The impact of inequality on economic growth has become a topic of broad and current interest. Multiple researches investigated the issue but the disparity of opinions and empirical results is huge. The present thesis revises the pri- mary literature through a meta-analytical approach applying Bayesian Model Averaging (BMA) estimation technique. We examine 562 estimates collected from 58 studies published between 1991 and 2015. I find the evidence of the publication bias presence in the literature. The authors of primary studies tend to report preferentially negative and significant estimates. The BMA results suggest that the effect of inequality on growth is not straightforward and is likely not linear. A single pattern for inequality/growth relationship is not fea- sible since the results vary across used income inequality measures, estimation methods and data structure and quality. JEL Classification D31, O10, C11, C82 Keywords meta-analysis, inequality, economic growth, Bayesian model averaging, publication bias Author's e-mail 23376990@fsv.cuni.cz Supervisor's e-mail zuzana.havrankova@fsv.cuni.cz

The main objective of our research was to develop a new bankruptcy prediction model for the Czech economy. For that purpose we used the logistic regression and 150,000 financial statements collected for the 2002-2016 period. We defined 41 explanatory variables (25 financial ratios and 16 dummy variables) and used Bayesian model averaging to select the best set of explanatory variables. The resulting model has been estimated for three prediction horizons: one, two, and three years before bankruptcy, so that we could assess the changes in the importance of explanatory variables and models' prediction accuracy. To deal with high skew in our dataset due to small number of bankrupt firms, we applied over- and under- sampling methods on the train sample (80% of data). These methods proved to enhance our classifier's accuracy for all specifications and periods. The accuracy of our models has been evaluated by Receiver operating characteristics curves, Sensitivity-Specificity curves, and Precision-Recall curves. In comparison with models examined on similar data, our model performed very well. In addition, we have selected the most powerful predictors for short- and long-term horizons, which is potentially of high relevance for practice. JEL Classification C11, C51, C53, G33, M21 Keywords Bankruptcy...

The dissertation is a compilation of three empirical papers on the effects of financial development. In the first paper, we examine finance's effect on long-term economic growth using Bayesian model averaging to address model uncertainty. Our global sample findings indicate that the efficiency of financial intermediation is robustly related to long-term growth. The second and third papers investigate the determinants of wealth and income inequality, capturing various economic, financial, political, institutional, and geographical factors. We reveal that finance plays a considerable role in shaping both distributions.

Despite the fact that each cell in an organism has the same genetic information, it is possible that cells fundamentally differ in their function. The molecular basis for the functional diversity of cells is governed by biochemical processes that regulate the expression of genes. Key to this regulatory process are proteins called transcription factors that recognize and bind specific DNA sequences of a few nucleotides. Here we tackle the problem of identifying the binding sites of a given transcription factor. The prediction of binding preferences from the structure of a transcription factor is still an unsolved problem. For that reason, binding sites are commonly identified by searching for overrepresented sites in a given collection of nucleotide sequences. Such sequences might be known regulatory regions of genes that are assumed to be coregulated, or they are obtained from so-called ChIP-seq experiments that identify approximately the sites that were bound by a given transcription factor. In both cases, the observed nucleotide sequences are much longer than the actual binding sites and computational tools are required to uncover the actual binding preferences of a factor. Aggravated by the fact that transcription factors recognize not only a single nucleotide sequence, the search for overrepresented patterns in a given collection of sequences has proven to be a challenging problem. Most computational methods merely relied on the given set of sequences, but additional information is required in order to make reliable predictions. Here, this information is obtained by looking at the evolution of nucleotide sequences. For that reason, each nucleotide sequence in the observed data is augmented by its orthologs, i.e. sequences from related species where the same transcription factor is present. By constructing multiple sequence alignments of the orthologous sequences it is possible to identify functional regions that are under selective pressure and therefore appear more conserved than others. The processing of the additional information exerted by ortholog sequences relies on a phylogenetic tree equipped with a nucleotide substitution model that not only carries information about the ancestry, but also about the expected similarity of functional sites. As a result, a Bayesian method for the identification of transcription factor binding sites is presented. The method relies on a phylogenetic tree that agrees with the assumptions of the nucleotide substitution process. Therefore, the problem of estimating phylogenetic trees is discussed first. The computation of point estimates relies on recent developments in Hadamard spaces. Second, the statistical model is presented that captures the enrichment and conservation of binding sites and other functional regions in the observed data. The performance of the method is evaluated on ChIP-seq data of transcription factors, where the binding preferences have been estimated in previous studies.

