Bayes factor BF+0 for the directional alternative vs point-null — twoarmbinbf_plus0

Computes the Bayes factor \(BF_{+0}\) comparing the directional alternative hypothesis \(H_+\) (p_2 > p_1) against the point-null \(H_0\) (p_1 = p_2).

Usage

twoarmbinbf_plus0_direct(
  y1,
  y2,
  n1,
  n2,
  a_0_a = 1,
  b_0_a = 1,
  a_1_a = 1,
  b_1_a = 1,
  a_2_a = 1,
  b_2_a = 1
)

Arguments

y1, y2: Integer counts of successes in arms 1 and 2.
n1, n2: Integer sample sizes in arms 1 and 2.
a_0_a, b_0_a: Shape parameters of the analysis prior for the common response probability under \(H_0\).
a_1_a, b_1_a: Shape parameters of the analysis prior for the response probability in arm 1 under \(H_+\).
a_2_a, b_2_a: Shape parameters of the analysis prior for the response probability in arm 2 under \(H_+\).

Value

Numeric scalar; the Bayes factor \(BF_{+0} = m_+(y_1, y_2) / m_0(y_1, y_2)\).

Details

Both marginal likelihoods are formed using the analysis priors, which represent inferential beliefs at the time the data are evaluated. The design priors are used only for computing Bayesian operating characteristics (predictive power / type-I error) and play no role here.