adequate convergence.

With 28 subjects, there are a total of 30 parameters being estimated.

how easy it is to implement a hierarchical model in JAGS

dgamma distribution generates a variable called kappaMinusTwo, and then kappa itself is kappaMinusTwo + 2. This

kappaMinusTwo

we must use one that adequately expresses our prior knowledge.

In real situations, we do not know the value of κ in advance, and instead we let the data inform us regarding its credible values. Intuitively, when the data from different coins show very similar proportions of heads, we have evidence that κ is high. But when the data from different coins show diverse proportions of heads, then we have evidence that κ is small.

K = 75 instead of K = 5. T

of the two subjects, and simultaneously estimate ω of the drug that influenced them.

θ depends on the value of ω

The value of κ governs how near θ is to θ,

Here is the “Bernoulli ones trick.” First, notice that dbern(1|θ) = θ. In other words, if we write JAGS code 1 ~ dbern( theta ), it yields a likelihood that is the value of theta. If we define, in another line of JAGS code, the value of theta as the desired likelihood at y[i], then the result is the likelihood at y[i] . Thus, the JAGS model statements together yield the same thing as y[i] ~ pdf ( parameters ). The variable name spy[i] stands for scaled probability of yi.

It is straight forward to have JAGS generate an MCMC sample from the prior: We simply run the program with no data included.

no signs of orphaned chains.

codaSamples

To install JAGS, s

orphaned

model {for(i in 1:Ntotal ) { y[i] ~ dbern( theta )} theta ~ dbeta(1, 1)}

sum(y)/length(y)

The MLE is the value of the parameter that maximizes the likelihood function, which is to say, the value of the parameter that maximizes the probability of the data.

JAGS employs comment syntax just like R<math><mstyle fontfamily="Centaur" is="true"><mi mathvariant="normal" is="true">R</mi></mstyle></math>.

To get the model specification into JAGS, we create the specification as a character string in R<math><mstyle fontfamily="Centaur" is="true"><mi mathvariant="normal" is="true">R</mi></mstyle></math>

model { for(i in 1:Ntotal ) { y[i] ~ dbern( theta ) # likelihood}theta ~ dbeta(1, 1) # prior}

To reiterate: when describing a model, the description logically flows from data to likelihood (with its parameters) to prior. If the representational medium is graphs of distributions, then the logical flow goes from bottom to top. If the representational medium is text such as English or computer code, then the logical flow goes from top to bottom.

Bernoulli distribution

and a prior distribution,

All we have to do is tell JAGS the data and the model

I will use a noncommittal and vague prior that places virtually equal prior credibility across a vast range of possible values for the slope and intercept, both centered at zero