bfactor_to_prob: Turn Bayes Factors Into Posterior Probabilities
In pcal: Calibration of P-Values for Point Null Hypothesis Testing

Description Usage Arguments Details Value References See Also Examples

View source: R/bfactor_to_prob.R

Update the prior probabilities of models/hypotheses to posterior probabilities using Bayes factors.

1	bfactor_to_prob(bf, prior_prob = 0.5)

`bf`	A numeric vector of non-negative values.
`prior_prob`	A numeric vector with values in the [0,1] interval. If `length(bf) == 1` then `prior_prob` can be of any positive `length`, but if `length(bf) > 1` then the `length` of `prior_prob` can only be `1` or equal to the `length` of `bf`.

bfactor_to_prob computes the posterior probability of the null hypothesis using the following equation from \insertCitebergerDelampady1987;textualpcal:

P(null hypothesis | data) = (1 + (1 - prior_prob) / prior_prob * (1 / bf)) ^(-1)

where bf is a Bayes factor if favor of the null hypothesis and prior_prob is the prior probability of the null hypothesis. The alternative hypothesis has prior probability 1 - prior_prob and posterior probability 1 - bfactor_to_prob(bf, prior_prob).

The prior_prob argument is optional and is set to 0.5 by default, implying prior equiprobability of hypotheses. prior_prob can only be of length equal to length(bf), in which case each prior probability in prior_prob will be updated using the corresponding element of bf, or of length 1, in which case it will be recycled (if length(bf) > 1) and each element of bf will update the same prior_prob value.

If length(bf) > 1 then bfactor_to_prob returns a numeric vector with the same length as bf, otherwise it returns a numeric vector with the same length as prior_prob.

\insertAllCited

bfactor_interpret and bfactor_interpret_kr for the interpretation of Bayes factors.
bfactor_log_interpret and bfactor_log_interpret_kr for the interpretation of the logarithms of Bayes factors.
bcal for a p-value calibration that returns lower bounds on Bayes factors in favor of point null hypotheses.
pcal for a p-value calibration that returns lower bounds on the posterior probabilities of point null hypotheses.

# With a Bayes factor that is indifferent between the null and the alternative hypotheses:
bfactor_to_prob(1)

# Same as above but the null hypothesis has high prior probability:
bfactor_to_prob(1, .99)

# Posterior probability of the null as a function of different prior probabilities:
bfactor_to_prob(1, seq(.5, 1, .1))

# With Bayes factors that favor the null hypothesis:
round(bfactor_to_prob(seq(2, 50, 2.5)), 3)

# Same as above but the null hypothesis has low prior probability:
round(bfactor_to_prob(seq(2, 50, 2.5), prior_prob = .01), 3)

# Posterior probabilities obtained with Bayes factors that favor the alternative hypothesis:
round(bfactor_to_prob(seq(0, 1, .05)), 3)

# Same as above but the null hypothesis has high prior probability:
round(bfactor_to_prob(seq(0, 1, .05), prior_prob = .99), 3)

# Application: chi-squared goodness-of-fit test,
# lower bound on the posterior probability of the null hypothesis:
x <- matrix(c(12, 41, 25, 33), ncol = 2)
bfactor_to_prob(bcal(chisq.test(x)[["p.value"]]), prior_prob = .9)