We develop statistical methods for tackling two important problems in genetic association studies. First, we propose a Bayesian approach to overcome the winner's curse in genetic studies. Second, we consider a Bayesian latent variable model for analyzing longitudinal family data with pleiotropic phenotypes. Winner's curse in genetic association studies refers to the estimation bias of the reported odds ratios (OR) for an associated genetic variant from the initial discovery samples. It is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in the low power studies. We investigate the performance of the method with simulations and applications to four real data examples. Pleiotropy occurs when a single genetic factor influences multiple quantitative or qualitative phenotypes, and it is present in many genetic studies of complex human traits. The longitudinal family studies combine the features of longitudinal studies in individuals and cross-sectional studies in families. Therefore, they provide more information about the genetic and environmental factors associated with the trait of interest. We propose a Bayesian latent variable modeling approach to model multiple phenotypes simultaneously in order to detect the pleiotropic effect and allow for longitudinal and/or family data. An efficient MCMC algorithm is developed to obtain the posterior samples by using hierarchical centering and parameter expansion techniques. We apply spike and slab prior methods to test whether the phenotypes are significantly associated with the latent disease status. We compute Bayes factors using path sampling and discuss their application in testing the significance of factor loadings and the indirect fixed effects. We examine the performance of our methods via extensive simulations and apply them to the blood pressure data from a genetic study of type 1 diabetes (T1D) complications.

We develop statistical methods for tackling two important problems in genetic association studies. First, we propose a Bayesian approach to overcome the winner's curse in genetic studies. Second, we consider a Bayesian latent variable model for analyzing longitudinal family data with pleiotropic phenotypes. Winner's curse in genetic association studies refers to the estimation bias of the reported odds ratios (OR) for an associated genetic variant from the initial discovery samples. It is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in the low power studies. We investigate the performance of the method with simulations and applications to four real data examples. Pleiotropy occurs when a single genetic factor influences multiple quantitative or qualitative phenotypes, and it is present in many genetic studies of complex human traits. The longitudinal family studies combine the features of longitudinal studies in individuals and cross-sectional studies in families. Therefore, they provide more information about the genetic and environmental factors associated with the trait of interest. We propose a Bayesian latent variable modeling approach to model multiple phenotypes simultaneously in order to detect the pleiotropic effect and allow for longitudinal and/or family data. An efficient MCMC algorithm is developed to obtain the posterior samples by using hierarchical centering and parameter expansion techniques. We apply spike and slab prior methods to test whether the phenotypes are significantly associated with the latent disease status. We compute Bayes factors using path sampling and discuss their application in testing the significance of factor loadings and the indirect fixed effects. We examine the performance of our methods via extensive simulations and apply them to the blood pressure data from a genetic study of type 1 diabetes (T1D) complications.

This thesis, which consists of four chapters, focuses on forecasting in a data-rich environment and related computational issues. Chapter 1, “An embarrassment of riches: Forecasting using large panels” explores the idea of combining forecasts from various indicator models by using Bayesian model averaging (BMA) and compares the predictive performance of BMA with predictive performance of factor models. The combination of these two methods is also implemented, together with a benchmark, a simple autoregressive model. The forecast comparison is conducted in a pseudo out-of-sample framework for three distinct datasets measured at different frequencies. These include monthly and quarterly US datasets consisting of more than 140 predictors, and a quarterly Swedish dataset with 77 possible predictors. The results show that none of the considered methods is uniformly superior and that no method consistently outperforms or underperforms a simple autoregressive process. Chapter 2. “Forecast combination using predictive measures” proposes using out-of-sample predictive likelihood as the basis for BMA and forecast combination. In addition to its intuitive appeal, the use of the predictive likelihood relaxes the need to specify proper priors for the parameters of each model. We show that the forecast weights based on the predictive likelihood have desirable asymptotic properties. And that these weights will have better small sample properties than the traditional in-sample marginal likelihood when uninformative priors are used. In order to calculate the weights for the combined forecast, a number of observations, a hold-out sample, is needed. There is a trade off involved in the size of the hold-out sample. The number of observations available for estimation is reduced, which might have a detrimental effect. On the other hand, as the hold-out sample size increases, the predictive measure becomes more stable and this should improve performance. When there is a true model in the model set, the predictive likelihood will select the true model asymptotically, but the convergence to the true model is slower than for the marginal likelihood. It is this slower convergence, coupled with protection against overfitting, which is the reason the predictive likelihood performs better when the true model is not in the model set. In Chapter 3. “Forecasting GDP with factor models and Bayesian forecast combination” the predictive likelihood approach developed in the previous chapter is applied to forecasting GDP growth. The analysis is performed on quarterly economic dataset from six countries: Canada, Germany, Great Britain, Italy, Japan and United States. The forecast combination technique based on both in-sample and out-of-sample weights is compared to forecasts based on factor models. The traditional point forecast analysis is extended by considering confidence intervals. The results indicate that forecast combinations based on the predictive likelihood weights have better forecasting performance compared with the factor models and forecast combinations based on the traditional in-sample weights. In contrast to common findings, the predictive likelihood does improve upon an autoregressive process for longer horizons. The largest improvement over the in-sample weights is for small values of hold-out sample sizes, which provides protection against structural breaks at the end of the sample period. The potential benefits of model averaging as a tool for extracting the relevant information from a large set of predictor variables come at the cost of considerable computational complexity. To avoid evaluating all the models, several approaches have been developed to simulate from the posterior distributions. Markov chain Monte Carlo methods can be used to directly draw from the model posterior distributions. It is desirable that the chain moves well through the model space and takes draws from regions with high probabilities. Several computationally efficient sampling schemes, either one at a time or in blocks, have been proposed for speeding up convergence. There is a trade-off between local moves, which make use of the current parameter values to propose plausible values for model parameters, and more global transitions, which potentially allow faster exploration of the distribution of interest, but may be much harder to implement efficiently. Local model moves enable use of fast updating schemes, where it is unnecessary to completely reestimate the new, slightly modified, model to obtain an updated solution. The last fourth chapter “Computational efficiency in Bayesian model and variable selection” investigates the possibility of increasing computational efficiency by using alternative algorithms to obtain estimates of model parameters as well as keeping track of their numerical accuracy. Also, various samplers that explore the model space are presented and compared based on the output of the Markov chain. / Diss. Stockholm : Handelshögskolan, 2006

