Sequential test of Bayesian posterior probabilities for simple hypotheses about species absence

Runs a Sequential test of Bayesian Posterior Probabilities for hypotheses about species absence of the form $H:\mu = 0$. Data is treated in a sequential framework.

Usage

stbp_simple(
  data,
  density_func,
  overdispersion = NA,
  prior = 0.5,
  upper_bnd = Inf,
  lower_criterion,
  upper_criterion
)

Arguments

data: For count data, either a vector (for purely sequential designs) o a matrix (group sequential designs) with sequential count data, with sampling bouts collected over time in columns and samples within bouts in rows. NAs are allowed in case sample size within bouts is unbalanced. For binomial data, a list of matrices with integer non-negative values of observations in col 1 and number of samples in col 2, so that each matrix within the list corresponds to a sampling bout. NAs are not allowed for binomial data.
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 in the interval $[0,1]$. If no prior information is available 0.5 (default) is recommended.
upper_bnd: Single number indicating the greatest possible value for $\mu$. For count data, is often Inf (default), but it must be $\leq 1$ for binomial data.
lower_criterion: Criterion to decide against the tested hypothesis. This is the lowest credibility to the hypothesis to stop sampling and decide against.
upper_criterion: Criterion to decide in favor of the tested hypothesis. This is the greatest credibility to the hypothesis to stop sampling and decide in favor.

Value

An object of class "STBP".

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, which describes the variance as a function of the mean with two parameters, $a$ and $b$. Overdispersion, $k$, can then be specified as: $$k = \frac{\mu^2}{a \mu^b - \mu}$$

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

# Testing the absence of a species in a given area from a sequential random
# sampling of 3 bouts made of 10 samples (counts) each (all absences). Upper
# criterion set to 0.9999

counts10 <- matrix(rep(0, 30), 10, 3)

test1G <- stbp_simple(data = counts10,
                        density_func = "poisson",
                        prior = 0.5,
                        upper_bnd = Inf,
                        lower_criterion = 0,
                        upper_criterion = 0.9999)
test1G
#> 
#> Sequential test of Bayesian posterior probabilities
#> Family: poisson
#> H: mu = 0
#> Probability: 0.999 from 3 sampling bouts
#> Recommendation based on provided criteria: keep sampling

# returns a recommendation of "keep sampling" due to insufficient evidence.

# Testing the same hypothesis with the same upper criterion but from a
# sequential random sampling of 3 bouts made of 30 samples (counts) each
# (all absences).

counts30 <- matrix(rep(0, 90), 30, 3)

test2G <- stbp_simple(data = counts30,
                        density_func= "poisson",
                        prior = 0.5,
                        upper_bnd = Inf,
                        lower_criterion = 0,
                        upper_criterion = 0.9999)
test2G
#> 
#> Sequential test of Bayesian posterior probabilities
#> Family: poisson
#> H: mu = 0
#> Probability: 0.99996 from 3 sampling bouts
#> Recommendation based on provided criteria: accept H

# returns a recommendation of "accept H" of the species being absent from
# that area.

## End (Not run)