Sensitivity analysis for the urn Bayes factor

Reports the bias tipping point for the urn Bayes factor: the smallest observation bias omega > 1 at which the Bayes factor first drops below threshold.

Usage

sens_urn(y_W, y_R, threshold = 20)

Arguments

y_W

Non-negative integer. Observed count favorable to the working theory.

y_R

Non-negative integer. Observed count favorable to the rival.

threshold

Positive numeric. Decision threshold the Bayes factor must remain at or above. Default 20.

Value

A list with elements:

bf

Bayes factor at omega = 1.

omega_star

Bias tipping point. 0 if bf < threshold at baseline; NA_real_ if bf does not cross threshold for any reachable omega.

Details

omega > 1 makes pro-\(H_1\) items more likely to be drawn than they are in the urn, so the apparent dominance of pro-\(H_1\) evidence is partly an artifact of observation, and the Bayes factor falls. omega_star is the value at which this fall first crosses threshold. If bf_urn(y_W, y_R) < threshold at baseline, omega_star is 0.

See also

bf_urn(), sens_binomial(), sens_coding().

Examples

# The paper's running example. bf_urn(9, 3) = 323 is far above 20, so
# pro-H_1 items must be ~2.4 times likelier to be observed before the
# urn BF reaches the threshold.
s <- sens_urn(9, 3)
s$bf
#> [1] 323
s$omega_star
#> [1] 2.433984