Stochastic Filtering

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Effects of environmental variation on ecological and evolutionary dynamics

Environmental variation is a fact of life for all the species on earth: for any population of any particular species, the local environmental conditions are liable to vary in both time and space. In today's world, anthropogenic activity is causing habitat loss and fragmentation for many species, which may profoundly alter the characteristics of environmental variation in remaining habitat. Previous research indicates that, as habitat is lost, the spatial configuration of remaining habitat will increasingly affect the dynamics by which populations are governed. Through the use of mathematical models, this thesis asks how environmental variation interacts with species properties to influence population dynamics, local adaptation, and dispersal evolution. More specifically, we couple continuous-time continuous-space stochastic population dynamic models to landscape models. We manipulate environmental variation via parameters such as mean patch size, patch density, and patch longevity. Among other findings, we show that a mixture of high and low quality habitat is commonly better for a population than uniformly mediocre habitat. This conclusion is justified by purely ecological arguments, yet the positive effects of landscape heterogeneity may be enhanced further by local adaptation, and by the evolution of short-ranged dispersal. The predicted evolutionary responses to environmental variation are complex, however, since they involve numerous conflicting factors. We discuss why the species that have high levels of local adaptation within their ranges may not be the same species that benefit from local adaptation during range expansion. We show how habitat loss can lead to either increased or decreased selection for dispersal depending on the type of habitat and the manner in which it is lost. To study the models, we develop a recent analytical method, Perturbation expansion, to enable the incorporation of environmental variation. Within this context, we use two methods to address evolutionary dynamics: Adaptive dynamics, which assumes mutations occur infrequently so that the ecological and evolutionary timescales can be separated, and via Genotype distributions, which assume mutations are more frequent. The two approaches generally lead to similar predictions yet, exceptionally, we show how the evolutionary response of dispersal behaviour to habitat turnover may qualitatively depend on the mutation rate.

The range expansion of the European map butterfly in Finland

Climate change will influence the living conditions of all life on Earth. For some species the change in the environmental conditions that has occurred so far has already increased the risk of extinction, and the extinction risk is predicted to increase for large numbers of species in the future. Some species may have time to adapt to the changing environmental conditions, but the rate and magnitude of the change are too great to allow many species to survive via evolutionary changes. Species responses to climate change have been documented for some decades. Some groups of species, like many insects, respond readily to changes in temperature conditions and have shifted their distributions northwards to new climatically suitable regions. Such range shifts have been well documented especially in temperate zones. In this context, butterflies have been studied more than any other group of species, partly for the reason that their past geographical ranges are well documented, which facilitates species-climate modelling and other analyses. The aim of the modelling studies is to examine to what extent shifts in species distributions can be explained by climatic and other factors. Models can also be used to predict the future distributions of species. In this thesis, I have studied the response to climate change of one species of butterfly within one geographically restricted area. The study species, the European map butterfly (Araschnia levana), has expanded rapidly northwards in Finland during the last two decades. I used statistical and dynamic modelling approaches in combination with field studies to analyse the effects of climate warming and landscape structure on the expansion. I studied possible role of molecular variation in phosphoglucose isomerase (PGI), a glycolytic enzyme affecting flight metabolism and thereby flight performance, in the observed expansion of the map butterfly at two separate expansion fronts in Finland. The expansion rate of the map butterfly was shown to be correlated with the frequency of warmer than average summers during the study period. The result is in line with the greater probability of occurrence of the second generation during warm summers and previous results on this species showing greater mobility of the second than first generation individuals. The results of a field study in this thesis indicated low mobility of the first generation butterflies. Climatic variables alone were not sufficient to explain the observed expansion in Finland. There are also problems in transferring the climate model to new regions from the ones from which data were available to construct the model. The climate model predicted a wider distribution in the south-western part of Finland than what has been observed. Dynamic modelling of the expansion in response to landscape structure suggested that habitat and landscape structure influence the rate of expansion. In southern Finland the landscape structure may have slowed down the expansion rate. The results on PGI suggested that allelic variation in this enzyme may influence flight performance and thereby the rate of expansion. Genetic differences of the populations at the two expansion fronts may explain at least partly the observed differences in the rate of expansion. Individuals with the genotype associated with high flight metabolic rate were most frequent in eastern Finland, where the rate of range expansion has been highest.

