variance estimation in model

[atredennick]

I think I had the size-based variance term wrong in the likelihood. If I am understanding everything correctly, the equation tau*exp(tauSize*mu[n]) estimates the variance (sigma^2). So, since rstan takes standard deviation as the scale parameter in the normal likelihood, we need to take the square root os that equation to get sigma. It looks like this:

for(n in 1:N){ mu[n] <- a[yid[n]] + gint[gid[n]] + b1[yid[n]]*X[n] + crowdEff[n] + climEff[n]; sigma[n] <- sqrt((fmax(tau*exp(tauSize*mu[n]), 0.0000001))); } #Likelihood (vectorized) Y ~ normal(mu, sigma);

@pbadler, mind double-checking this? This seems right since in WinBUGS/JAGS you guys used 1/tau*exp(tauSize*mu[n]) as the precision in the likelihood (1/variance).

[pbadler]

This seems correct, although you are pushing the limits of my memory...

On 5/19/2015 8:29 AM, Andrew Tredennick wrote:

I think I had the size-based variance term wrong in the likelihood. If I am understanding everything correctly, the equation |tau_exp(tauSize_mu[n])| estimates the variance (|sigma^2|). So, since rstan takes standard deviation as the scale parameter in the normal likelihood, we need to take the square root os that equation to get |sigma|. It looks like this:

|for(n in 1:N){| |mu[n] <- a[yid[n]] + gint[gid[n]] + b1[yid[n]]_X[n] + crowdEff[n] + climEff[n];| |sigma[n] <- sqrt((fmax(tau_exp(tauSize*mu[n]), 0.0000001)));| |}| |#Likelihood (vectorized)| |Y ~ normal(mu, sigma);|

@pbadler https://github.com/pbadler, mind double-checking this? This seems right since in WinBUGS/JAGS you guys used |1/tau_exp(tauSize_mu[n])| as the precision in the likelihood (1/variance).

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Peter Adler Department of Wildland Resources and the Ecology Center Utah State University http://www.cnr.usu.edu/htm/facstaff/adler-web