*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.