Paradigms in Statistical Inference for Finite Populations; Up to the 1950s

Modern sample surveys started to spread after statistician at the U.S. Bureau of the Census in the 1940s had developed a sampling design for the Current Population Survey (CPS). A significant factor was also that digital computers became available for statisticians. In the beginning of 1950s, the theory was documented in textbooks on survey sampling. This thesis is about the development of the statistical inference for sample surveys. For the first time the idea of statistical inference was enunciated by a French scientist, P. S. Laplace. In 1781, he published a plan for a partial investigation in which he determined the sample size needed to reach the desired accuracy in estimation. The plan was based on Laplace s Principle of Inverse Probability and on his derivation of the Central Limit Theorem. They were published in a memoir in 1774 which is one of the origins of statistical inference. Laplace s inference model was based on Bernoulli trials and binominal probabilities. He assumed that populations were changing constantly. It was depicted by assuming a priori distributions for parameters. Laplace s inference model dominated statistical thinking for a century. Sample selection in Laplace s investigations was purposive. In 1894 in the International Statistical Institute meeting, Norwegian Anders Kiaer presented the idea of the Representative Method to draw samples. Its idea was that the sample would be a miniature of the population. It is still prevailing. The virtues of random sampling were known but practical problems of sample selection and data collection hindered its use. Arhtur Bowley realized the potentials of Kiaer s method and in the beginning of the 20th century carried out several surveys in the UK. He also developed the theory of statistical inference for finite populations. It was based on Laplace s inference model. R. A. Fisher contributions in the 1920 s constitute a watershed in the statistical science He revolutionized the theory of statistics. In addition, he introduced a new statistical inference model which is still the prevailing paradigm. The essential idea is to draw repeatedly samples from the same population and the assumption that population parameters are constants. Fisher s theory did not include a priori probabilities. Jerzy Neyman adopted Fisher s inference model and applied it to finite populations with the difference that Neyman s inference model does not include any assumptions of the distributions of the study variables. Applying Fisher s fiducial argument he developed the theory for confidence intervals. Neyman s last contribution to survey sampling presented a theory for double sampling. This gave the central idea for statisticians at the U.S. Census Bureau to develop the complex survey design for the CPS. Important criterion was to have a method in which the costs of data collection were acceptable, and which provided approximately equal interviewer workloads, besides sufficient accuracy in estimation.

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.

Designing a blended learning model for primary school language learning

In Finland, there is a desperate need for flexible, reliable and functional multi-e-learning settings for pupils aged 11-13. Southern Finland has several ongoing e-learning projects, but none that develop a multiple setting, with learning and teaching occurring between more than two schools. In 2006, internet connections were not broadband and data transfer was mainly audio data. Connections and technical problems occurred, which were an obstacle to multi-e-learning. Internet connections today enable web-based learning in major parts of
Lapland and by 2015, broadband will reach even the remotest villages up north. Therefore, it is important to research the possibilities of multi-e-learning and to build collaborative, learner-centred, versatile network models for primary school-aged pupils. The resulting model will facilitate distance learning to extend education to rural, sparsely populated areas, and it will give a model of using mobile devices in language portfolios. This will promote regional equality and prevent exclusion. Working with portfolios provides the opportunity to develop mobility from a pedagogical point of view. It is important to study the pros and cons of mobile devices in producing artefacts on portfolios in e-learning and language learning settings.
The current study represents a design-based research approach. The design research approach includes two important aspects concerning the current research: ‘a teacher as researcher’ aspect, which means there is the possibility to be strongly involved in developing processes and an obstacle-aspect, which means that problems while developing, are seen as a
promoter in evolving the designed model, as apposed to negative results.

