poisson_quantile: Quantile of bayesian estimators for samples of a poisson...

In momeara/MPStats: Tools for analyzing Morphological Profiling data

Quantile of bayesian estimators for samples of a poisson process

Description

The gamma distribution is the congugate prior for the poisson distribution. Given a prior 'Gamma(k,theta)“, and poisson observations 'k_1, k_2, ..., k_n', the bayesian estimator for the posterior is

Usage

poisson_quantile(count, p)

Arguments

count	vector of n counts, assumed to be samples from a poisson process
probability	quantile to return

Details

Gamma(k + sum k_i, n + theta)

So the prior can be thought of as adding 'theta' pseudo observations each with a count value of 'k/theta'.

Example:

Say we have collected a sample of 3 counts with values 'counts <- c(120, 130, 125)' then the 95

low <- poisson_quantile(counts, .025) high <- poisson_quantile(counts, .975)

Now say we have a prior equivilent to a single count with 124, then we would add 124 to the counts vector:

counts <- c(120, 130, 125) + c(124) low <- poisson_quantile(counts, .025) high <- poisson_quantile(counts, .975)

Value

count value of the given quantile of the posterior estimator for the poisson process

momeara/MPStats documentation built on July 19, 2022, 3:34 p.m.