Markov random fields and spatial smoothing in improving of forest inventory estimates

Markov random fields (MRF) are popular in image processing applications to describe spatial dependencies between image units. Here, we take a look at the theory and the models of MRFs with an application to improve forest inventory estimates. Typically, autocorrelation between study units is a nuisance in statistical inference, but we take an advantage of the dependencies to smooth noisy measurements by borrowing information from the neighbouring units. We build a stochastic spatial model, which we estimate with a Markov chain Monte Carlo simulation method. The smooth values are validated against another data set increasing our confidence that the estimates are more accurate than the originals.

A Probabilistic Approach to the Primary Visual Cortex

What can the statistical structure of natural images teach us about the human brain? Even though the visual cortex is one of the most studied parts of the brain, surprisingly little is known about how exactly images are processed to leave us with a coherent percept of the world around us, so we can recognize a friend or drive on a crowded street without any effort. By constructing probabilistic models of natural images, the goal of this thesis is to understand the structure of the stimulus that is the raison d etre for the visual system. Following the hypothesis that the optimal processing has to be matched to the structure of that stimulus, we attempt to derive computational principles, features that the visual system should compute, and properties that cells in the visual system should have. Starting from machine learning techniques such as principal component analysis and independent component analysis we construct a variety of sta- tistical models to discover structure in natural images that can be linked to receptive field properties of neurons in primary visual cortex such as simple and complex cells. We show that by representing images with phase invariant, complex cell-like units, a better statistical description of the vi- sual environment is obtained than with linear simple cell units, and that complex cell pooling can be learned by estimating both layers of a two-layer model of natural images. We investigate how a simplified model of the processing in the retina, where adaptation and contrast normalization take place, is connected to the nat- ural stimulus statistics. Analyzing the effect that retinal gain control has on later cortical processing, we propose a novel method to perform gain control in a data-driven way. Finally we show how models like those pre- sented here can be extended to capture whole visual scenes rather than just small image patches. By using a Markov random field approach we can model images of arbitrary size, while still being able to estimate the model parameters from the data.

Bayesian Inference for Retrospective Population Genetics Models Using Markov Chain Monte Carlo Methods

Genetics, the science of heredity and variation in living organisms, has a central role in medicine, in breeding crops and livestock, and in studying fundamental topics of biological sciences such as evolution and cell functioning. Currently the field of genetics is under a rapid development because of the recent advances in technologies by which molecular data can be obtained from living organisms. In order that most information from such data can be extracted, the analyses need to be carried out using statistical models that are tailored to take account of the particular genetic processes. In this thesis we formulate and analyze Bayesian models for genetic marker data of contemporary individuals. The major focus is on the modeling of the unobserved recent ancestry of the sampled individuals (say, for tens of generations or so), which is carried out by using explicit probabilistic reconstructions of the pedigree structures accompanied by the gene flows at the marker loci. For such a recent history, the recombination process is the major genetic force that shapes the genomes of the individuals, and it is included in the model by assuming that the recombination fractions between the adjacent markers are known. The posterior distribution of the unobserved history of the individuals is studied conditionally on the observed marker data by using a Markov chain Monte Carlo algorithm (MCMC). The example analyses consider estimation of the population structure, relatedness structure (both at the level of whole genomes as well as at each marker separately), and haplotype configurations. For situations where the pedigree structure is partially known, an algorithm to create an initial state for the MCMC algorithm is given. Furthermore, the thesis includes an extension of the model for the recent genetic history to situations where also a quantitative phenotype has been measured from the contemporary individuals. In that case the goal is to identify positions on the genome that affect the observed phenotypic values. This task is carried out within the Bayesian framework, where the number and the relative effects of the quantitative trait loci are treated as random variables whose posterior distribution is studied conditionally on the observed genetic and phenotypic data. In addition, the thesis contains an extension of a widely-used haplotyping method, the PHASE algorithm, to settings where genetic material from several individuals has been pooled together, and the allele frequencies of each pool are determined in a single genotyping.

The Networks of Learning in Technological Innovation : The Emergence of Collaboration Across Fields of Expertise

This study addresses four issues concerning technological product innovations. First, the nature of the very early phases or "embryonic stages" of technological innovation is addressed. Second, this study analyzes why and by what means people initiate innovation processes outside the technological community and the field of expertise of the established industry. In other words, this study addresses the initiation of innovation that occurs without the expertise of established organizations, such as technology firms, professional societies and research institutes operating in the technological field under consideration. Third, the significance of interorganizational learning processes for technological innovation is dealt with. Fourth, this consideration is supplemented by considering how network collaboration and learning change when formalized product development work and the commercialization of innovation advance. These issues are addressed through the empirical analysis of the following three product innovations: Benecol margarine, the Nordic Mobile Telephone system (NMT) and the ProWellness Diabetes Management System (PDMS). This study utilizes the theoretical insights of cultural-historical activity theory on the development of human activities and learning. Activity-theoretical conceptualizations are used in the critical assessment and advancement of the concept of networks of learning. This concept was originally proposed by the research group of organizational scientist Walter Powell. A network of learning refers to the interorganizational collaboration that pools resources, ideas and know-how without market-based or hierarchical relations. The concept of an activity system is used in defining the nodes of the networks of learning. Network collaboration and learning are analyzed with regard to the shared object of development work. According to this study, enduring dilemmas and tensions in activity explain the participants' motives for carrying out actions that lead to novel product concepts in the early phases of technological innovation. These actions comprise the initiation of development work outside the relevant fields of expertise and collaboration and learning across fields of expertise in the absence of market-based or hierarchical relations. These networks of learning are fragile and impermanent. This study suggests that the significance of networks of learning across fields of expertise becomes more and more crucial for innovation activities.