Designing a blended learning model for primary school language learning

In Finland, there is a desperate need for flexible, reliable and functional multi-e-learning settings for pupils aged 11-13. Southern Finland has several ongoing e-learning projects, but none that develop a multiple setting, with learning and teaching occurring between more than two schools. In 2006, internet connections were not broadband and data transfer was mainly audio data. Connections and technical problems occurred, which were an obstacle to multi-e-learning. Internet connections today enable web-based learning in major parts of Lapland and by 2015, broadband will reach even the remotest villages up north. Therefore, it is important to research the possibilities of multi-e-learning and to build collaborative, learner-centred, versatile network models for primary school-aged pupils. The resulting model will facilitate distance learning to extend education to rural, sparsely populated areas, and it will give a model of using mobile devices in language portfolios. This will promote regional equality and prevent exclusion. Working with portfolios provides the opportunity to develop mobility from a pedagogical point of view. It is important to study the pros and cons of mobile devices in producing artefacts on portfolios in e-learning and language learning settings. The current study represents a design-based research approach. The design research approach includes two important aspects concerning the current research: ‘a teacher as researcher’ aspect, which means there is the possibility to be strongly involved in developing processes and an obstacle-aspect, which means that problems while developing, are seen as a promoter in evolving the designed model, as apposed to negative results.

Language universals and linguistic complexity : Three case studies in core argument marking

In this dissertation I study language complexity from a typological perspective. Since the structuralist era, it has been assumed that local complexity differences in languages are balanced out in cross-linguistic comparisons and that complexity is not affected by the geopolitical or sociocultural aspects of the speech community. However, these assumptions have seldom been studied systematically from a typological point of view. My objective is to define complexity so that it is possible to compare it across languages and to approach its variation with the methods of quantitative typology. My main empirical research questions are: i) does language complexity vary in any systematic way in local domains, and ii) can language complexity be affected by the geographical or social environment? These questions are studied in three articles, whose findings are summarized in the introduction to the dissertation. In order to enable cross-language comparison, I measure complexity as the description length of the regularities in an entity; I separate it from difficulty, focus on local instead of global complexity, and break it up into different types. This approach helps avoid the problems that plagued earlier metrics of language complexity. My approach to grammar is functional-typological in nature, and the theoretical framework is basic linguistic theory. I delimit the empirical research functionally to the marking of core arguments (the basic participants in the sentence). I assess the distributions of complexity in this domain with multifactorial statistical methods and use different sampling strategies, implementing, for instance, the Greenbergian view of universals as diachronic laws of type preference. My data come from large and balanced samples (up to approximately 850 languages), drawn mainly from reference grammars. The results suggest that various significant trends occur in the marking of core arguments in regard to complexity and that complexity in this domain correlates with population size. These results provide evidence that linguistic patterns interact among themselves in terms of complexity, that language structure adapts to the social environment, and that there may be cognitive mechanisms that limit complexity locally. My approach to complexity and language universals can therefore be successfully applied to empirical data and may serve as a model for further research in these areas.

Society by Numbers : Studies on Model-Based Explanations in the Social Sciences

The aim of this dissertation is to provide conceptual tools for the social scientist for clarifying, evaluating and comparing explanations of social phenomena based on formal mathematical models. The focus is on relatively simple theoretical models and simulations, not statistical models. These studies apply a theory of explanation according to which explanation is about tracing objective relations of dependence, knowledge of which enables answers to contrastive why and how-questions. This theory is developed further by delineating criteria for evaluating competing explanations and by applying the theory to social scientific modelling practices and to the key concepts of equilibrium and mechanism. The dissertation is comprised of an introductory essay and six published original research articles. The main theses about model-based explanations in the social sciences argued for in the articles are the following. 1) The concept of explanatory power, often used to argue for the superiority of one explanation over another, compasses five dimensions which are partially independent and involve some systematic trade-offs. 2) All equilibrium explanations do not causally explain the obtaining of the end equilibrium state with the multiple possible initial states. Instead, they often constitutively explain the macro property of the system with the micro properties of the parts (together with their organization). 3) There is an important ambivalence in the concept mechanism used in many model-based explanations and this difference corresponds to a difference between two alternative research heuristics. 4) Whether unrealistic assumptions in a model (such as a rational choice model) are detrimental to an explanation provided by the model depends on whether the representation of the explanatory dependency in the model is itself dependent on the particular unrealistic assumptions. Thus evaluating whether a literally false assumption in a model is problematic requires specifying exactly what is supposed to be explained and by what. 5) The question of whether an explanatory relationship depends on particular false assumptions can be explored with the process of derivational robustness analysis and the importance of robustness analysis accounts for some of the puzzling features of the tradition of model-building in economics. 6) The fact that economists have been relatively reluctant to use true agent-based simulations to formulate explanations can partially be explained by the specific ideal of scientific understanding implicit in the practise of orthodox economics.

