% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/bayes_factors.R
\name{twoarmbinbf_plus0_direct}
\alias{twoarmbinbf_plus0_direct}
\title{Bayes factor BF+0 for the directional alternative vs point-null}
\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{
\item{y1, y2}{Integer counts of successes in arms 1 and 2.}

\item{n1, n2}{Integer sample sizes in arms 1 and 2.}

\item{a_0_a, b_0_a}{Shape parameters of the \strong{analysis} prior for the common
response probability under \eqn{H_0}.}

\item{a_1_a, b_1_a}{Shape parameters of the \strong{analysis} prior for the
response probability in arm 1 under \eqn{H_+}.}

\item{a_2_a, b_2_a}{Shape parameters of the \strong{analysis} prior for the
response probability in arm 2 under \eqn{H_+}.}
}
\value{
Numeric scalar; the Bayes factor
\eqn{BF_{+0} = m_+(y_1, y_2) / m_0(y_1, y_2)}.
}
\description{
Computes the Bayes factor \eqn{BF_{+0}} comparing the directional
alternative hypothesis \eqn{H_+} (p_2 > p_1) against the point-null
\eqn{H_0} (p_1 = p_2).
}
\details{
Both marginal likelihoods are formed using the \strong{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.
}
