poisBayes {plpoisson}

Bayesian Prediction Limits for Poisson Distribution (Gamma Prior)

Description

The function provides the Bayesian prediction limits of a Poisson random variable derived based on a gamma prior. The resulting prediction bounds quantify the uncertainty associated with the predicted future number of occurences in a time window of size t.

Usage

poisBayes(xobs, n, s, t, a, b, alpha = 0.05)

Arguments

xobs

a numeric value denoting the number of the observed occurrencies.

n

a numeric value representing the total number of the time windows s in the past (observed time windows).

s

a numeric value corresponding to the fixed size (or average size) of the observed time windows.

t

a numeric value indicating the size of the future time window.

a

a poisitive real number denoting the shape hyperparameter of a gamma prior distribution.

b

a poisitive real number representing the rate hyperparameter of a gamma prior distribution.

alpha

a numeric value associated to the credible probability. By default alpha = 0.05, thus an prediction interval at 95% will be returned.

Details

When the argument b = Inf, one can obtain prediction limits with uniform prior by setting the argument a = 1. Similarly, one can get the limits with a Jeffreys prior by setting the argument a = 0.

Value

A list containing the following components:

lower

An integer value representing the lower bound of the prediction limit.

upper

An integer value representing the upper bound of the prediction limit.

Author(s)

Valbona Bejleri, Luca Sartore and Balgobin Nandram

References

Bejleri, V., & Nandram, B. (2018). Bayesian and frequentist prediction limits for the Poisson distribution. Communications in Statistics-Theory and Methods, 47(17), 4254-4271.

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

See Also

poiss, poisJEFF, poisUNIF

Examples

# Loading the package
library(plpoisson)
set.seed(2020L)

# 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)
) 

## Bayesian prediction limits 
##  (with gamma prior)
poisBayes(sum(data$occ_obs), # Past occurrencies 
    nrow(data), # Total past time windows
    mean(data$win_siz), # Window size
    333, # Size of future window
    2, 2.22) # Hyper-parameters for gamma prior