Sampling with heuristics
Kevin H. Knuth · The Journal of the Acoustical Society of America · 2007
Algorithms that rely on heuristics are attractive to those interested in solving acoustic problems. The main reason is that heuristics often derive from solutions to a simplified problem and, as such, they are able to accurately estimate a subset of model parameters. However, algorithms that rely on heuristics are not sufficiently robust as they ignore vast regions of the parameter space. For this reason, sampling techniques that focus on exploration increase the probability of finding a difficult solution. However, sampling algorithms can become trapped in difficult problems that possess vast plateaus in the parameter space upon which the solution space occupies an extremely small volume. In these cases, heuristics at least have a chance to succeed where sampling is likely to fail. This work considers incorporating heuristically-obtained samples into a relatively new sampling algorithm called nested sampling. Nested sampling strives to localize the solution space while simultaneously integrating the posterior probability to compute the Bayesian evidence. The challenge is that nested sampling accomplishes this by working with uniformly distributed samples, whereas heuristics necessarily result in nonuniformly distributed samples. The difficulties and benefits in combining these two search strategies are described in the context of acoustic source separation.