PhD Defense Birgit Sollie
Birgit Sollie will defend her PhD thesis entitled 'Statistical inverse problems for population processes' on June 7th 2021.
Birgit's promotors are Michel Mandjes and Mathisca de Gunst.
The PhD defense will take place online and will start at 9.45 hrs. The defense will be livestreamed on the VU YouTube channel.
In April 2021 Birgit started as a postdoc at the Amsterdam UMC within the Department of Epidemiology and Data Science, where she conducts research on the impact and transmissibility of the HPV virus and works on cost-effectiveness assessments of HPV vaccination strategies.
Population processes are stochastic processes that record the dynamics of the number of individuals in a population, and have many different applications in a broad range of areas. This thesis considers population processes of which the parameters are affected by an underlying background process, which accounts for a higher variability in some, or all, model parameters. The aim is to find reliable inference techniques to estimate the parameters, including those related to the background process, from discrete-time observations of the population size.
The statistical inference is complicated severely by the fact that a substantial amount of the process is unobserved. First, the underlying background process is not observed. Second, only the population size is observed, which is the net effect of all the transitions in the dynamics of the population. Last, the population size is observed in discrete time, hence the transitions in between two consecutive observations are not observed. In this thesis we show a collection of techniques to overcome this complication for a variety of population processes. We show how the EM algorithm can be used to estimate the parameters of population processes under Markov-modulation. We use the Erlangization technique to evaluate the likelihood function for quasi birth-death processes, and implement this on a specific model for a population of mRNA molecules using real-life data. Last but not least, we introduce the saddlepoint technique and how it can be used to evaluate the likelihood function for multivariate population processes under modulation. We investigate the accuracy of all inverse methods by extensive simulation studies.
You can read the thesis here.