Acceleration of the Cosmological Expansion as an Effect of Inhomogeneities

The cosmological observations of light from type Ia supernovae, the cosmic microwave background and the galaxy distribution seem to indicate that the expansion of the universe has accelerated during the latter half of its age. Within standard cosmology, this is ascribed to dark energy, a uniform fluid with large negative pressure that gives rise to repulsive gravity but also entails serious theoretical problems. Understanding the physical origin of the perceived accelerated expansion has been described as one of the greatest challenges in theoretical physics today. In this thesis, we discuss the possibility that, instead of dark energy, the acceleration would be caused by an effect of the nonlinear structure formation on light, ignored in the standard cosmology. A physical interpretation of the effect goes as follows: due to the clustering of the initially smooth matter with time as filaments of opaque galaxies, the regions where the detectable light travels get emptier and emptier relative to the average. As the developing voids begin to expand the faster the lower their matter density becomes, the expansion can then accelerate along our line of sight without local acceleration, potentially obviating the need for the mysterious dark energy. In addition to offering a natural physical interpretation to the acceleration, we have further shown that an inhomogeneous model is able to match the main cosmological observations without dark energy, resulting in a concordant picture of the universe with 90% dark matter, 10% baryonic matter and 15 billion years as the age of the universe. The model also provides a smart solution to the coincidence problem: if induced by the voids, the onset of the perceived acceleration naturally coincides with the formation of the voids. Additional future tests include quantitative predictions for angular deviations and a theoretical derivation of the model to reduce the required phenomenology. A spin-off of the research is a physical classification of the cosmic inhomogeneities according to how they could induce accelerated expansion along our line of sight. We have identified three physically distinct mechanisms: global acceleration due to spatial variations in the expansion rate, faster local expansion rate due to a large local void and biased light propagation through voids that expand faster than the average. A general conclusion is that the physical properties crucial to account for the perceived acceleration are the growth of the inhomogeneities and the inhomogeneities in the expansion rate. The existence of these properties in the real universe is supported by both observational data and theoretical calculations. However, better data and more sophisticated theoretical models are required to vindicate or disprove the conjecture that the inhomogeneities are responsible for the acceleration.

Agricultural expansion and climate change in the Taita Hills, Kenya: an assessment of potential environmental impacts

The indigenous cloud forests in the Taita Hills have suffered substantial degradation for several centuries due to agricultural expansion. Currently, only 1% of the original forested area remains preserved in this region. Furthermore, climate change imposes an imminent threat for local economy and environmental sustainability. In such circumstances, elaborating tools to conciliate socioeconomic growth and natural resources conservation is an enormous challenge. This dissertation tackles essential aspects for understanding the ongoing agricultural activities in the Taita Hills and their potential environmental consequences in the future. Initially, alternative methods were designed to improve our understanding of the ongoing agricultural activities. Namely, methods for agricultural survey planning and to estimate evapotranspiration were evaluated, taking into account a number of limitations regarding data and resources availability. Next, this dissertation evaluates how upcoming agricultural expansion, together with climate change, will affect the natural resources in the Taita Hills up to the year 2030. The driving forces of agricultural expansion in the region were identified as aiming to delineate future landscape scenarios and evaluate potential impacts from the soil and water conservation point of view. In order to investigate these issues and answer the research questions, this dissertation combined state of the art modelling tools with renowned statistical methods. The results indicate that, if current trends persist, agricultural areas will occupy roughly 60% of the study area by 2030. Although the simulated land use changes will certainly increase soil erosion figures, new croplands are likely to come up predominantly in the lowlands, which comprise areas with lower soil erosion potential. By 2030, rainfall erosivity is likely to increase during April and November due to climate change. Finally, this thesis addressed the potential impacts of agricultural expansion and climate changes on Irrigation Water Requirements (IWR), which is considered another major issue in the context of the relations between land use and climate. Although the simulations indicate that climate change will likely increase annual volumes of rainfall during the following decades, IWR will continue to increase due to agricultural expansion. By 2030, new cropland areas may cause an increase of approximately 40% in the annual volume of water necessary for irrigation.

