DIC and BMA in BUGS Biotieteellinen tiedekunta / Henkilön nimi / Esityksen nimi 15.9.2018

DIC and BMA Deviance Information Criterion Bayesian Model Averaging Compare how well models fit to data Penalize parameters Do not care whether the data is from any of the models Easy to calculate in BUGS Bayesian Model Averaging Assume that one of the models is ”true” P(model[i] = true | data)=? Use weighted average of the models Difficult to calculate, also in BUGS Biotieteellinen tiedekunta / Henkilön nimi / Esityksen nimi 15.9.2018

DIC in BUGS Run the model until it has converged Inference -> DIC… DIC tool -> set Run the model until you have a good sample from the posterior distribution DIC tool -> stats Model with smallest total DIC is the most efficient ”copying machine”: best balance between number of parameters and fit Biotieteellinen tiedekunta / Henkilön nimi / Esityksen nimi 15.9.2018

Interpreting DIC Model with smallest DIC is ”best” Models that have almost the same DIC (difference less than 2) as the best one have ”substantial support” Difference between 4 to 7: ”considerably less support” Difference > 10: ”essentially no support” Biotieteellinen tiedekunta / Henkilön nimi / Esityksen nimi 15.9.2018

BMA in BUGS Method of Carlin & Chib is the easiest, but does not always work Based on the idea of having the ”model” as one more parameter to estimate Write all the models in the same piece of code, use an index to separate the model Give a categorical prior for the index Biotieteellinen tiedekunta / Henkilön nimi / Esityksen nimi 15.9.2018

Carlin & Chib method: an example model{ for(i in 1:10){ x[i]~dnorm(mu[i,model],tau) mu[i,1]<-alpha # model 1 mu[i,2]<-alpha+beta*y[i] # model 2 } model~dcat(p[1:2]) # categorical prior for the model p[1]<-? # prior prob. Of model 1 p[2]<-? # prior prob of model 2 Pmodel1<-equals(model,1) # posterior prob of model 1 Pmodel2<-equals(model,2) # posterior prob of model 2 Biotieteellinen tiedekunta / Henkilön nimi / Esityksen nimi 15.9.2018

Carlin & Chib method: to remember If priors of some parameters are the same in different models, model indicator is not generally needed for the these parameters. If priors are different in different models,they must be separated with the model index Always use multiple MCMC chains Use high number of MCMC iterations If the chains do not jump between the models at all, then this method does not work! But there are some tricks to make it work… Biotieteellinen tiedekunta / Henkilön nimi / Esityksen nimi 15.9.2018