# #StackBounty: #bayesian #model-comparison Test for comparing log likelihoods that include error terms

### Bounty: 50

Suppose I have two models with likelihoods calculated through thermodynamic integration. `thermodynamic_integration_log_evidence` in PTSampler returns both an estimate of the integral and an error term for it, which the docs say arises from sampling at a finite number of temperatures.

If I was confident in the likelihoods \$L_1, L_2\$ for my models \$M_1,M_2\$ then I could just compute the Bayes factor \$L_1/L_2\$ (or \$exp(LL_1-LL_2)\$ for log likelihoods) to see how many times more likely is \$M_1\$ than \$M_2\$.

But as \$L_1, L_2\$ come with corresponding errors \$sigma_{L1}, sigma_{L2}\$ how can I take these into account in the comparison?

Get this bounty!!!