fbst (version 2.2)

fbst: fbst

Description

The function computes the Full Bayesian Significance Test (FBST) and the e-value, which is the Bayesian evidence against a precise null hypothesis. The function assumes posterior MCMC draws and constructs a posterior density based on a kernel density estimator subsequently.

Usage

fbst(posteriorDensityDraws, nullHypothesisValue, FUN, par, 
dimensionTheta, dimensionNullset, dim, gridSize)

Value

Returns an object of class fbst.

Arguments

posteriorDensityDraws

Vector of (MCMC) posterior parameter draws.

nullHypothesisValue

Parameter value of the precise null hypothesis.

FUN

Reference function.

par

Additional parameters of the reference function.

dimensionTheta

Dimension of the parameter space, defaults to 1 and can be changed to 2. Dimensions larger than 2 are currently not supported.

dimensionNullset

Dimension of the null set corresponding to the null hypothesis.

dim

Dimension of the posterior subspace over which integration is required. Defaults to 1. Can be changed to 2 if required.

gridSize

Grid size for the multivariate two-dimensional kernel density estimation in case dimensionTheta=2. Defaults to 1000.

Author

Riko Kelter

Details

If no reference function is specified, a flat reference function \(r(\theta)=1\) is used as default reference function. Note that the posterior dimension dim defaults to 1, and if dim=2, only flat reference functions are supported. Thus, specifying FUN or par has no effect when dim=2.

References

For a details, see: https://link.springer.com/article/10.3758/s13428-021-01613-6.

Examples

set.seed(57)
grp1=rnorm(50,0,1.5)
grp2=rnorm(50,0.8,3.2)

p = as.vector(BayesFactor::ttestBF(x=grp1,y=grp2, 
  posterior = TRUE, iterations = 3000, 
  rscale = "medium")[,4])

# flat reference function
res = fbst(posteriorDensityDraws = p, nullHypothesisValue = 0, 
dimensionTheta = 2, dimensionNullset = 1)
summary(res)
plot(res)

# medium Cauchy C(0,1) reference function
res_med = fbst(posteriorDensityDraws = p, nullHypothesisValue = 0, dimensionTheta = 2, 
dimensionNullset = 1, FUN = dcauchy, par = list(location = 0, scale = sqrt(2)/2))
summary(res_med)
plot(res_med)