Statistical analysis of the associations of hereditary factors with the risk of Type 1 diabetes and Diabetic Nephropathy based on the familial data collected through ascertaiment from population-based registers

In genetic epidemiology, population-based disease registries are commonly used to collect genotype or other risk factor information concerning affected subjects and their relatives. This work presents two new approaches for the statistical inference of ascertained data: a conditional and full likelihood approaches for the disease with variable age at onset phenotype using familial data obtained from population-based registry of incident cases. The aim is to obtain statistically reliable estimates of the general population parameters. The statistical analysis of familial data with variable age at onset becomes more complicated when some of the study subjects are non-susceptible, that is to say these subjects never get the disease. A statistical model for a variable age at onset with long-term survivors is proposed for studies of familial aggregation, using latent variable approach, as well as for prospective studies of genetic association studies with candidate genes. In addition, we explore the possibility of a genetic explanation of the observed increase in the incidence of Type 1 diabetes (T1D) in Finland in recent decades and the hypothesis of non-Mendelian transmission of T1D associated genes. Both classical and Bayesian statistical inference were used in the modelling and estimation. Despite the fact that this work contains five studies with different statistical models, they all concern data obtained from nationwide registries of T1D and genetics of T1D. In the analyses of T1D data, non-Mendelian transmission of T1D susceptibility alleles was not observed. In addition, non-Mendelian transmission of T1D susceptibility genes did not make a plausible explanation for the increase in T1D incidence in Finland. Instead, the Human Leucocyte Antigen associations with T1D were confirmed in the population-based analysis, which combines T1D registry information, reference sample of healthy subjects and birth cohort information of the Finnish population. Finally, a substantial familial variation in the susceptibility of T1D nephropathy was observed. The presented studies show the benefits of sophisticated statistical modelling to explore risk factors for complex diseases.

Digital elevation model error in terrain analysis

Digital elevation models (DEMs) have been an important topic in geography and surveying sciences for decades due to their geomorphological importance as the reference surface for gravita-tion-driven material flow, as well as the wide range of uses and applications. When DEM is used in terrain analysis, for example in automatic drainage basin delineation, errors of the model collect in the analysis results. Investigation of this phenomenon is known as error propagation analysis, which has a direct influence on the decision-making process based on interpretations and applications of terrain analysis. Additionally, it may have an indirect influence on data acquisition and the DEM generation. The focus of the thesis was on the fine toposcale DEMs, which are typically represented in a 5-50m grid and used in the application scale 1:10 000-1:50 000. The thesis presents a three-step framework for investigating error propagation in DEM-based terrain analysis. The framework includes methods for visualising the morphological gross errors of DEMs, exploring the statistical and spatial characteristics of the DEM error, making analytical and simulation-based error propagation analysis and interpreting the error propagation analysis results. The DEM error model was built using geostatistical methods. The results show that appropriate and exhaustive reporting of various aspects of fine toposcale DEM error is a complex task. This is due to the high number of outliers in the error distribution and morphological gross errors, which are detectable with presented visualisation methods. In ad-dition, the use of global characterisation of DEM error is a gross generalisation of reality due to the small extent of the areas in which the decision of stationarity is not violated. This was shown using exhaustive high-quality reference DEM based on airborne laser scanning and local semivariogram analysis. The error propagation analysis revealed that, as expected, an increase in the DEM vertical error will increase the error in surface derivatives. However, contrary to expectations, the spatial au-tocorrelation of the model appears to have varying effects on the error propagation analysis depend-ing on the application. The use of a spatially uncorrelated DEM error model has been considered as a 'worst-case scenario', but this opinion is now challenged because none of the DEM derivatives investigated in the study had maximum variation with spatially uncorrelated random error. Sig-nificant performance improvement was achieved in simulation-based error propagation analysis by applying process convolution in generating realisations of the DEM error model. In addition, typology of uncertainty in drainage basin delineations is presented.

