While sampling from a posterior with Markov chains, BAT will store the maximum value of the posterior that it has seen (and the corresponing point in parameter space). But the sampling algorithm is designed to sample, not to find a maximum value. To find the maximum point, BAT includes optimization methods. These are called via BCIntegrate::FindMode, which takes optional arguments: You may give it a starting point; if you do not specify one, BAT will start from the current maximum point. You can also specify the optimization method when you call the function; or you can specify it in advance via BCIntegrate::SetOptimzationMethod.

By default, BAT replaces its currently held maximum point only if the newly found one has a greater posterior. You can tell BAT to replace the currently held one regardless of whether optimization improves upon the currently stored one via the function BCIntegrate::SetFlagIgnorePrevOptimization.

Minuit

BAT uses Minuit through ROOT's interface to it. To use it, set the optimization method to BCIntegrate::kOptMinuit.

Minuit is what is known as a gradient follower—it moves from a starting point in the direction that increases the posterior until it finds a maximum. Minuit is much better at finding the exact location of a maximum than sampling with Markov chains is, but it does not gaurantee that this maximum is the global maximum or only a local one. Sampling with Markov chains can better identify the region of the global maximum than Minuit can. So we recommend that you first marginalize your model and then call FindMode.

Simulated Annealing

BAT provides a simulated annealing algorithm for optimization. To use it, set the optimization method to BCIntegrate::kOptSimAnn.

This algorithm is similar to the Metropolis-Hastings sampling one in that involves proposal of new points to move to randomly in a neighborhood of the current point. But the neighborhood and the acceptance criteria are regulated in such a way as to encourage motion towards the global maximum.

Using BAT, simulated annealing will in general not find the maximum point as precisely or rapidly as Minuit, but it can more reliably find the global maximum instead of a local maximum. We therefore recommend calling FindMode with BCIntegrate::kOptMinuit after calling it with kOptSimAnn. This is similar to first sampling and then optimizing with Minuit; but simulated annealing is less calculationally expensive than sampling—that is, it will call your likelihood less often. However, simulated annealing is not a sampling technique and will not provide output samples for further offline use.

There are several parameters that govern the running of simulated annealing. Please consult the code documentation and C. Brachem's Implementation and test of a simulated annealing algorithm in the Bayesian Analysis Tookit (2009) for how to set them. The most important option you may change is the proposal function. This is set via BCIntegrate::SetSASchedule. The options are BCIntegrate::kSACauchy, BCIntegrate::kSABoltzmann, and BCIntegrate::kSACustom. (The latter requires you to set your own proposal function.)