Beasts on Fields. Human-Wildlife Conflicts in Nature-Culture Borderlands

Human-wildlife conflicts are today an integral part of the rural development discourse. In this research, the main focus is on the spatial explanation which is not a very common approach in the reviewed literature. My research hypothesis is based on the assumption that human-wildlife conflicts occur when a wild animal crosses a perceived borderline between the nature and culture and enters into the realms of the other. The borderline between nature and culture marks a perceived division of spatial content in our senses of place. The animal subject that crosses this border becomes a subject out of place meaning that the animal is then spatially located in a space where it should not be or where it does not belong according to tradition, custom, rules, law, public opinion, prevailing discourse or some other criteria set by human beings. An appearance of a wild animal in a domesticated space brings an uncontrolled subject into that space where humans have previously commanded total control of all other natural elements. A wild animal out of place may also threaten the biosecurity of the place in question. I carried out a case study in the Liwale district in south-eastern Tanzania to test my hypothesis during June and July 2002. I also collected documents and carried out interviews in Dar es Salaam in 2003. I studied the human-wildlife conflicts in six rural villages, where a total of 183 persons participated in the village meetings. My research methods included semi-structured interviews, participatory mapping, questionnaire survey and Q- methodology. The rural communities in the Liwale district have a long-history of co-existing with wildlife and they still have traditional knowledge of wildlife management and hunting. Wildlife conservation through the establishment of game reserves during the colonial era has escalated human-wildlife conflicts in the Liwale district. This study shows that the villagers perceive some wild animals differently in their images of the African countryside than the district and regional level civil servants do. From the small scale subsistence farmers point of views, wild animals continue to challenge the separation of the wild (the forests) and the domestics spaces (the cultivated fields) by moving across the perceived borders in search of food and shelter. As a result, the farmers may loose their crops, livestock or even their own lives in the confrontations of wild animals. Human-wildlife conflicts in the Liwale district are manifold and cannot be explained simply on the basis of attitudes or perceived images of landscapes. However, the spatial explanation of these conflicts provides us some more understanding of why human-wildlife conflicts are so widely found across the world.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Bayesian fisheries stock assessment: integrating and updating knowledge

In this thesis the use of the Bayesian approach to statistical inference in fisheries stock assessment is studied. The work was conducted in collaboration of the Finnish Game and Fisheries Research Institute by using the problem of monitoring and prediction of the juvenile salmon population in the River Tornionjoki as an example application. The River Tornionjoki is the largest salmon river flowing into the Baltic Sea. This thesis tackles the issues of model formulation and model checking as well as computational problems related to Bayesian modelling in the context of fisheries stock assessment. Each article of the thesis provides a novel method either for extracting information from data obtained via a particular type of sampling system or for integrating the information about the fish stock from multiple sources in terms of a population dynamics model. Mark-recapture and removal sampling schemes and a random catch sampling method are covered for the estimation of the population size. In addition, a method for estimating the stock composition of a salmon catch based on DNA samples is also presented. For most of the articles, Markov chain Monte Carlo (MCMC) simulation has been used as a tool to approximate the posterior distribution. Problems arising from the sampling method are also briefly discussed and potential solutions for these problems are proposed. Special emphasis in the discussion is given to the philosophical foundation of the Bayesian approach in the context of fisheries stock assessment. It is argued that the role of subjective prior knowledge needed in practically all parts of a Bayesian model should be recognized and consequently fully utilised in the process of model formulation.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

On gravitational fields of stars in f(R) gravity theories

Einstein's general relativity is a classical theory of gravitation: it is a postulate on the coupling between the four-dimensional, continuos spacetime and the matter fields in the universe, and it yields their dynamical evolution. It is believed that general relativity must be replaced by a quantum theory of gravity at least at extremely high energies of the early universe and at regions of strong curvature of spacetime, cf. black holes. Various attempts to quantize gravity, including conceptually new models such as string theory, have suggested that modification to general relativity might show up even at lower energy scales. On the other hand, also the late time acceleration of the expansion of the universe, known as the dark energy problem, might originate from new gravitational physics. Thus, although there has been no direct experimental evidence contradicting general relativity so far - on the contrary, it has passed a variety of observational tests - it is a question worth asking, why should the effective theory of gravity be of the exact form of general relativity? If general relativity is modified, how do the predictions of the theory change? Furthermore, how far can we go with the changes before we are face with contradictions with the experiments? Along with the changes, could there be new phenomena, which we could measure to find hints of the form of the quantum theory of gravity? This thesis is on a class of modified gravity theories called f(R) models, and in particular on the effects of changing the theory of gravity on stellar solutions. It is discussed how experimental constraints from the measurements in the Solar System restrict the form of f(R) theories. Moreover, it is shown that models, which do not differ from general relativity at the weak field scale of the Solar System, can produce very different predictions for dense stars like neutron stars. Due to the nature of f(R) models, the role of independent connection of the spacetime is emphasized throughout the thesis.