Perfect simulation and the EM algorithm are the main topics in this thesis. In paper I, we present coupling from the past (CFTP) algorithms that generate perfectly distributed samples from the multi-type Widom--Rowlin-son (W--R) model and some generalizations of it. The classical W--R model is a point process in the plane or the space consisting of points of several different types. Points of different types are not allowed to be closer than some specified distance, whereas points of the same type can be arbitrary close. A stick-model and soft-core generalizations are also considered. Further, we generate samples without edge effects, and give a bound on sufficiently small intensities (of the points) for the algorithm to terminate. In paper II, we consider the forestry problem on how to estimate seedling dispersal distributions and effective plant fecundities from spatially data of adult trees and seedlings, when the origin of the seedlings are unknown. Traditional models for fecundities build on allometric assumptions, where the fecundity is related to some characteristic of the adult tree (e.g.\ diameter). However, the allometric assumptions are generally too restrictive and lead to nonrealistic estimates. Therefore we present a new model, the unrestricted fecundity (UF) model, which uses no allometric assumptions. We propose an EM algorithm to estimate the unknown parameters. Evaluations on real and simulated data indicates better performance for the UF model. In paper III, we propose EM algorithms to estimate the passage time distribution on a graph.Data is obtained by observing a flow only at the nodes -- what happens on the edges is unknown. Therefore the sample of passage times, i.e. the times it takes for the flow to stream between two neighbors, consists of right censored and uncensored observations where it sometimes is unknown which is which. For discrete passage time distributions, we show that the maximum likelihood (ML) estimate is strongly consistent under certain weak conditions. We also show that our propsed EM algorithm converges to the ML estimate if the sample size is sufficiently large and the starting value is sufficiently close to the true parameter. In a special case we show that it always converges. In the continuous case, we propose an EM algorithm for fitting phase-type distributions to data.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:umu-33779 |
| Date | January 2010 |
| Creators | Larson, Kajsa |
| Publisher | Umeå universitet, Institutionen för matematik och matematisk statistik, Umeå : Print & Media |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Doctoral thesis, comprehensive summary, info:eu-repo/semantics/doctoralThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | Doctoral thesis / Umeå University, Department of Mathematics, 1102-8300 |
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