MCMC – Implementing Winbugs and Other MCMC Without Prior Distribution Information

bayesianbugsmarkov-chain-montecarlorwinbugs

What happens when you don't have an idea of the parameters distribution? What approach should we use?

Most of the time we aim to undersatnd if a certain variable has any influence over the presence/absence of a certain species, and the variable is accepted or not according to the variable importance. This means that most of the times we are not thinking on the expetcted distribution a parameter should have.

Is it correct to assume that all parameters follow a normal distribution, when all i know is that b1,b2,b3 and b4 should vary between -2 and 2, and b0 can vary between -5 and 5 ?

model {
    # N observations
    for (i in 1:N) {
        species[i] ~ dbern(p[i])
        logit(p[i]) <- b0 + b1*var1[i] + b2*var2[i] + 
            b3*var3[i] + b4*var4[i]
    }
    # Priors
    b0     ~ dnorm(0,10)
    b1   ~ dnorm(0,10)
    b2 ~ dnorm(0,10)
    b3  ~ dnorm(0,10)
    b4  ~ dnorm(0,10)
}

Best Answer

Parameters in linear predictor are t-distributed. When the number of records goes to infinity, it converges to normal distribution. So yes, normally it is considered correct to assume normal distribution of parameters.

Anyways, in bayesian statistics, you need not to assume parameter distribution. Normally you specify so called uninformative priors. For each case, different uninformative priors are recommended. In this case, people often use something like (you can tweak the values of course):

dunif(-100000, 100000)

or

dnorm(0, 1/10^10)

The second one is preferred, because it is not limited to particular values. With uninformative priors, you have take no risk. You can of course limit them to particular interval, but be careful.

So, you specify uninformative prior and the parameter distribution will come out itself! No need to make any assumptions about it.

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