Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.

Minimum error contrast enhancement

Contrast enhancement is an image processing technique where the objective is to preprocess the image so that relevant information can be either seen or further processed more reliably. These techniques are typically applied when the image itself or the device used for image reproduction provides poor visibility and distinguishability of different regions of interest inthe image. In most studies, the emphasis is on the visualization of image data,but this human observer biased goal often results to images which are not optimal for automated processing. The main contribution of this study is to express the contrast enhancement as a mapping from N-channel image data to 1-channel gray-level image, and to devise a projection method which results to an image with minimal error to the correct contrast image. The projection, the minimum-error contrast image, possess the optimal contrast between the regions of interest in the image. The method is based on estimation of the probability density distributions of the region values, and it employs Bayesian inference to establish the minimum error projection.

A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

Spectral Color Appearance Modeling

Kuvien laatu on tutkituimpia ja käytetyimpiä aiheita. Tässä työssä tarkastellaan värin laatu ja spektrikuvia. Työssä annetaan yleiskuva olemassa olevista pakattujen ja erillisten kuvien laadunarviointimenetelmistä painottaen näiden menetelmien soveltaminen spektrikuviin. Tässä työssä esitellään spektriväriulkomuotomalli värikuvien laadunarvioinnille. Malli sovelletaan spektrikuvista jäljennettyihin värikuviin. Malli pohjautuu sekä tilastolliseen spektrikuvamalliin, joka muodostaa yhteyden spektrikuvien ja valokuvien parametrien välille, että kuvan yleiseen ulkomuotoon. Värikuvien tilastollisten spektriparametrien ja fyysisten parametrien välinen yhteys on varmennettu tietokone-pohjaisella kuvamallinnuksella. Mallin ominaisuuksien pohjalta on kehitetty koekäyttöön tarkoitettu menetelmä värikuvien laadunarvioinnille. On kehitetty asiantuntija-pohjainen kyselymenetelmä ja sumea päättelyjärjestelmä värikuvien laadunarvioinnille. Tutkimus osoittaa, että spektri-väri –yhteys ja sumea päättelyjärjestelmä soveltuvat tehokkaasti värikuvien laadunarviointiin.

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.

Apteeraustuloksen mittarina käytetyn jakauma-asteen tilastollisista ominaisuuksista

Seloste artikkelista: Koskela, L., Sinha, B. K. & Nummi, T. 2007. Some aspects of the sampling distribution of the apportionment index and related inference. Silva Fennica 41 (4) : 699-715

Adessiivin funktion päättely paikallisessa kontekstissa

Summary: Determining the function of the Finnish adessive case through inference in a local context

Threat Simulation- The Function of Dreaming?

Dreaming is a pure form of phenomenality, created by the brain untouched by external stimulation or behavioral activity, yet including a full range of phenomenal contents. Thus, it has been suggested that the dreaming brain could be used as a model system in a biological research program on consciousness (Revonsuo, 2006). In the present thesis, the philosophical view of biological realism is accepted, and thus, dreaming is considered as a natural biological phenomenon, explainable in naturalistic terms. The major theoretical contribution of the present thesis is that it explores dreaming from a multidisciplinary perspective, integrating information from various fields of science, such as dream research, consciousness research, evolutionary psychology, and cognitive neuroscience. Further, it places dreaming into a multilevel framework, and investigates the constitutive, etiological, and contextual explanations for dreaming. Currently, the only theory offering a full multilevel explanation for dreaming, that is, a theory including constitutive, etiological, and contextual level explanations, is the Threat Simulation Theory (TST) (Revonsuo, 2000a; 2000b). The empirical significance of the present thesis lies in the tests conducted to test this specific theory put forth to explain the form, content, and biological function of dreaming. The first step in the empirical testing of the TST was to define exact criteria for what is a ‘threatening event’ in dreams, and then to develop a detailed and reliable content analysis scale with which it is possible to empirically explore and quantify threatening events in dreams. The second step was to seek answers to the following questions derived from the TST: How frequent threatening events are in dreams? What kind of qualities these events have? How threatening events in dreams relate to the most recently encoded or the most salient memory traces of threatening events experienced in waking life? What are the effects of exposure to severe waking life threat on dreams? The results reveal that threatening events are relatively frequent in dreams, and that the simulated threats are realistic. The most common threats include aggression, are targeted mainly against the dream self, and include simulations of relevant and appropriate defensive actions. Further, real threat experiences activate the threat simulation system in a unique manner, and dream content is modulated by the activation of long term episodic memory traces with highest negative saliency. To sum up, most of the predictions of the TST tested in this thesis received considerable support. The TST presents a strong argument that explains the specific design of dreams as threat simulations. The TST also offers a plausible explanation for why dreaming would have been selected for: because dreaming interacted with the environment in such a way that enhanced fitness of ancestral humans. By referring to a single threat simulation mechanism it furthermore manages to explain a wide variety of dream content data that already exists in the literature, and to predict the overall statistical patterns of threat content in different samples of dreams. The TST and the empirical tests conducted to test the theory are a prime example of what a multidisciplinary approach to mental phenomena can accomplish. Thus far, dreaming seems to have always resided in the periphery of science, never regarded worth to be studied by the mainstream. Nevertheless, when brought to the spotlight, the study of dreaming can greatly benefit from ideas in diverse branches of science. Vice versa, knowledge learned from the study of dreaming can be applied in various disciplines. The main contribution of the present thesis lies in putting dreaming back where it belongs, that is, into the spotlight in the cross-road of various disciplines.

