Particle-Based Online Bayesian Learning of Static Parameters with Application to Mixture Models
Rutger Fuglesang · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2020
This thesis investigates the possibility of using Sequential Monte Carlo methods (SMC) to create an online algorithm to infer properties from a dataset, such as unknown model parameters. Statistical inference from data streams tends to be difficult, and this is particularly the case for parametric models, which will be the focus of this paper. We develop a sequential Monte Carlo algorithm sampling sequentially from the model's posterior distributions. As a key ingredient of this approach, unknown static parameters are jittered towards the shrinking support of the posterior on the basis of an artificial Markovian dynamic allowing for correct pseudo-marginalisation of the target distributions. We then test the algorithm on a simple Gaussian model, a Gausian Mixture Model (GMM), as well as a variable dimension GMM. All tests and coding were done using Matlab. The outcome of the simulation is promising, but more extensive comparisons to other online algorithms for static parameter models are needed to really gauge the computational efficiency of the developed algorithm.