Neste trabalho foi proposta uma estratégia de modelagem hidrológica para a transformação chuva vazão da Bacia do Ribeirão da Onça (B.R.O) utilizando-se técnicas de auto calibração com análise de incertezas e de ponderação de modelos. Foi utilizado o modelo hidrológico Soil and Water Assessment Tool (SWAT), por ser um modelo que possui uma descrição física e de maneira distribuída dos processos hidrológicos da bacia. Foram propostas cinco diferentes séries de precipitação e esquemas de interpolação espacial a serem utilizados como dados de entrada para o modelo SWAT. Em seguida, utilizou-se o método semiautomático Sequential Uncertainty Fitting ver.-2 (SUFI-2) para a auto calibração e análise de incertezas dos parâmetros do modelo e produção de respostas com intervalos de incerteza para cada uma das séries de precipitação utilizadas. Por fim, foi utilizado o método de ponderação bayesiana de modelos (BMA) para o pós-processamento estocástico das respostas. Os resultados da análise de incerteza dos parâmetros do modelo SWAT indicam uma não adequação do método Soil Conservation Service (SCS) para simulação da geração do escoamento superficial, juntamente com uma necessidade de maior investigação das propriedades físicas do solo da bacia. A análise da precisão e acurácia dos resultados das séries de precipitação em comparação com a resposta combinada pelo método BMA sugerem a última como a mais adequada para a simulação chuva-vazão na B.R.O. / This study proposed an approach to the hydrological modeling of the Ribeirão da Onças Basin (B.R.O) based on automatic calibration and uncertainty analysis methods, together with model averaging. The Soil and Water Assessment Tool (SWAT) was used due to its distributed nature and physical description of hydrologic processes. An ensemble, composed by five different precipitation schemes, based on different sources and spatial interpolation methods was used. The Sequential Uncertainty Fitting ver-2 (SUFI-2) procedure was used for automatic calibration and uncertainty analysis of the SWAT model parameters, together with generation of streamflow simulations with uncertainty intervals. Following, the Bayesian Model Averaging (BMA) was used to merge the different responses into a single probabilistic forecast. The results of the uncertainty analysis for the SWAT parameters show that the Soil Conservation Service (SCS) model for surface runoff prediction may not be suitable for the B.R.O, and that more investigations about the soil physical properties at the Basin are recommended. An analysis of the accuracy and precision of the simulations produced by the precipitation ensemble members against the BMA simulation supports the use of the latter as a suitable framework for streamflow simulations at the B.R.O.

