telescope (version 0.2-1)

priorOnK_spec: Specify prior on \(K\).

Description

Obtain a function to evaluate the log prior specified for \(K\).

Usage

priorOnK_spec(
  P = c("fixedK", "Unif", "BNB_111", "BNB_212", "BNB_143", "BNB_443", "BNB_943",
    "Pois_1", "Pois_4", "Pois_9", "Geom_05", "Geom_02", "Geom_01", "NB_11", "NB_41",
    "NB_91"),
  K
)

Value

A named list containing:

• "log_pK": a function of the log prior of \(K\).

• "param": a list with the parameters.

Arguments

P

A character indicating which specification should be used. See Details for suitable values.

K

A numeric or integer scalar specifying the fixed (if P equals "fixedK") or maximum value (if P equals "Unif") of \(K\).

Details

The following prior specifications are supported:

• "fixedK": K has the fixed value K (second argument).

• "Unif": \(K \sim\) Unif\([1,K]\), where the upper limit is given by K (second argument).

• "BNB_111": \(K-1 \sim\) BNB(1,1,1), i.e., \(K-1\) follows a beta-negative binomial distribution with parameters \((1,1,1)\).

• "BNB_212": \(K-1 \sim\) BNB(2,1,2), i.e., \(K-1\) follows a beta-negative binomial distribution with parameters \((2,1,2)\).

• "BNB_143": \(K-1 \sim\) BNB(1,2,1), i.e., \(K-1\) follows a beta-negative binomial distribution with parameters \((1,4,3)\).

• "BNB_443": \(K-1 \sim\) BNB(4,4,3), i.e., \(K-1\) follows a beta-negative binomial distribution with parameters \((4,4,3)\).

• "BNB_943": \(K-1 \sim\) BNB(9,4,3), i.e., \(K-1\) follows a beta-negative binomial distribution with parameters \((9,4,3)\).

• "Pois_1": \(K-1 \sim\) pois(1), i.e., \(K-1\) follows a Poisson distribution with rate 1.

• "Pois_4": \(K-1 \sim\) pois(4), i.e., \(K-1\) follows a Poisson distribution with rate 4.

• "Pois_9": \(K-1 \sim\) pois(9), i.e., \(K-1\) follows a Poisson distribution with rate 9.

• "Geom_05": \(K-1 \sim\) geom(0.5), i.e., \(K-1\) follows a geometric distribution with success probability \(p=0.5\) and density \(f(x)=p(1-p)^x\).

• "Geom_02": \(K-1 \sim\) geom(0.2), i.e., \(K-1\) follows a geometric distribution with success probability \(p=0.2\) and density \(f(x)=p(1-p)^x\).

• "Geom_01": \(K-1 \sim\) geom(0.1), i.e., \(K-1\) follows a geometric distribution with success probability \(p=0.1\) and density \(f(x)=p(1-p)^x\).

• "NB_11": \(K-1 \sim\) nbinom(1,0.5), i.e., \(K-1\) follows a negative-binomial distribution with \(size=1\) and \(p=0.5\).

• "NB_41": \(K-1 \sim\) nbinom(4,0.5), i.e., \(K-1\) follows a negative-binomial distribution with \(size=4\) and \(p=0.5\).

• "NB_91": \(K-1 \sim\) nbinom(9,0.5), i.e., \(K-1\) follows a negative-binomial distribution with \(size=9\) and \(p=0.5\).