The relationship between income inequality and happiness is central to a host of welfare policies. If higher income inequality puts people down, advocating for income redistribution from the rich to the poor could make society happier. We show, however, that this popular consensus on the relationship's direction is rather absent in the academic literature. Based on the 868 observations col- lected from 53 studies and controlling for 62 aspects of study design, we use state-of-the-art meta-analysis techniques to identify several important drivers of the efect. Unless each study gets the same weight, the literature is driven by publication bias pushing the estimates against the popular consensus. While geographical diferences dominate among the systematic infuences of the re- lationship's magnitude, the relationship is also strongly afected by various methods and data the authors use in the primary studies. Most prominently, it matters if authors control for diferent individual's characteristics, such as perceived trust in people or their health status.

The outbreak of the Ebola virus was declared a Public Health Emergency of International Concern by the World Health Organisation (WHO). Due to the complex nature of the outbreak, the Centers for Disease Control and Prevention (CDC) had created interim guidance for monitoring people potentially exposed to Ebola and for evaluating their intended travel and restricting the movements of carriers when needed. Tools to evaluate the risk of individuals and groups of individuals contracting the disease could mitigate the growing anxiety and fear. The goal is to understand and analyze the nature of risk an individual would face when he/she comes in contact with a carrier. This thesis presents a tool that makes use of contextual data intelligence to predict the risk factor of individuals who come in contact with the carrier.