Type II aromatic polyketide biosynthetic tailoring enzymes: diversity and adaptation in Streptomyces secondary metabolism.

Members of the bacterial genus Streptomyces are well known for their ability to produce an exceptionally wide selection of diverse secondary metabolites. These include natural bioactive chemical compounds which have potential applications in medicine, agriculture and other fields of commerce. The outstanding biosynthetic capacity derives from the characteristic genetic flexibility of Streptomyces secondary metabolism pathways: i) Clustering of the biosynthetic genes in chromosome regions redundant for vital primary functions, and ii) the presence of numerous genetic elements within these regions which facilitate DNA rearrangement and transfer between non-progeny species. Decades of intensive genetic research on the organization and function of the biosynthetic routes has led to a variety of molecular biology applications, which can be used to expand the diversity of compounds synthesized. These include techniques which, for example, allow modification and artificial construction of novel pathways, and enable gene-level detection of silent secondary metabolite clusters. Over the years the research has expanded to cover molecular-level analysis of the enzymes responsible for the individual catalytic reactions. In vitro studies of the enzymes provide a detailed insight into their catalytic functions, mechanisms, substrate specificities, interactions and stereochemical determinants. These are factors that are essential for the thorough understanding and rational design of novel biosynthetic routes. The current study is a part of a more extensive research project (Antibiotic Biosynthetic Enzymes; www.sci.utu.fi/projects/biokemia/abe), which focuses on the post-PKS tailoring enzymes involved in various type II aromatic polyketide biosynthetic pathways in Streptomyces bacteria. The initiative here was to investigate specific catalytic steps in anthracycline and angucycline biosynthesis through in vitro biochemical enzyme characterization and structural enzymology. The objectives were to elucidate detailed mechanisms and enzyme-level interactions which cannot be resolved by in vivo genetic studies alone. The first part of the experimental work concerns the homologous polyketide cyclases SnoaL and AknH. These catalyze the closure of the last carbon ring of the tetracyclic carbon frame common to all anthracycline-type compounds. The second part of the study primarily deals with tailoring enzymes PgaE (and its homolog CabE) and PgaM, which are responsible for a cascade of sequential modification reactions in angucycline biosynthesis. The results complemented earlier in vivo findings and confirmed the enzyme functions in vitro. Importantly, we were able to identify the amino acid -level determinants that influence AknH and SnoaL stereoselectivity and to determine the complex biosynthetic steps of the angucycline oxygenation cascade of PgaE and PgaM. In addition, the findings revealed interesting cases of enzyme-level adaptation, as some of the catalytic mechanisms did not coincide with those described for characterised homologs or enzymes of known function. Specifically, SnoaL and AknH were shown to employ a novel acid-base mechanism for aldol condenzation, whereas the hydroxylation reaction catalysed by PgaM involved unexpected oxygen chemistry. Owing to a gene-level fusion of two ancestral reading frames, PgaM was also shown to adopt an unusual quaternary sturucture, a non-covalent fusion complex of two alternative forms of the protein. Furthermore, the work highlighted some common themes encountered in polyketide biosynthetic pathways such as enzyme substrate specificity and intermediate reactivity. These are discussed in the final chapters of the work.

Rouhintasorvauksen säätöjärjestelmä

Tässä työssä kuvataan menetelmä, jonka avulla on mahdollista sorvausprosessista mitattujen signaalien perusteella muokata lastuamisprosessin parametreja siten, että prosessissa mahdollisesti esiintyvät ongelmatilanteet korjataan. Työ on tehty osana Feedchip-tutkimushanketta ja tukeutuu tutkimushankkeessa aiemmin tehtyyn työhön vaadittavien korjaustoimenpiteiden, signaaleja mittaavien antureiden instrumentoinnin sekä alustavan ongelmatilanteiden ominaispiirteiden signaaleista tunnistuksen osalta. Tämä työ keskittyy esittelemään toiminnot, joiden avulla aiemmat tulokset voidaan koota yhteen kokonaisuuteen. Järjestelmän toiminta edellyttää sen osien toiminnan korkean tason koordinointia. Lisäksi määritellään päättelyjärjestelmä, joka kykenee mitatuista arvoista tunnistettujen ongelmatilanteiden esiintymisasteiden perusteella määrittämään tarvittavat toimenpiteet ongelmatilanteiden poistamiseksi. Kandidaatintyön rinnalla toteutetaan ohjelmisto Lappeenrannan teknillisen yliopiston konepajatekniikan laboratorion sorvausjärjestelmän yhteyteen rakennetun prototyyppilaitteiston ohjaamiseksi.

