Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.

Automated, adaptive methods for forest inventory

Forest inventories are used to estimate forest characteristics and the condition of forest for many different applications: operational tree logging for forest industry, forest health state estimation, carbon balance estimation, land-cover and land use analysis in order to avoid forest degradation etc. Recent inventory methods are strongly based on remote sensing data combined with field sample measurements, which are used to define estimates covering the whole area of interest. Remote sensing data from satellites, aerial photographs or aerial laser scannings are used, depending on the scale of inventory. To be applicable in operational use, forest inventory methods need to be easily adjusted to local conditions of the study area at hand. All the data handling and parameter tuning should be objective and automated as much as possible. The methods also need to be robust when applied to different forest types. Since there generally are no extensive direct physical models connecting the remote sensing data from different sources to the forest parameters that are estimated, mathematical estimation models are of "black-box" type, connecting the independent auxiliary data to dependent response data with linear or nonlinear arbitrary models. To avoid redundant complexity and over-fitting of the model, which is based on up to hundreds of possibly collinear variables extracted from the auxiliary data, variable selection is needed. To connect the auxiliary data to the inventory parameters that are estimated, field work must be performed. In larger study areas with dense forests, field work is expensive, and should therefore be minimized. To get cost-efficient inventories, field work could partly be replaced with information from formerly measured sites, databases. The work in this thesis is devoted to the development of automated, adaptive computation methods for aerial forest inventory. The mathematical model parameter definition steps are automated, and the cost-efficiency is improved by setting up a procedure that utilizes databases in the estimation of new area characteristics.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Adaptive Dynamics of Resource Specialization

Ecological specialization in resource utilization has various facades ranging from nutritional resources via host use of parasites or phytophagous insects to local adaptation in different habitats. Therefore, the evolution of specialization affects the evolution of most other traits, which makes it one of the core issues in the theory of evolution. Hence, the evolution of specialization has gained enormous amounts of research interest, starting already from Darwin’s Origin of species in 1859. Vast majority of the theoretical studies has, however, focused on the mathematically most simple case with well-mixed populations and equilibrium dynamics. This thesis explores the possibilities to extend the evolutionary analysis of resource usage to spatially heterogeneous metapopulation models and to models with non-equilibrium dynamics. These extensions are enabled by the recent advances in the field of adaptive dynamics, which allows for a mechanistic derivation of the invasion-fitness function based on the ecological dynamics. In the evolutionary analyses, special focus is set to the case with two substitutable renewable resources. In this case, the most striking questions are, whether a generalist species is able to coexist with the two specialist species, and can such trimorphic coexistence be attained through natural selection starting from a monomorphic population. This is shown possible both due to spatial heterogeneity and due to non-equilibrium dynamics. In addition, it is shown that chaotic dynamics may sometimes inflict evolutionary suicide or cyclic evolutionary dynamics. Moreover, the relations between various ecological parameters and evolutionary dynamics are investigated. Especially, the relation between specialization and dispersal propensity turns out to be counter-intuitively non-monotonous. This observation served as inspiration to the analysis of joint evolution of dispersal and specialization, which may provide the most natural explanation to the observed coexistence of specialist and generalist species.

Estimates of genetic parameters of trotting performance traits for repeated annual records

Selostus: Ravihevosten jalostettavia ominaisuuksia kuvaavien kilpailumittojen perinnölliset tunnusluvut

Genetic parameters for growth traits in pigs estimated using third degree polynomial functions

Selostus: Sian kasvuominaisuuksien perinnölliset tunnusluvut arvioituna kolmannen asteen polynomifunktion avulla

A method for using random parameters in analyzing permanent sample plots

Summary

Estimation of genetic parameters for test-day milk production at different stages of lactation of Finnish Ayrshire heifers

Selostus: Ayrshire-ensikoiden koelypsykohtaisen maidontuotannon perinnölliset tunnusluvut laktaation eri vaiheissa

Progeny Trial Estimates of Genetic Parameters for Growth and Quality Traits in Scots Pine

Summary

Effects of group size and early handling on some behavioural and physiological welfare parameters in farmed blue foxes

Selostus: Ryhmäkoon ja varhaisen käsittelyn vaikutus tarhattujen sinikettujen hyvinvointiin

Effects of group size and space allocation on physiological, behavioural and production-related welfare parameters in farmed silver fox cubs

Selostus: Ryhmäkoon ja käytössä olevan tilan vaikutus tarhattujen hopeakettupentujen hyvinvointiin

Temporal trends in chemical parameters of upland forest soils in southern Finland

Abstract

Inventory of sparse forest populations using adaptive cluster sampling

Abstract

Use of individual race results in the estimation of genetic parameters of trotting performance for Finnhorse and Standardbred trotters

Selostus: Ravikilpailumenestysmittojen periytymisasteet ja toistumiskertoimet kilpailukohtaisten tulosten perusteella