abf.t: Calculate approximate Bayes factor (ABF) for t distribution...

In tobyjohnson/gtx: Genetics ToolboX

Description

Calculates an approximation to the Bayes Factor for an alternative model where the parameter beta is a priori t distributed, against a smaller model where beta is zero, by approximating the likelihood function with a normal distribution.

Usage

abf.t(beta, se, priorscale, df = 1, gridrange = 3, griddensity = 20)

Arguments

beta	Vector of effect size estimates.
se	Vector of associated standard errors.
priorscale	Scalar specifying the scale (standard deviation) of the prior on true effect sizes.
df	Degrees of freedom for t distribution prior.
gridrange	Parameter controlling range of grid for numerical integration.
griddensity	Parameter controlling density of points in grid for numerical integration.

Details

This uses the same normal approximation for the likelihood function as “Bayes factors for genome-wide association studies: comparison with P-values” by John Wakeley, 2009, Genetic Epidemiology 33(1):79-86 at http://dx.doi.org/10.1002/gepi.20359. However, in contrast to that work, a t distribution is used for the prior, which means it is necessary to use a numerical algorithm to calculate the (approximate) Bayes factor.

Value

A vector of approximate Bayes factors.

Author(s)

Toby Johnson [e-mail]

Examples

data(agtstats)
agtstats$pval <- with(agtstats, pchisq((beta/se.GC)^2, df = 1, lower.tail = FALSE))
max1 <- function(bf) return(bf/max(bf, na.rm = TRUE))
agtstats$BF.normal <- with(agtstats, max1(abf.Wakefield(beta, se.GC, 0.05)))
agtstats$BF.t <- with(agtstats, max1(abf.t(beta, se.GC, 0.0208)))
with(agtstats, plot(-log10(pval), log(BF.normal)))
with(agtstats, plot(-log10(pval), log(BF.t)))

tobyjohnson/gtx documentation built on Aug. 30, 2019, 8:07 p.m.