abc {gk}

Approximate Bayesian computation inference

Description

Approximate Bayesian computation (ABC) inference for the g-and-k or g-and-h distribution.

Usage

abc(
  x,
  N,
  model = c("gk", "generalised_gh", "tukey_gh", "gh"),
  logB = FALSE,
  rprior,
  M,
  sumstats = c("all order statistics", "octiles", "moment estimates"),
  silent = FALSE
)

Arguments

x

Vector of observations.

N

Number of iterations to perform.

model

Which model to check: "gk", "generalised_gh" or "tukey_gh". For backwards compatibility, "gh" acts the same as "generalised_gh".

logB

When true, the second parameter is log(B) rather than B.

rprior

A function with single argument, n, which returns a matrix with n rows consisting of samples from the prior distribution for 4 parameters e.g. (A,B,g,k).

M

Number of simulations to accept.

sumstats

Which summary statistics to use.

silent

When FALSE (the default) a progress bar is shown.

Details

This function performs approximate Bayesian inference for iid data from a g-and-k or g-and-h distribution, avoiding expensive density calculations. The algorithm samples many parameter vectors from the prior and simulates corresponding data from the model. The parameters are accepted or rejected based on how similar the simulations are to the observed data. Similarity is measured using weighted Euclidean distance between summary vectors of the simulations and observations. Several summaries can be used, including the complete order statistics or summaries based on octiles. In the latter case only the corresponding order statistics are simulated, speeding up the method.

Value

Matrix whose rows are accepted parameter estimates plus a column giving the ABC distances.

References

D. Prangle. gk: An R package for the g-and-k and generalised g-and-h distributions, 2017.

Examples

set.seed(1)
x = rgk(10, A=3, B=1, g=2, k=0.5) ##An unusually small dataset for fast execution of this example
rprior = function(n) { matrix(runif(4*n,0,10), ncol=4) }
abc(x, N=1E4, rprior=rprior, M=100)