ABSTRACT
Chapter 3 explains how independent priors for ˜xed effects are formally speci˜ed in BugsXLA. If a factor is de˜ned as random in BugsXLA, then the effects, αi, associated with the levels of this factor are given the prior:
α τi 2N( )~ ,0
where τ2 is the variance component associated with this term, which has itself a prior distribution. It is this hierarchy in the parameters that is referred to when these models are termed Hierarchical Linear Models. There
is still some debate about the most appropriate default vague prior to use for τ2 (see Chapter 5 of Spiegelhalter et al. (2004) for a thorough discussion). BugsXLA offers the following options:
τ ~Half-N(K)
The Half-Normal prior on the standard deviation of the effects is the default, as this has been recommended by both Spiegelhalter et al. (2004) and Gelman (2006).
