Supprimer priorOnK_spec.R
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priorOnK_spec.R
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priorOnK_spec.R
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#' Specify prior on \eqn{K}.
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#'
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#' @description Obtain a function to evaluate the log prior
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#' specified for \eqn{K}.
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#' @param P A character indicating which specification should be
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#' used. See Details for suitable values.
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#' @param K A numeric or integer scalar specifying the fixed (if `P`
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#' equals `"fixedK"`) or maximum value (if `P` equals `"Unif"`) of
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#' \eqn{K}.
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#' @return A named list containing:
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#' * `"log_pK"`: a function of the log prior of \eqn{K}.
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#' * `"param"`: a list with the parameters.
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#'
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#' @details
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#' The following prior specifications are supported:
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#' * `"fixedK"`: K has the fixed value K (second argument).
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#' * `"Unif"`: \eqn{K \sim} Unif\eqn{[1,K]}, where the upper limit is given by K (second argument).
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#' * `"BNB_111"`: \eqn{K-1 \sim} BNB(1,1,1), i.e., \eqn{K-1} follows a beta-negative binomial distribution with parameters \eqn{(1,1,1)}.
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#' * `"BNB_121"`: \eqn{K-1 \sim} BNB(1,2,1), i.e., \eqn{K-1} follows a beta-negative binomial distribution with parameters \eqn{(1,2,1)}.
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#' * `"BNB_143"`: \eqn{K-1 \sim} BNB(1,2,1), i.e., \eqn{K-1} follows a beta-negative binomial distribution with parameters \eqn{(1,4,3)}.
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#' * `"BNB_443"`: \eqn{K-1 \sim} BNB(4,4,3), i.e., \eqn{K-1} follows a beta-negative binomial distribution with parameters \eqn{(4,4,3)}.
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#' * `"BNB_943"`: \eqn{K-1 \sim} BNB(9,4,3), i.e., \eqn{K-1} follows a beta-negative binomial distribution with parameters \eqn{(9,4,3)}.
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#' * `"Pois_1"`: \eqn{K-1 \sim} pois(1), i.e., \eqn{K-1} follows a Poisson distribution with rate 1.
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#' * `"Pois_4"`: \eqn{K-1 \sim} pois(4), i.e., \eqn{K-1} follows a Poisson distribution with rate 4.
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#' * `"Pois_9"`: \eqn{K-1 \sim} pois(9), i.e., \eqn{K-1} follows a Poisson distribution with rate 9.
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#' * `"Geom_05"`: \eqn{K-1 \sim} geom(0.5), i.e., \eqn{K-1} follows a geometric distribution with success probability \eqn{p=0.5} and density \eqn{f(x)=p(1-p)^x}.
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#' * `"Geom_02"`: \eqn{K-1 \sim} geom(0.2), i.e., \eqn{K-1} follows a geometric distribution with success probability \eqn{p=0.2} and density \eqn{f(x)=p(1-p)^x}.
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#' * `"Geom_01"`: \eqn{K-1 \sim} geom(0.1), i.e., \eqn{K-1} follows a geometric distribution with success probability \eqn{p=0.1} and density \eqn{f(x)=p(1-p)^x}.
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#' * `"NB_11"`: \eqn{K-1 \sim} nbinom(1,0.5), i.e., \eqn{K-1} follows a negative-binomial distribution with \eqn{size=1} and \eqn{p=0.5}.
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#' * `"NB_41"`: \eqn{K-1 \sim} nbinom(4,0.5), i.e., \eqn{K-1} follows a negative-binomial distribution with \eqn{size=4} and \eqn{p=0.5}.
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#' * `"NB_91"`: \eqn{K-1 \sim} nbinom(9,0.5), i.e., \eqn{K-1} follows a negative-binomial distribution with \eqn{size=9} and \eqn{p=0.5}.