Technologies such as micro-expression arrays and high-throughput sequenc- ing assays have accelerated research of genetic transcription in biological cells. Furthermore, many links between the gene expression levels and the pheno- typic characteristics of cells have been discovered. Our current understanding of transcriptomics as an intermediate regulatory layer between genomics and proteomics raises hope that we will soon be able to decipher many more cel- lular mechanisms through the exploration of gene transcription. However, although large amounts of expression data are measured, only lim- ited information can be extracted. One general problem is the large set of considered genomic features. Expression levels are often analyzed individually because of limited computational resources and unknown statistical dependen- cies among the features. This leads to multiple testing issues or can lead to overfitting models, commonly referred to as the “curse of dimensionality.” Another problem can arise from ignorance of measurement uncertainty. In particular, approaches that consider statistical significance can suffer from underestimating uncertainty for weakly expressed genes and consequently re- quire subjective manual measures to produce consistent results (e.g., domain- specific gene filters). In this thesis, we lay out a theoretical foundation for a Bayesian interpretation of gene expression data based on subtle assumptions. Expression measure- ments are related to latent information (e.g., the transcriptome composition), which we formulate as a probability distribution that represents the uncer- tainty over the composition of the original sample. Instead of analyzing univariate gene expression levels, we use the multivari- ate transcriptome composition space. To realize computational feasibility, we develop a scalable dimensional reduction that aims to produce the best approximation that can be used with the computational resources available. To enable the deconvolution of gene expression, we describe subtissue specific probability distributions of expression profiles. We demonstrate the suitabil- ity of our approach with two deconvolution applications: first, we infer the composition of immune cells, and second we reconstruct tumor-specific ex- pression patterns from bulk-RNA-seq data of prostate tumor tissue samples.:1 Introduction 1 1.1 State of the Art and Motivation 2 1.2 Scope of this Thesis 5 2 Notation and Abbreviations 7 2.1 Notations 7 2.2 Abbreviations 9 3 Methods 10 3.1 The Convolution Assumption 10 3.2 Principal Component Analysis 11 3.3 Expression Patterns 11 3.4 Bayes’ Theorem 12 3.5 Inference Algorithms 13 3.5.1 Inference Through Sampling 13 3.5.2 Variationa lInference 14 4 Prior and Conditional Probabilities 16 4.1 Mixture Coefficients 16 4.2 Distribution of Tumor Cell Content 18 4.2.1 Optimal Tumor Cell Content Drawing 20 4.3 Transcriptome Composition Distribution 21 4.3.1 Sequencing Read Distribution 21 4.3.1.1 Empirical Plausibility Investigation 25 4.3.2 Dirichletand Normality 29 4.3.3 Theta◦logTransformation 29 4.3.4 Variance Stabilization 32 4.4 Cell and Tissue-Type-Specific Expression Pattern Distributions 32 4.4.1 Method of Moments and Factor Analysis 33 4.4.1.1 Tumor Free Cells 33 4.4.1.2 Tumor Cells 34 4.4.2 Characteristic Function 34 4.4.3 Gaussian Mixture Model 37 4.5 Prior Covariance Matrix Distribution 37 4.6 Bayesian Survival Analysis 38 4.7 Demarcation from Existing Methods 40 4.7.1 Negative Binomial Distribution 40 4.7.2 Steady State Assumption 41 4.7.3 Partial Correlation 41 4.7.4 Interaction Networks 42 5 Feasibility via Dimensional Reduction 43 5.1 DR for Deconvolution of Expression Patterns 44 5.1.1 Systematically Differential Expression 45 5.1.2 Internal Distortion 46 5.1.3 Choosinga DR 46 5.1.4 Testing the DR 47 5.2 Transformed Density Functions 49 5.3 Probability Distribution of Mixtures in DR Space 50 5.3.1 Likelihood Gradient 51 5.3.2 The Theorem 52 5.3.3 Implementation 52 5.4 DR for Inference of Cell Composition 53 5.4.1 Problem Formalization 53 5.4.2 Naive PCA 54 5.4.3 Whitening 55 5.4.3.1 Covariance Inflation 56 5.4.4 DR Through Optimization 56 5.4.4.1 Starting Point 57 5.4.4.2 The Optimization Process 58 5.4.5 Results 59 5.5 Interpretation of DR 61 5.6 Comparison to Other DRs 62 5.6.1 Weighted Correlation Network Analysis 62 5.6.2 t-Distributed Stochastic Neighbor Embedding 65 5.6.3 Diffusion Map 66 5.6.4 Non-negativeMatrix Factorization 66 5.7 Conclusion 67 6 Data for Example Application 68 6.1 Immune Cell Data 68 6.1.1 Provided List of Publicly Available Data 68 6.1.2 Obtaining the Publicly Available RNA-seq Data 69 6.1.3 Obtaining the Publicly Available Expression Microarray Data 71 6.1.4 Data Sanitization 71 6.1.4.1 A Tagging Tool 72 6.1.4.2 Tagging Results 73 6.1.4.3 Automatic Sanitization 74 6.1.5 Data Unification 75 6.1.5.1 Feature Mapping 76 6.1.5.2 Feature Selection 76 6.2 Examples of Mixtures with Gold Standard 79 6.2.1 Expression Microarray Data 81 6.2.2 Normalized Expression 81 6.2.3 Composition of the Gold Standard 82 6.3 Tumor Expression Data 82 6.3.1 Tumor Content 82 6.4 Benchmark Reference Study 83 6.4.1 Methodology 83 6.4.2 Reproduction 84 6.4.3 Reference Hazard Model 85 7 Bayesian Models in Example Applications 87 7.1 Inference of Cell Composition 87 7.1.1 The Expression Pattern Distributions (EPDs) 88 7.1.2 The Complete Model 89 7.1.3 Start Values 89 7.1.4 Resource Limits 90 7.2 Deconvolution of Expression Patterns 91 7.2.1 The Distribution of Expression Pattern Distribution 91 7.2.2 The Complete Model 92 7.2.3 SingleSampleDeconvolution 93 7.2.4 A Simplification 94 7.2.5 Start Values 94 8 Results of Example Applications 96 8.1 Inference of Cell Composition 96 8.1.1 Single Composition Output 96 8.1.2 ELBO Convergence in Variational Inference 97 8.1.3 Difficulty-Divergence 97 8.1.3.1 Implementing an Alternative Stick-Breaking 98 8.1.3.2 Using MoreGeneral Inference Methods 99 8.1.3.3 UsingBetterData 100 8.1.3.4 Restriction of Variance of Cell-Type-Specific EPDs 100 8.1.3.5 Doing Fewer Iterations 100 8.1.4 Difficulty-Bias 101 8.1.5 Comparison to Gold Standard 101 8.1.6 Comparison to Competitors 101 8.1.6.1 Submission-Aginome-XMU 105 8.1.6.2 Submission-Biogem 105 8.1.6.3 Submission-DA505 105 8.1.6.4 Submission-AboensisIV 105 8.1.6.5 Submission-mittenTDC19 106 8.1.6.6 Submission-CancerDecon 106 8.1.6.7 Submission-CCB 106 8.1.6.8 Submission-D3Team 106 8.1.6.9 Submission-ICTD 106 8.1.6.10 Submission-Patrick 107 8.1.6.11 Conclusion for the Competitor Review 107 8.1.7 Implementation 107 8.1.8 Conclusion 108 8.2 Deconvolution of Expression Patterns 108 8.2.1 Difficulty-Multimodality 109 8.2.1.1 Order of Kernels 109 8.2.1.2 Posterior EPD Complexity 110 8.2.1.3 Tumor Cell Content Estimate 110 8.2.2 Difficulty-Time 110 8.2.3 The Inference Process 111 8.2.3.1 ELBO Convergence in Variational Inference 111 8.2.4 Posterior of Tumor Cell Content 112 8.2.5 Posterior of Tissue Specific Expression 112 8.2.6 PosteriorHazardModel 113 8.2.7 Gene Marker Study with Deconvoluted Tumor Expression 115 8.2.8 Hazard Model Comparison Overview 116 8.2.9 Implementation 116 9 Discussion 117 9.1 Limitations 117 9.1.1 Simplifying Assumptions 117 9.1.2 Computation Resources 118 9.1.3 Limited Data and Suboptimal Format 118 9.1.4 ItIsJustConsistency 119 9.1.5 ADVI Uncertainty Estimation 119 9.2 Outlook 119 9.3 Conclusion 121 A Appendix 123 A.1 Optimalα 123 A.2 Digamma Function and Logarithm 123 A.3 Common Normalization 124 A.3.1 CPMNormalization 124 A.3.2 TPMNormalization 124 A.3.3 VSTNormalization 125 A.3.4 PCA After Different Normalizations 125 A.4 Mixture Prior Per Tissue Source 125 A.5 Data 125 A.6 Cell Type Characterization without Whitening 133 B Proofs 137 Bibliography 140