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.

Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

Conceptual and statistical modelling of environmental effects in population dynamics

Population dynamics are generally viewed as the result of intrinsic (purely density dependent) and extrinsic (environmental) processes. Both components, and potential interactions between those two, have to be modelled in order to understand and predict dynamics of natural populations; a topic that is of great importance in population management and conservation. This thesis focuses on modelling environmental effects in population dynamics and how effects of potentially relevant environmental variables can be statistically identified and quantified from time series data. Chapter I presents some useful models of multiplicative environmental effects for unstructured density dependent populations. The presented models can be written as standard multiple regression models that are easy to fit to data. Chapters II IV constitute empirical studies that statistically model environmental effects on population dynamics of several migratory bird species with different life history characteristics and migration strategies. In Chapter II, spruce cone crops are found to have a strong positive effect on the population growth of the great spotted woodpecker (Dendrocopos major), while cone crops of pine another important food resource for the species do not effectively explain population growth. The study compares rate- and ratio-dependent effects of cone availability, using state-space models that distinguish between process and observation error in the time series data. Chapter III shows how drought, in combination with settling behaviour during migration, produces asymmetric spatially synchronous patterns of population dynamics in North American ducks (genus Anas). Chapter IV investigates the dynamics of a Finnish population of skylark (Alauda arvensis), and point out effects of rainfall and habitat quality on population growth. Because the skylark time series and some of the environmental variables included show strong positive autocorrelation, the statistical significances are calculated using a Monte Carlo method, where random autocorrelated time series are generated. Chapter V is a simulation-based study, showing that ignoring observation error in analyses of population time series data can bias the estimated effects and measures of uncertainty, if the environmental variables are autocorrelated. It is concluded that the use of state-space models is an effective way to reach more accurate results. In summary, there are several biological assumptions and methodological issues that can affect the inferential outcome when estimating environmental effects from time series data, and that therefore need special attention. The functional form of the environmental effects and potential interactions between environment and population density are important to deal with. Other issues that should be considered are assumptions about density dependent regulation, modelling potential observation error, and when needed, accounting for spatial and/or temporal autocorrelation.

Language learning in infancy

Although immensely complex, speech is also a very efficient means of communication between humans. Understanding how we acquire the skills necessary for perceiving and producing speech remains an intriguing goal for research. However, while learning is likely to begin as soon as we start hearing speech, the tools for studying the language acquisition strategies in the earliest stages of development remain scarce. One prospective strategy is statistical learning. In order to investigate its role in language development, we designed a new research method. The method was tested in adults using magnetoencephalography (MEG) as a measure of cortical activity. Neonatal brain activity was measured with electroencephalography (EEG). Additionally, we developed a method for assessing the integration of seen and heard syllables in the developing brain as well as a method for assessing the role of visual speech when learning phoneme categories. The MEG study showed that adults learn statistical properties of speech during passive listening of syllables. The amplitude of the N400m component of the event-related magnetic fields (ERFs) reflected the location of syllables within pseudowords. The amplitude was also enhanced for syllables in a statistically unexpected position. The results suggest a role for the N400m component in statistical learning studies in adults. Using the same research design with sleeping newborn infants, the auditory event-related potentials (ERPs) measured with EEG reflected the location of syllables within pseudowords. The results were successfully replicated in another group of infants. The results show that even newborn infants have a powerful mechanism for automatic extraction of statistical characteristics from speech. We also found that 5-month-old infants integrate some auditory and visual syllables into a fused percept, whereas other syllable combinations are not fully integrated. Auditory syllables were paired with visual syllables possessing a different phonetic identity, and the ERPs for these artificial syllable combinations were compared with the ERPs for normal syllables. For congruent auditory-visual syllable combinations, the ERPs did not differ from those for normal syllables. However, for incongruent auditory-visual syllable combinations, we observed a mismatch response in the ERPs. The results show an early ability to perceive speech cross-modally. Finally, we exposed two groups of 6-month-old infants to artificially created auditory syllables located between two stereotypical English syllables in the formant space. The auditory syllables followed, equally for both groups, a unimodal statistical distribution, suggestive of a single phoneme category. The visual syllables combined with the auditory syllables, however, were different for the two groups, one group receiving visual stimuli suggestive of two separate phoneme categories, the other receiving visual stimuli suggestive of only one phoneme category. After a short exposure, we observed different learning outcomes for the two groups of infants. The results thus show that visual speech can influence learning of phoneme categories. Altogether, the results demonstrate that complex language learning skills exist from birth. They also suggest a role for the visual component of speech in the learning of phoneme categories.

