Density and Random Function

Users must specify one of the two function types (stats::?func). Either the Density Function (d-func) or the Random Function (r-func)

• Density Function (stats::dfunc) represents the prior distribution the free parameters are assumed to follow

• Random Function (stats::rfunc) represents the sampling distribution for generating random numbers

Users do not need to memorize when to input the d-func or the r-func; the program will handle the necessary conversion automatically. Since this conversion function relies on regular expressions for string transformation, it is relatively brittle. Users must strictly follow the examples provided below.

Class

priors [List]

Density Function

 # standard format dfunc (Only the numerical values can be modified.)
 function(x) {stats::dbeta(x, shape1 = 2, shape2 = 2, log = TRUE)}
 function(x) {stats::dexp(x, rate = 1, log = TRUE)}
 function(x) {stats::dunif(x, min = 0, max = 1, log = TRUE)}
 function(x) {stats::dnorm(x, mean = 0.5, sd = 0.1, log = TRUE)}
 function(x) {stats::dlnorm(x, meanlog = 0.5, sdlog = 0.1, log = TRUE)}
 function(x) {stats::dgamma(x, shape = 2, rate = 3, log = TRUE)}
 function(x) {stats::dlogis(x, location = 0, scale = 1, log = TRUE)}

Random Function

 # standard format rfunc  (Only the numerical values can be modified.)
 function(x) {stats::rbeta(n = 1, shape1 = 2, shape2 = 2)}
 function(x) {stats::rexp(n = 1, rate = 1)}
 function(x) {stats::runif(n = 1, min = 0, max = 1)}
 function(x) {stats::rnorm(n = 1, mean = 0.5, sd = 0.1)}
 function(x) {stats::rlnorm(n = 1, meanlog = 0.5, sdlog = 0.1)}
 function(x) {stats::rgamma(n = 1, shape = 2, rate = 3)}
 function(x) {stats::rlogis(n = 1, location = 0, scale = 1)}

Example

 # TD
 params = list(
   free = list(
     alpha = x[1],
     beta = x[2]
   ),
   fixed = list(
     gamma = 1,
     delta = 0.1,
     epsilon = NA_real_,
     zeta = 0
   ),
   constant = list(
     Q0 = NA_real_,
     lapse = 0.01,
     threshold = 1,
     bonus = 0
   )
 )

 priors = list(
   alpha = function(x) {stats::rbeta(n = 1, shape1 = 2, shape2 = 2)},
   beta = function(x) {stats::rexp(n = 1, rate = 1)}
 )