The BUGS Language

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The BUGS language

The BUGS language is described in detail in the NIMBLE User Manual, and in the relevant section of the BUGS manual.

An HTML version of the User Manual is also available.

Stochastic declarations

• x ~ dgamma(shape, scale) (x follows a gamma distribution with parameters shape and scale)

Deterministic declarations

• y <- 2 * x

For loops

for(i in 1:10) {
   lambda[i] <- exp(mu[i])
   y[i] ~ dpois(lambda[i])
}

 

Classic BUGS examples

There are lots of example models originally provided by the BUGS project:

• Included in NIMBLE (classic-bugs directory) or found here on the JAGS website.
• Information provided here: Volume 1, Volume 2, and Volume 3 of the WinBUGS example manuals.

We’ll see a variety of example models later today.

 

NIMBLE’s dialect of BUGS

• The BUGS syntax used in NIMBLE has minor differences from that used in WinBUGS, OpenBUGS and/or JAGS.
• These differences are described in Section 5 of the NIMBLE Users Manual.
• There’s also a blog post describing these differences.
• The main things you’d have to watch for when converting jags code:
  • Provide full indexing for vectors and arrays: v[1:5], or X[1:N, 1:M]
  • There are differences in notation for trunction: x ~ T(dnorm(0, 0.001), 0, Inf)
  • NIMBLE allows for named arguments to distributions, and different parameterizations: x ~ dnorm(0, sd = 1000)
  • NIMBLE distinguishes between model constant values (consts), and model data values (data).

 

A basic example

We’ll use the litters model example from the original BUGS examples, available with NIMBLE in the classic-bugs/vol1/litters directory of the installed package.

The data set describes the survival rates of rat pups in an experiment.

Here’s the original litters model.

• There are G=2 groups of rat litters, with N=16 litters (i.e., mothers) in each group, and a variable number of pups in each litter.
• Survival of the pups in a litter is governed by a survival probability for each litter, p[i,j].
• The probabilities for the litters within a group are considered to come from a common distribution, thereby borrowing strength across the litters in a group.
• The common distributions are \(p_{1,j} \sim \text{Beta}(a_1, b_1)\) for Group 1 and \(p_{2,j} \sim \text{Beta}(a_2, b_2)\) for Group 2.

 

Specifying the BUGS code for a model

Here we specify the litters model code directly in R. We can walk through some of details via the comments in the BUGS code.