Discovering hidden structures in molecular data using a Bayesian partition model approach

Advancements in the analysis techniques have led to a rapid accumulation of biological data in databases. Such data often are in the form of sequences of observations, examples including DNA sequences and amino acid sequences of proteins. The scale and quality of the data give promises of answering various biologically relevant questions in more detail than what has been possible before. For example, one may wish to identify areas in an amino acid sequence, which are important for the function of the corresponding protein, or investigate how characteristics on the level of DNA sequence affect the adaptation of a bacterial species to its environment. Many of the interesting questions are intimately associated with the understanding of the evolutionary relationships among the items under consideration. The aim of this work is to develop novel statistical models and computational techniques to meet with the challenge of deriving meaning from the increasing amounts of data. Our main concern is on modeling the evolutionary relationships based on the observed molecular data. We operate within a Bayesian statistical framework, which allows a probabilistic quantification of the uncertainties related to a particular solution. As the basis of our modeling approach we utilize a partition model, which is used to describe the structure of data by appropriately dividing the data items into clusters of related items. Generalizations and modifications of the partition model are developed and applied to various problems. Large-scale data sets provide also a computational challenge. The models used to describe the data must be realistic enough to capture the essential features of the current modeling task but, at the same time, simple enough to make it possible to carry out the inference in practice. The partition model fulfills these two requirements. The problem-specific features can be taken into account by modifying the prior probability distributions of the model parameters. The computational efficiency stems from the ability to integrate out the parameters of the partition model analytically, which enables the use of efficient stochastic search algorithms.

Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Data-assimilaatiomenetelmistä ja niiden soveltamisesta ROSE-kemiakuljetusmalllin

Data-assimilaatio on tekniikka, jossa havaintoja yhdistetään dynaamisiin numeerisiin malleihin tarkoituksena tuottaa optimaalista esitystä esimerkiksi ilmankehän muuttuvasta tilasta. Data-assimilaatiota käytetään muun muassa operaativisessa sään ennustamisessa. Tässä työssä esitellään eri data-assimilaatiomenetelmiä, jotka jakautuvat pääpiirteittäin Kalmanin suotimiin ja variaatioanaalisiin menetelmiin. Lisäksi esitellään erilaisia data-assimilaatiossa tarvittavia apuvälineitä kuten optimointimenetelmiä. Eri data-assimilaatiomenetelmien toimintaa havainnollistetaan esimerkkien avulla. Tässä työssä data-assimilaatiota sovelletaan muun muassa Lorenz95-malliin. Käytännön data-assimilaatio-ongelmana on GOMOS-instrumentista saatavan otsonin assimiloiminen käyttäen hyväksi ROSE-kemiakuljetusmallia.

Making the most of spatial information in health: A tutorial in Bayesian disease mapping for areal data

Disease maps are effective tools for explaining and predicting patterns of disease outcomes across geographical space, identifying areas of potentially elevated risk, and formulating and validating aetiological hypotheses for a disease. Bayesian models have become a standard approach to disease mapping in recent decades. This article aims to provide a basic understanding of the key concepts involved in Bayesian disease mapping methods for areal data. It is anticipated that this will help in interpretation of published maps, and provide a useful starting point for anyone interested in running disease mapping methods for areal data. The article provides detailed motivation and descriptions on disease mapping methods by explaining the concepts, defining the technical terms, and illustrating the utility of disease mapping for epidemiological research by demonstrating various ways of visualising model outputs using a case study. The target audience includes spatial scientists in health and other fields, policy or decision makers, health geographers, spatial analysts, public health professionals, and epidemiologists.