Bayes factors

BF10 <- function(estimate, lower, upper, null = 0, priormean = null, priorsd = 2) {se <- (log(upper) - log(lower)) / 3.92;bf <- dnorm(x = log(estimate), mean = ifelse(is.null(priormean), null, priormean), sd = sqrt(se^2 + priorsd^2))/dnorm(x = log(estimate), mean = null, sd = se);return(bf)} # Savage-Dickey density ratio

BF10 <- function(estimate, lower, upper, n1, n2){se <- (log(upper) - log(lower)) / 3.92;library(BayesFactor);BF <- exp(ttest.tstat(t = log(estimate)/se, n1 = n1, n2=n2, nullInterval = c(-Inf, 0), rscale = "medium")$bf);return(BF)} # marginal likelihood

# Savage-Dickey density ratio is better if informative priors, small sample size, post dist is available, marginal likelihood is difficult to compute in complex models. Assumptions: continuous parameters, point null, conjugate priors, proper priors, nested models, 

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