Why Don't Students Talk? Causes of Foreign Language Communication Apprehension in English Classes: A Comparison of High Apprehensive and Low Apprehensive Upper Secondary Students.

OBJECTIVES. Oral foreign language skills are an integral part of one's social, academic and professional competence. This can be problematic for those suffering from foreign language communication apprehension (CA), or a fear of speaking a foreign language. CA manifests itself, for example, through feelings of anxiety and tension, physical arousal and avoidance of foreign language communication situations. According to scholars, foreign language CA may impede the language learning process significantly and have detrimental effects on one's language learning, academic achievement and career prospects. Drawing on upper secondary students' subjective experiences of communication situations in English as a foreign language, this study seeks, first, to describe, analyze and interpret why upper secondary students experience English language communication apprehension in English as a foreign language (EFL) classes. Second, this study seeks to analyse what the most anxiety-arousing oral production tasks in EFL classes are, and which features of different oral production tasks arouse English language communication apprehension and why. The ultimate objectives of the present study are to raise teachers' awareness of foreign language CA and its features, manifestations and impacts in foreign language classes as well as to suggest possible ways to minimize the anxiety-arousing features in foreign language classes. METHODS. The data was collected in two phases by means of six-part Likert-type questionnaires and theme interviews, and analysed using both quantitative and qualitative methods. The questionnaire data was collected in spring 2008. The respondents were 122 first-year upper secondary students, 68 % of whom were girls and 31 % of whom were boys. The data was analysed by statistical methods using SPSS software. The theme interviews were conducted in spring 2009. The interviewees were 11 second-year upper secondary students aged 17 to 19, who were chosen by purposeful selection on the basis of their English language CA level measured in the questionnaires. Six interviewees were classified as high apprehensives and five as low apprehensives according to their score in the foreign language CA scale in the questionnaires. The interview data was coded and thematized using the technique of content analysis. The analysis and interpretation of the data drew on a comparison of the self-reports of the highly apprehensive and low apprehensive upper secondary students. RESULTS. The causes of English language CA in EFL classes as reported by the students were both internal and external in nature. The most notable causes were a low self-assessed English proficiency, a concern over errors, a concern over evaluation, and a concern over the impression made on others. Other causes related to a high English language CA were a lack of authentic oral practise in EFL classes, discouraging teachers and negative experiences of learning English, unrealistic internal demands for oral English performance, high external demands and expectations for oral English performance, the conversation partner's higher English proficiency, and the audience's large size and unfamiliarity. The most anxiety-arousing oral production tasks in EFL classes were presentations or speeches with or without notes in front of the class, acting in front of the class, pair debates with the class as audience, expressing thoughts and ideas to the class, presentations or speeches without notes while seated, group debates with the class as audience, and answering to the teacher's questions involuntarily. The main features affecting the anxiety-arousing potential of an oral production task were a high degree of attention, a large audience, a high degree of evaluation, little time for preparation, little linguistic support, and a long duration.