Statistical Analysis of an SEIR Epidemic Model

This thesis was focussed on statistical analysis methods and proposes the use of Bayesian inference to extract information contained in experimental data by estimating Ebola model parameters. The model is a system of differential equations expressing the behavior and dynamics of Ebola. Two sets of data (onset and death data) were both used to estimate parameters, which has not been done by previous researchers in (Chowell, 2004). To be able to use both data, a new version of the model has been built. Model parameters have been estimated and then used to calculate the basic reproduction number and to study the disease-free equilibrium. Estimates of the parameters were useful to determine how well the model fits the data and how good estimates were, in terms of the information they provided about the possible relationship between variables. The solution showed that Ebola model fits the observed onset data at 98.95% and the observed death data at 93.6%. Since Bayesian inference can not be performed analytically, the Markov chain Monte Carlo approach has been used to generate samples from the posterior distribution over parameters. Samples have been used to check the accuracy of the model and other characteristics of the target posteriors.

A Diagnostic view of the Genetics of CASADIL

Cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL, OMIM #125310) is an inherited vascular disease. The main symptoms include migraineous headache, recurrent strokes and progressive cognitive impairment. CADASIL is caused by mutations in the NOTCH3 gene which result in degeneration of vascular smooth muscle cells, arteriolar stenosis and impaired cerebral blood flow. The aims of this study were assessment of the genetic background of Finnish and Swedish CADASIL patients, analysis of genetic and environmental factors that may influence the phenotype, and identification of the optimal diagnostic strategy. The majority of Finnish CADASIL patients carry the p.Arg133Cys mutation. Haplotype analysis of 18 families revealed a region of linkage disequilibrium around the NOTCH3 locus, which is evidence for a founder effect and a common ancestral mutation. Despite the same mutational background, the clinical course of CADASIL is highly variable between and even within families. The association of several genetic factors with the phenotypic variation was investigated in 120 CADASIL patients. Apolipoprotein E allele 4 was associated with earlier occurrence of strokes, especially in younger patients. Study of a pair of monozygotic twins with CADASIL revealed environmental factors which may influence the phenotype, i.e. smoking, statin medication and physical activity. Knowledge of these factors is useful, since life-style choices may influence the disease progression. The clinical CADASIL diagnosis can be confirmed by detection of either the NOTCH3 mutation or granular osmiophilic material by electron microscopy in skin biopsy, although the sensitivity estimates have been contradictory. Comparison of these two methods in a group of 131 diagnostic cases from Finland, Sweden and France demonstrated that both methods are highly sensitive and reliable.

The Importance of Semantics: Visual World Studies on Drawing Inferences and Resolving Anaphors

The present thesis investigated the importance of semantics in generating inferences during discourse processing. Three aspects of semantics, gender stereotypes, implicit causality information and proto-role properties, were used to investigate whether semantics is activated elaboratively during discourse comprehension and what its relative importance is in backward inferencing compared to discourse/structural cues. Visual world eye-tracking studies revealed that semantics plays an important role in both backward and forward inferencing: Gender stereotypes and implicit causality information is activated elaboratively during online discourse comprehension. Moreover, gender stereotypes, implicit causality and proto-role properties of verbs are all used in backward inferencing. Importantly, the studies demonstrated that semantic cues are weighed against discourse/structural cues. When the structural cues consist of a combination of cues that have been independently shown to be important in backward inferencing, semantic effects may be masked, whereas when the structural cues consist of a combination of fewer prominent cues, semantics can have an earlier effect than structural factors in pronoun resolution. In addition, the type of inference matters, too: During anaphoric inferencing semantics has a prominent role, while discourse/structural salience attains more prominence during non-anaphoric inferencing. Finally, semantics exhibits a strong role in inviting new inferences to revise earlier made inferences even in the case the additional inference is not needed to establish coherence in discourse. The findings are generally in line with the Mental Model approaches. Two extended model versions are presented that incorporate the current findings into the earlier literature. These models allow both forward and backward inferencing to occur at any given moment during the course of processing; they also allow semantic and discourse/structural cues to contribute to both of these processes. However, while the Mental Model 1 does not assume interactions between semantic and discourse/structural factors in forward inferencing, the Mental Model 2 does assume such a link.

Ratiomuuttujat ja näennäinen korrelaatio

Eri tieteenalojen tutkijat ovat kiistelleet jo yli vuosisadan ajan ratiomuodossa olevien muuttujien käytön vaikutuksista korrelaatio- ja regressioanalyysien tuloksiin ja niiden oikeaan tulkintaan. Strategiatutkimuksen piirissä aiheeseen ei ole kuitenkaan kiinnitetty suuresti huomiota. Tämä on yllättävää, sillä ratiomuuttujat ovat hyvin yleisesti käytettyjä empiirisen strategiatutkimuksen piirissä. Tässä työssä luodaan katsaus ratiomuuttujien ympärillä käytyyn debattiin. Lisäksi selvitetään artikkelikatsauksen avulla niiden käytön yleisyyttä nykypäivän strategiatutkimuksessa. Työssä tutkitaan Monte Carlo –simulaatioiden avulla ratiomuuttujien ominaisuuksien vaikutuksia korrelaatio- ja regressioanalyysin tuloksiin erityisesti yhteisen nimittäjän tapauksissa.