testFunction_EPA: Test Function: Encompassing Prior

In hardmanko/CMBBHT: Cell Means Based Bayesian Hypothesis Tests

Test Function: Encompassing Prior

Description

See the "Encompassing Prior Approach" section of the package manual for an explanation of this approach to estimating Bayes factors. There is some encompassing model, M_1, and a constrained model, M_0, which is created by placing some constraint on some of the parameters of M_1. The function I_M0 that is passed to this function determines whether the constraint is satisfied.

Note that you cannot pass this function directly as the testFunction argument of testHypothesis because there is no default value for I_M0. Thus, you must create a curried function to pass to testHypothesis or use create_EPA_intervalTF. See the examples for an example of currying.

Usage

testFunction_EPA(priorEffects, postEffects, I_M0)

Arguments

priorEffects	A numeric matrix of prior effect parameters. Rows are samples and columns are parameters.
postEffects	A numeric matrix of posterior effect parameters. Rows are samples and columns are parameters.
I_M0	The indicator function for the constrained model, M_0. This is a function that takes a vector of effect parameters, checks some constraint on those parameters, and returns 1 (or TRUE) if the constraint is satisfied or 0 (or FALSE) if the constraint is not satisfied.

Value

A list for the following elements:

• success: Logical. Whether or not the test was successful. This is FALSE if the Bayes factors are infinte, NaN, or NA, or TRUE otherwise.

• bf10: The Bayes factor in favor of the encompassing/alternative model, M_1.

• bf01: The Bayes factor in favor of the constrained/null model, M_0.

• prior_satisfied, post_satisfied: The proportions of the prior and posterior, respectively, that satisfy the constraint of I_M0. If these are both low and the number of samples satisfying the constraint is small, it indicates that your constraint is possibly too restrictive and that the estimated Bayes factor may be noisy. You should either use a less-restrictive constraint or take more prior and posterior samples.

Examples

## Not run: 
curriedTestFun = function(priorEffects, postEffects) {
  #M_0: Constrain the effects to be less than 2 units from 0
  I_M0 = function(eff) {
    all(abs(eff) < 2)
  }
  testFunction_EPA(priorEffects, postEffects, I_M0)
}

testHypothesis(..., testFunction = curriedTestFun)

## End(Not run)

hardmanko/CMBBHT documentation built on June 9, 2022, 12:44 a.m.