Tid: 1 oktober 2007 kl 15.15-16.00
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Johannes Thoms
Titel: Adaptive Markov Chain Monte Carlo Algorithms for improved Sampling (Examensarbete)
Sammanfattning: The purpose of this project is the development of an adaptive Markov chain Monte Carlo (MCMC) algorithm that improves the online tuning of the proposal distribution's parameters. The latter takes the form of a mixture of Gaussian distributions. This aim is achieved by enhancing an existing scheme with three main building blocks: variance scaling, to ensure a targeted acceptance probability for accept-reject methods. Secondly, adaptive mixture weights to improve the coverage of the target distribution's support and finally probabilistic principal component analysis to include the target's orientation by proposing random walk increments in directions associated with large variance. Chapter 1 introduces the project's different aspects briefly. Chapter 2 describes adaptive MCMC through a comparison with the standard method. The adaptation process renders the chain non-Markovian, entailing the need for constraints that have to be adhered to when constructing the proposal kernel in order to ensure the chain's ergodicity and convergence to the correct target. This is outlined in greater detail in Chapter 3. The algorithm itself is described in Chapter 4 and benchmarked in the following section, where also a data application of a change point process is given. The final chapter holds conclusions as well as suggestions for further developments and applications. The benchmark tests indicate a good performance of the building blocks, particularly the possibility of estimating the target's normalizing constant. The data application, while showing promising signs, also points to several areas of possible improvements.