sequential.pops (version 0.1.1)

stbp_posterior_composite: Posterior probability calculation for composite hypotheses

Description

This function calculates a posterior probability for hypotheses about population densities of the form \(H:\mu > \psi\) or \(H:\mu < \psi\), given the data at a single iteration. This function is to be used in a sequential framework, and called on the sequential test stbp_composite.

Usage

stbp_posterior_composite(
  data,
  greater_than,
  hypothesis,
  density_func,
  overdispersion = NA,
  prior,
  lower_bnd = 0,
  upper_bnd = Inf
)

Value

A single probability

Arguments

data

For count data, a numeric vector with for a single sampling bout (NAs allowed). For binomial data, a matrix with observations in col 1 and samples in col 2 (NAs not allowed).

greater_than

logical; if TRUE, the tested hypothesis is of the form \(H:\mu > \psi\) otherwise, \(H:\mu < \psi\).

hypothesis

Single non-negative value with the hypothesized value of \(\mu\).

density_func

Kernel probability density function for the data. See details.

overdispersion

A character string (if a function) or a number specifying the overdispersion parameter. Only required when using "negative binomial" or "beta-binomial" as kernel densities. See details.

prior

Single number with initial prior. Must be on the interval \([0,1]\).

lower_bnd

Single number indicating the lower bound of the parameter space for \(\mu\). Most cases is \(0\) (default).

upper_bnd

Single number indicating the upper bound of the parameter space for \(\mu\). For count data, is often Inf (default), but it must be \(\leq 1\) for binomial data.

Details

The density_func argument should be specified as character string. Acceptable options are "poisson", "negative binomial", "binomial" and "beta-binomial". The overdispersion parameter for "negative binomial" and "beta-binomial" can be either a constant or a function of the mean. If a function, it should be specified as a character string with the name of an existing function. For options of empirical functions to describe overdispersion as a function of the mean see Binns et al. (2000). The most common approach for the negative binomial family is Taylor's Power Law.

References

Binns, M.R., Nyrop, J.P. & Werf, W.v.d. (2000) Sampling and monitoring in crop protection: the theoretical basis for developing practical decision guides. CABI Pub., Wallingford, Oxon, UK; New York, N.Y.

Rincon, D.F., McCabe, I. & Crowder, D.W. (2025) Sequential testing of complementary hypotheses about population density. Methods in Ecology and Evolution. <https://doi.org/10.1111/2041-210X.70053>

Examples

# Counts collected in a single sampling bout
counts <- c(1, 2, 3)

# Calculate posterior probability from a naive 0.5 prior for H1:mu>2
# (a population being >2 individuals per sampling unit) with
# a poisson kernel

stbp_posterior_composite(data = counts,
                          greater_than = TRUE,
                          hypothesis = 2,
                          density_func = "poisson",
                          prior = 0.5,
                          lower_bnd = 0,
                          upper_bnd = Inf) # returns 0.60630278

# Same analysis but with a negative binomial kernel.
# Note that 'overdispersion' can either be a positive number or a function.

stbp_posterior_composite(data = counts,
                          greater_than = TRUE,
                          hypothesis = 2,
                          density_func = "negative binomial",
                          overdispersion = 2,
                          prior = 0.5,
                          lower_bnd = 0,
                          upper_bnd = Inf) # returns 0.72558593
## End (Not run)