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#'
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priorOnK_spec <- function(P = c("fixedK", "Unif",
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"BNB_111", "BNB_121", "BNB_143", "BNB_443", "BNB_943",
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"Pois_1", "Pois_4", "Pois_9",
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"Geom_05", "Geom_02", "Geom_01",
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"NB_11", "NB_41", "NB_91"), K) {
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P <- match.arg(P)
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if (P %in% c("fixedK", "Unif")) {
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stopifnot(is.numeric(K), length(K) == 1, K >= 1)
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K <- as.integer(K)
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}
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if (P == "fixedK") {
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param <- list(K_0 = K)
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log_pK <-function (x) log(x == K)
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}
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if (P == "Unif") {
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param <- list(Kmax = K)
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log_pK <-function (x) log(1/K)
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}
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if (P == "BNB_111") {
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alpha.B <- 1
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a_pi <- 1
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b_pi <- 1
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param <- list(alpha.B = alpha.B, a_pi = a_pi, b_pi = b_pi)
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log_pK <- function (x)
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dbnbinom(x, size = alpha.B, alpha = a_pi, beta = b_pi, log = TRUE) - log(0.5)
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}
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if (P == "BNB_212") {
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alpha.B <- 2
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a_pi <- 1
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b_pi <- 2
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param <- list(alpha.B = alpha.B, a_pi = a_pi, b_pi = b_pi)
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log_pK <- function (x)
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dbnbinom(x-1, size = alpha.B, alpha = a_pi, beta = b_pi, log = TRUE)
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}
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if (P == "BNB_143") {
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alpha.B <- 1
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a_pi <- 4
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b_pi <- 3
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param <- list(alpha.B = alpha.B, a_pi = a_pi, b_pi = b_pi)
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log_pK <- function (x)
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dbnbinom(x-1, size = alpha.B, alpha = a_pi, beta = b_pi, log = TRUE)
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}
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if (P == "BNB_443") {
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alpha.B <- 4
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a_pi <- 4
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b_pi <- 3
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param <- list(alpha.B = alpha.B, a_pi = a_pi, b_pi = b_pi)
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log_pK <- function (x)
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dbnbinom(x-1, size = alpha.B, alpha = a_pi, beta = b_pi, log = TRUE)
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}
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if (P == "BNB_943") {
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alpha.B <- 9
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a_pi <- 4
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b_pi <- 3
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param <- list(alpha.B = alpha.B, a_pi = a_pi, b_pi = b_pi)
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log_pK <- function (x)
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dbnbinom(x-1, size = alpha.B, alpha = a_pi, beta = b_pi, log = TRUE)
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}
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if (P == "Pois_1") {
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lambda <- 1
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param <- list(lambda = lambda)
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log_pK <- function(x) dpois(x-1, lambda, log = TRUE)
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}
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if (P == "Pois_4") {
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lambda <- 4
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param <- list(lambda = lambda)
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log_pK <- function(x) dpois(x-1, lambda, log = TRUE)
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}
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if (P == "Pois_9") {
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lambda <- 9
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param <- list(lambda = lambda)
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log_pK <- function(x) dpois(x-1, lambda, log = TRUE)
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}
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if (P == "Geom_05") {
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p_geom <- 0.5
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param <- list(p_geom = p_geom)
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log_pK <- function(x) dgeom(x-1, p_geom, log = TRUE)
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}
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if (P == "Geom_02") {
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p_geom <- 0.2
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param <- list(p_geom = p_geom)
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log_pK <- function(x) dgeom(x-1, p_geom, log = TRUE)
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}
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if (P == "Geom_01") {
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p_geom <- 0.1
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param <- list(p_geom = p_geom)
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log_pK <- function(x) dgeom(x-1, p_geom, log = TRUE)
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}
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if (P == "NB_11") {
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alpha.nb <- 1
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beta.nb <- 1
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param <- list(alpha.nb = alpha.nb, beta.nb = beta.nb)
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log_pK <- function (x)
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dnbinom(x-1, size = alpha.nb, prob = beta.nb/(beta.nb+1), log = TRUE)
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}
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if (P == "NB_41") {
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alpha.nb <- 4
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beta.nb <- 1
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param <- list(alpha.nb = alpha.nb, beta.nb = beta.nb)
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log_pK <- function (x)
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dnbinom(x-1, size = alpha.nb, prob = beta.nb/(beta.nb+1), log = TRUE)
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}
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if (P == "NB_91") {
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alpha.nb <- 9
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beta.nb <- 1
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param <- list(alpha.nb = alpha.nb, beta.nb = beta.nb)
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log_pK <- function (x)
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dnbinom(x-1, size = alpha.nb, prob = beta.nb/(beta.nb+1), log = TRUE)
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}
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return(list(log_pK = log_pK, param = param))
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}
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