, V., Sartore, L. & Nandram, B. (2021). Asymptotic equivalence between frequentist and Bayesian prediction limits for the Poisson distribution. Journal of the Korean Statistical Society doi: 10.1007/s42952-021-00157-x

Bejleri, V. (2005). Bayesian Prediction Intervals for the hyperbootstrapon Model, Noninformative Priors, Ph.D. Dissertation, American University, Washington, DC.

See Also

poisBayes, poisJEFF, poisUNIF

Examples

# Loading the package
library(plpoisson)
set.seed(2021L)

# Number of observed time windows
n <- 555L

# Simulating a dataset
data <- cbind.data.frame(
    occ_obs = rpois(n, rgamma(n, 5.5, .5)),
    win_siz = rgamma(n, 1.44, .777)
) 

## Compute bootstrap estimates using all methods
hyperbootstrap(data$occ_obs, 10L) # only 10 iterations