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The Brigham Young University Women's Volleyball Team recorded and rated all skills (pass, set, attack, etc.) and recorded rally outcomes (point for BYU, rally continues, point for opponent) for the entire 2006 home volleyball season. Only sequences of events occurring on BYU's side of the net were considered. Events followed one of these general patterns: serve-outcome, pass-set-attack-outcome, or block-dig-set-attack-outcome. These sequences of events were assumed to be first-order Markov chains where the quality of each contact depended only explicitly on the quality of the previous contact but not on contacts further removed in the sequence. We represented these sequences in an extensive matrix of transition probabilities where the elements of the matrix were the probabilities of moving from one state to another. The count matrix consisted of the number of times play moved from one transition state to another during the season. Data in the count matrix were assumed to have a multinomial distribution. A Dirichlet prior was formulated for each row of the count matrix, so posterior estimates of the transition probabilities were then available using Gibbs sampling. The different paths in the transition probability matrix were followed through the possible sequences of events at each step of the MCMC process to compute the posterior probability density that a perfect pass results in a point, a perfect set results in a point, and so forth. These posterior probability densities are used to address questions about skill performance in BYU women's volleyball.

The time-course of interaction formation or breaking can be studied using LigandTracer, and the data obtained from an experiment can be analyzed using a model of ligand-target binding kinetics. There are different kinetic models, and the choice of model is currently motivated by knowledge about the interaction, which is problematic when the knowledge about the interaction is unsatisfactory. In this project, a Bayesian model selection procedure was implemented to motivate the model choice using the data obtained from studying a biological system. The model selection procedure was implemented for four kinetic models, the 1:1 model, the 1:2 model, the bivalent model and a new version of the bivalent model.Bayesian inference was performed on the data using each of the models to obtain the posterior distributions of the parameters. Afterwards, the Bayes factor was approximated from numerical calculations of the marginal likelihood. Four numerical methods were implemented to approximate the marginal likelihood, the Naïve Monte Carlo estimator, the method of Harmonic Means of the likelihood, Importance Sampling and Sequential Monte Carlo. When tested on simulated data, the method of Importance Sampling seemed to yield the most reliable prediction of the most likely model. The model selection procedure was then tested on experimental data which was expected to be from a 1:1 interaction and the result of the model selection procedure did not agree with the expectation on the experimental test dataset. Therefore no reliable conclusion could be made when the model selection procedure was used to analyze the interaction between the anti-CD20 antibody Rituximab and Daudi cells. / Interaktioner kan analyseras med hjälp av LigandTracer. Data från ett LigandTracer experiment kan sedan analyseras med avseende på en kinetisk modell. Det finns olika kinetiska modeller, och modellvalet motiveras vanligen utifrån tidigare kunskap om interaktionen, vilket är problematiskt när den tillgängliga informationen om en interaktion är otillräcklig. I det här projektet implementerades en Bayesiansk metod för att motivera valet av modell utifrån data från ett LigandTracer experiment. Modellvalsmetoden implementerades för fyra kinetiska modeller, 1:1 modellen, 1:2 modellen, den bivalenta modellen och en ny version av den bivalenta modellen. Bayesiansk inferens användes för att få fram aposteriorifördelningarna för de olika modellernas parametrar utifrån den givna datan. Sedan beräknades Bayes faktor utifrån numeriska approximationer av marginalsannolikeheten. Fyra numeriska metoder implementerades för att approximera marginalsannolikheten; Naïve Monte Carlo estimator, det harmoniska medelvärdet av likelihood-funktionen, Importance Sampling och Sekventiell Monte Carlo. När modellvalsmetoden testades på simulerad data gav metoden Importance Sampling den mest tillförlitliga förutsägelsen om vilken modell som generade datan. Metoden testades också på experimentell data som förväntades följa en 1:1 interaktion och resultatet avvek från det förväntade resultatet. Följaktligen kunde ingen slutsas dras av resultet från modelvalsmetoden när den sedan används för att analysera interaktionen mellan anti-CD antikroppen Rituximab och Daudi-celler.