dupiR (version 1.2)

computePosterior: Compute the posterior probability distribution of the population size

Description

Compute the posterior probability distribution of the population size using a discrete uniform prior and a binomial likelihood (DUP method). When applicable, an approximation using a Gamma prior and a Poisson likelihood is used instead (GP method, see Clough et al).

Usage

computePosterior(object, n1, n2, replacement = FALSE, b, alg = "DUP")

Arguments

object

An object of class 'Counts'

n1

Left endpoint of the prior support interval (Optional). If not provided and total counts are not zero, computed using the maximum likelihood estimate (mle) of the population size as 0.5 * mle

n2

Right endpoint of the prior support interval (Optional). If not provided and total counts are not zero, computed using the maximum likelihood estimate (mle) of the population size as 2 * mle

replacement

Whether sampling has been performed with replacement. Default to FALSE.

b

Prior rate parameter of the gamma distribution used to compute the posterior with Clough. Default is 1e-10.

alg

Algorithm to be used to perform computations. Default to DUP.

Methods

signature(object = "Counts")

an object of class Counts.

Value

Returns an object of class Counts.

References

Comoglio F, Fracchia L and Rinaldi M (2013) Bayesian inference from count data using discrete uniform priors. PLOS ONE, to appear

Clough HE et al. (2005) Quantifying Uncertainty Associated with Microbial Count Data: A Bayesian Approach. Biometrics 61: 610-616

See Also

Counts, plotPosterior

Examples

K <- newCounts( counts = c(20,30), fractions = c(0.075, 0.10))

#using default parameters (DUP, sampling without replacement and default prior support)
K.dup <- computePosterior(K)

#using custom prior support (DUP)
K.cust <- computePosterior(K, n1 = 0, n2 = 1e3)

#using a Gamma prior (GP method)
K.gp <- computePosterior(K, alg = 'GP')

#plot the results (compare DUP with GP)
plotPosterior(K.dup, type = 'l', lwd = 3, col = 'blue3', low = 0.025, up = 0.975)
lines(K.gp@posterior, lwd = 3, col = 'red3')

#for sampling with replacement:
computePosterior(K, replacement = TRUE)