**
****
**Eyes: Normal Mixture Model

Bowmaker et al (1985) analyse data on the peak sensitivity wavelengths for individual microspectrophotometric records on a small set of monkey's eyes. Data for one monkey (S14 in the paper) are given below (500 has been subtracted from each of the 48 measurements).

Part of the analysis involves fitting a mixture of two normal distributions with common variance to this distribution, so that each observation y

y

T

We note that this formulation easily generalises to additional components to the mixture, although for identifiability an order constraint must be put onto the group means.

Robert (1994) points out that when using this model, there is a danger that at some iteration,

l

l

{

for( i in 1 : N ) {

y[i] ~ dnorm(mu[i], tau)

mu[i] <- lambda[T[i]]

T[i] ~ dcat(P[])

}

P[1:2] ~ ddirich(alpha[])

theta ~ dunif(0.0, 1000)

lambda[2] <- lambda[1] + theta

lambda[1] ~ dnorm(0.0, 1.0E-6)

tau ~ dgamma(0.001, 0.001) sigma <- 1 / sqrt(tau)

}

Results

A 1000 update burn in followed by a further 10000 updates gave the parameter estimates