R/mixbeta.R

In RBesT: R Bayesian Evidence Synthesis Tools

#' @name mixbeta
#'
#' @title Beta Mixture Density
#'
#' @description The Beta mixture density and auxilary functions.
#'
#' @param ... List of mixture components.
#' @param param Determines how the parameters in the list
#' are interpreted. See details.
#' @param m Vector of means of beta mixture components.
#' @param s Vector of standard deviations of beta mixture components.
#' @param n Vector of number of observations.
#' @param drop Delete the dimensions of an array which have only one level.
#' @param object Beta mixture object.
#' @param probs Quantiles reported by the \code{summary} function.
#'
#' @details Each entry in the \code{...} argument list is expected to
#' be a triplet of numbers which defines the weight \eqn{w_k}, first
#' and second parameter of the mixture component \eqn{k}. A triplet
#' can optionally be named which will be used appropriately.
#'
#' The first and second parameter can be given in different
#' parametrizations which is set by the \code{param} option:
#' \describe{
#' \item{ab}{Natural parametrization of Beta density (\code{a}=shape1 and \code{b}=shape2). Default. }
#' \item{ms}{Mean and standard deviation, \eqn{m=a/(a+b)} and \eqn{s=\sqrt{\frac{m(1-m)}{1+n}}}, where \eqn{n=a+b} is the number of observations. Note that \eqn{s} must be less than \eqn{\sqrt{m(1-m)}}.}
#' \item{mn}{Mean and number of observations, \eqn{n=a+b}.}
#' }
#'
#' @family mixdist
#'
#' @return \code{mixbeta} returns a beta mixture with the specified mixture components. \code{ms2beta} and
#' \code{mn2beta} return the equivalent natural \code{a} and \code{b} parametrization given parameters \code{m},
#' \code{s}, or \code{n}.
#'
#' @examples
#' ## a beta mixture
#' bm <- mixbeta(rob=c(0.2, 2, 10), inf=c(0.4, 10, 100), inf2=c(0.4, 30, 80))
#'
#' # mean/standard deviation parametrization
#' bm2 <- mixbeta(rob=c(0.2, 0.3, 0.2), inf=c(0.8, 0.4, 0.01), param="ms")
#'
#' # mean/observations parametrization
#' bm3 <- mixbeta(rob=c(0.2, 0.3, 5), inf=c(0.8, 0.4, 30), param="mn")
#'
#' # even mixed is possible
#' bm4 <- mixbeta(rob=c(0.2, mn2beta(0.3, 5)), inf=c(0.8, ms2beta(0.4, 0.1)))
#'
#' # print methods are defined
#' bm4
#' print(bm4)
#'
NULL

#' @rdname mixbeta
#' @export
mixbeta <- function(..., param=c("ab", "ms", "mn")) {
    mix <- mixdist3(...)
    assert_matrix(mix, nrows=3, any.missing=FALSE)
    param <- match.arg(param)
    mix[c(2,3),] <- switch(param,
                           ab=mix[c(2,3),],
                           ms=t(ms2beta(mix[2,], mix[3,], FALSE)),
                           mn=t(mn2beta(mix[2,], mix[3,], FALSE)))
    rownames(mix) <- c("w", "a", "b")
    assert_that(all(mix["a",]>=0))
    assert_that(all(mix["b",]>=0))
    class(mix) <- c("betaMix", "mix")
    likelihood(mix) <- "binomial"
    mix
}

#' @rdname mixbeta
#' @export
ms2beta <- function(m, s, drop=TRUE) {
    n <- m*(1-m)/s^2 - 1
    assert_that(all(n>=0))
    ab <- cbind(a=n*m, b=n*(1-m))
    if(drop) ab <- drop(ab)
    ab
}

#' @rdname mixbeta
#' @export
mn2beta <- function(m, n, drop=TRUE) {
    assert_that(all(n>=0))
    ab <- cbind(a=n*m, b=n*(1-m))
    if(drop) ab <- drop(ab)
    ab
}

#' @rdname mixbeta
#' @method print betaMix
#' @param x The mixture to print
#' @export
print.betaMix <- function(x, ...) {
    cat("Univariate beta mixture\n")
    NextMethod()
}

#' @rdname mixbeta
#' @method print betaBinomialMix
#' @param x The mixture to print
#' @export
print.betaBinomialMix <- function(x, ...) {
    cat("Univariate beta binomial mixture\nn = ", attr(x, "n"),"\n", sep="")
    NextMethod()
}

#' @rdname mixbeta
#' @method summary betaMix
#' @export
summary.betaMix <- function(object, probs=c(0.025,0.5,0.975), ...) {
    p <- object[1,]
    a <- object[2,]
    b <- object[3,]
    m <- a/(a+b)
    v <- m*(1-m)/(a+b+1)
    ## calculate mean of the second moment
    m2 <- v + m^2
    ## from this we can get the mean and variance of the mixture
    mmix <- sum(p * m)
    vmix <- sum(p * (m2 - (mmix)^2) )
    q <- c()
    if(length(probs) != 0) {
        q <- qmix.betaMix(object, p=probs)
        names(q) <- paste(format(probs*100,digits=2), "%", sep="")
    }
    c(mean=mmix, sd=sqrt(vmix), q)
}

#' @rdname mixbeta
#' @method summary betaBinomialMix
#' @export
summary.betaBinomialMix <- function(object, probs=c(0.025,0.5,0.975), ...) {
    n <- attr(object, "n")
    p <- object[1,]
    a <- object[2,]
    b <- object[3,]
    m <- n * a/(a+b)
    v <- n*a*b*(a+b+n)/( (a+b)^2 * ( a + b + 1 ) )
    ## calculate mean of the second moment
    m2 <- v + m^2
    ## from this we can get the mean and variance of the mixture
    mmix <- sum(p * m)
    vmix <- sum(p * (m2 - (mmix)^2) )
    q <- qmix.betaBinomialMix(object, p=probs)
    if(length(q) != 0)
        names(q) <- paste(format(probs*100,digits=2), "%", sep="")
    c(mean=mmix, sd=sqrt(vmix), q)
}