Pricing Index Options with Stochastic Volatility

The objective of this paper is to investigate the pricing accuracy under stochastic volatility where the volatility follows a square root process. The theoretical prices are compared with market price data (the German DAX index options market) by using two different techniques of parameter estimation, the method of moments and implicit estimation by inversion. Standard Black & Scholes pricing is used as a benchmark. The results indicate that the stochastic volatility model with parameters estimated by inversion using the available prices on the preceding day, is the most accurate pricing method of the three in this study and can be considered satisfactory. However, as the same model with parameters estimated using a rolling window (the method of moments) proved to be inferior to the benchmark, the importance of stable and correct estimation of the parameters is evident.

Trafficking in human beings and Foucauldian biopower : A case study in the expansion of the human rights phenomenon

Trafficking in human beings has become one of the most talked about criminal concerns of the 21st century. But this is not all that it has become. Trafficking has also been declared as one of the most pressing human rights issues of our time. In this sense, it has become a part of the expansion of the human rights phenomenon. Although it is easy to see that the crime of trafficking violates several of the human rights of its victims, it is still, in its essence, a fairly conventional although particularly heinous and often transnational crime, consisting of acts between private actors, and lacking, therefore, the vertical effect associated traditionally with human rights violations. This thesis asks, then, why, and how, has the anti-trafficking campaign been translated in human rights language. And even more fundamentally: in light of the critical, theoretical studies surrounding the expansion of the human rights phenomenon, especially that of Costas Douzinas, who has declared that we have come to the end of human rights as a consequence of the expansion and bureaucratization of the phenomenon, can human rights actually bring salvation to the victims of trafficking? The thesis demonstrates that the translation process of the anti-trafficking campaign into human rights language has been a complicated process involving various actors, including scholars, feminist NGOs, local activists and global human rights NGOs. It has also been driven by a complicated web of interests, the most prevalent one the sincere will to help the victims having become entangled with other aims, such as political, economical, and structural goals. As a consequence of its fragmented background, the human rights approach to trafficking seeks still its final form, consisting of several different claims. After an assessment of these claims from a legal perspective, this thesis concludes that the approach is most relevant regarding the mistreatment of victims of trafficking in the hands of state authorities. It seems to be quite common that authorities have trouble identifying the victims of trafficking, which means that the rights granted to themin international and national documents are not realized in practice, but victims of trafficking are systematically deported as illegal immigrants. It is argued that in order to understand the measures of the authorities, and to assess the usefulness of human rights, it is necessary to adopt a Foucauldian perspective and to observe the measures as biopolitical defence mechanisms. From a biopolitical perspective, the victims of trafficking can be seen as a threat to the population a threat that must be eliminated either by assimilating them to the main population with the help of disciplinary techniques, or by excluding them completely from the society. This biopolitical aim is accomplished through an impenetrable net of seemingly insignificant practices and discourses that not even the participants are aware of. As a result of these practices and discourses, trafficking victims only very few of fit the myth of the perfect victim, produced by biopolitical discourses become invisible and therefore subject to deportation as (risky) illegal immigrants, turning them into bare life in the Agambenian sense, represented by the homo sacer, who cannot be sacrificed, yet does not enjoy the protection of the society and its laws. It is argued, following Jacques Rancière and Slavoj i ek, that human rights can, through their universality and formal equality, provide bare life the tools to formulate political claims and therefore utilize their politicization through their exclusion to return to the sphere of power and politics. Even though human rights have inevitably become entangled with biopolitical practices, they are still perhaps the most efficient way to challenge biopower. Human rights have not, therefore, become useless for the victims of trafficking, but they must be conceived as a universal tool to formulate political claims and challenge power .In the case of trafficking this means that human rights must be utilized to constantly renegotiate the borders of the problematic concept of victim of trafficking created by international instruments, policies and discourses, including those that are sincerely aimed to provide help for the victims.