For which distributions are the parameterizations in BUGS and R different?

Question

I have found some distributions for which BUGS and R have different parameterizations: Normal, log-Normal, and Weibull.

For each of these, I gather that the second parameter used by R needs to be inverse transformed (1/parameter) before being used in BUGS (or JAGS in my case).

Does anyone know of a comprehensive list of these transformations that currently exists?

The closest I can find would be comparing the distributions in table 7 of the JAGS 2.2.0 user manual with the results of ?rnorm etc. and perhaps a few probability texts. This approach appears to require that the transformations will need to be deduced from the pdfs separately.

I would prefer to avoid this task (and possible errors) if it has already been done, or else start the list here.

Update

Based on Ben's suggestions, I have written the following function to transform a dataframe of parameters from R to BUGS parameterizations.

##' convert R parameterizations to BUGS paramaterizations
##' 
##' R and BUGS have different parameterizations for some distributions. 
##' This function transforms the distributions from R defaults to BUGS 
##' defaults. BUGS is an implementation of the BUGS language, and these 
##' transformations are expected to work for bugs.
##' @param priors data.frame with colnames c('distn', 'parama', 'paramb')
##' @return priors with jags parameterizations
##' @author David LeBauer

r2bugs.distributions <- function(priors) {

  norm   <- priors$distn %in% 'norm'
  lnorm  <- priors$distn %in% 'lnorm'
  weib   <- priors$distn %in% 'weibull'
  bin    <- priors$distn %in% 'binom'

  ## Convert sd to precision for norm & lnorm
  priors$paramb[norm | lnorm] <-  1/priors$paramb[norm | lnorm]^2
  ## Convert R parameter b to JAGS parameter lambda by l = (1/b)^a
  priors$paramb[weib] <-   1 / priors$paramb[weib]^priors$parama[weib]
  ## Reverse parameter order for binomial
  priors[bin, c('parama', 'paramb')] <-  priors[bin, c('parama', 'paramb')]

  ## Translate distribution names
  priors$distn <- gsub('weibull', 'weib',
                       gsub('binom', 'bin',
                            gsub('chisq', 'chisqr',
                                 gsub('nbinom', 'negbin',
                                      as.vector(priors$distn)))))
  return(priors)
}

##' @examples
##' priors <- data.frame(distn = c('weibull', 'lnorm', 'norm', 'gamma'),
##'                     parama = c(1, 1, 1, 1),
##'                     paramb = c(2, 2, 2, 2))
##' r2bugs.distributions(priors)

Answer 1

I don't know of a canned list. Here is my list (edits provided by original questioner):

Normal and log-normal are parameterized in terms of $\tau$ (precision) rather than $\sigma$ or $\sigma^2$ (std. dev. or variance); $\tau = 1/\sigma^2 = 1/\mbox{var}$

Beta, Poisson, Exponential, Uniform are all the same

Negative binomial in BUGS has only the discrete parameterization (size,prob), not the "ecological" (size,mu, where size can be non-integer) parameterization.

edit: Weibull in BUGS is ($\nu$=shape,$\lambda$=lambda), in R is ($a$=shape,$b$=scale) [the math notation is consistent with the notation used in the respective documentation] As pointed out at How do I parameterize a Weibull distribution in JAGS / BUGS? , $\lambda= (1/b)^a$

Gamma in BUGS is (shape,rate). This is the default in R, but R also allows (shape,scale) [if the scale argument is named]; rate = 1/scale

Order matters, especially in BUGS (which doesn't have named arguments), e.g. R dbinom(x,size,prob) vs BUGS dbin(p,n) [same parameters, opposite order].

Name differences:

• Binomial: R=dbinom,BUGS=dbin
• Chi-squared: R=dchisq,BUGS=dchisqr
• Weibull: R=dweibull,BUGS=dweib
• Negative binomial: R=dnbinom, BUGS=dnegbin

edit: for truncated distributions BUGS uses I(), JAGS uses dinterval() [it's worth looking in the JAGS documentation if you're going to use this, there may be other subtle differences]