priorOnK_spec {telescope}

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_121", "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
)

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_121": K-1 \sim BNB(1,2,1), i.e., K-1 follows a beta-negative binomial distribution with parameters (1,2,1).

• "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.

Value

A named list containing:

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

• "param": a list with the parameters.