This thesis aims to identify main driving market risk factors of different strategies implemented by hedge funds by looking at correlation coefficients, implementing Principal Component Analysis and analyzing "loadings" for first three principal components, which explain the largest portion of the variation of hedge funds' returns. In the next step, a stepwise regression through iteration process includes and excludes market risk factors for each strategy, searching for the combination of risk factors which will offer a model with the best "fit", based on The Akaike Information Criterion - AIC and Bayesian Information Criterion - BIC. Lastly, to avoid counterfeit results and overcome model uncertainty issues a Bayesian Model Average - BMA approach was taken. Key words: Hedge Funds, hedge funds' strategies, market risk, principal component analysis, stepwise regression, Akaike Information Criterion, Bayesian Information Criterion, Bayesian Model Averaging Author's e-mail: aleksaradosavcevic@gmail.com Supervisor's e-mail: mp.princ@seznam.cz

01 Abstract Foreign exchange reserves are a useful tool and a buffer but maintaining an amount that is too large can be costly to the economy. Recent accumulation of these reserves points to the importance of this topic. This thesis focuses on one specific part of the effect of FX reserves on the economy - the inflation. I use panel data for 74 countries from the year 1996 to the year 2017. There is a certain degree of model uncertainty for which this thesis accounts for by using Bayesian model averaging (BMA) estimation technique. The findings from my model averaging estimations show FX reserves to not be of importance for inflation determination with close to no change when altering lags, variables, when limiting the sample to fixed FX regimes nor when limiting the sample to inflation targeting regimes. The most important variables are estimated to be a central bank financial strength proxy, exchange rate depreciation, money supply, inflation targeting, and capital account openness. These results are robust to lag changes, prior changes, and for the most part remain the same when Pooled OLS is used.

Valuation of used cars, affected by various technical attributes and information asymmetry, is the key objective of all agents operating on the automobile mar- ket. This thesis, focusing on a hedonic price analysis, aims to determine basic as well as additional attributes as determinants of a used car market price. In addition, the analysis sheds light upon novel attributes (service records, cigarette smoke pollution of a vehicle interior, selling channel factor in the e- commerce environment, and a German geographical division). The hedonic price research uses the unique data sample of the German used car market, extracted from the database of the e-commerce platform AutoScout24 com- prised of almost 51 thousand vehicles and 57 attributes. The model selection is specified by the incorporation of the Bayesian model averaging approach. The research proves the complexity of a valuation of a used vehicle in a term of a substantial number of relevant variables. The most interesting innovative conclusions are non-significant effect of selling channels and small local price differences among two German regions. Remarkable are also the significant effect of the status of previous owners, bodywork colour, and smoke pollution. The estimated vehicle lifespan of 10 years shows that cars have shorter than...

Islam and Economic Performance: A Meta-Analysis Patrik Kratochvíla June 28, 2021 Abstract The ongoing economic supremacy of the West has prompted debates on the ability of non-Christian religions to generate economic growth. The academic literature focusing on the Islamic religion o↵ers multiple answers, leaving the matter unresolved and with no definite conclusion. Based on a quantitative sur- vey of 315 estimates collected from 41 relevant academic studies, Islam exerts a positive and statistically significant e↵ect on economic growth in 40% of cases, a negative and statistically significant e↵ect in 10% of cases, and virtually zero e↵ect in 50% of cases. Tests for publication bias indicate slightly preferential reporting against negative estimates. When I correct for this bias, I find that the mean e↵ect of Islam on economic growth is positive but economically small. I also construct 79 moderator variables capturing methodological heterogeneity among the primary studies and apply the method of Bayesian model averaging to deal with model uncertainty in meta-analysis. The analysis shows that the heterogeneity in the results is primarily driven by di↵erences in the sample com- position and the choice of control variables, and to a lesser extent by estimation characteristics and proxies for Islam employed. 1

This thesis consists of three chapters on economic and econometric applications of Bayesian parameter estimation and model comparison. The first two chapters study the incidental parameter problem mainly under a linear autoregressive (AR) panel data model with fixed effect. The first chapter investigates the problem from a model comparison perspective. The major finding in the first chapter is that consistency in parameter estimation and model selection are interrelated. The reparameterization of the fixed effect parameter proposed by Lancaster (2002) may not provide a valid solution to the incidental parameter problem if the wrong set of exogenous regressors are included. To estimate the model consistently and to measure its goodness of fit, the Bayes factor is found to be more preferable for model comparson than the Bayesian information criterion based on the biased maximum likelihood estimates. When the model uncertainty is substantial, Bayesian model averaging is recommended. The method is applied to study the relationship between financial development and economic growth. The second chapter proposes a correction function approach to solve the incidental parameter problem. It is discovered that the correction function exists for the linear AR panel model of order p when the model is stationary with strictly exogenous regressors. MCMC algorithms are developed for parameter estimation and to calculate the Bayes factor for model comparison. The last chapter studies how stock return's predictability and model uncertainty affect a rational buy-and-hold investor's decision to allocate her wealth for different lengths of investment horizons in the UK market. The FTSE All-Share Index is treated as the risky asset, and the UK Treasury bill as the riskless asset in forming the investor's portfolio. Bayesian methods are employed to identify the most powerful predictors by accounting for model uncertainty. It is found that though stock return predictability is weak, it can still affect the investor's optimal portfolio decisions over different investment horizons.

In this thesis Generalized Additive Neural Networks (GANNs) are studied in the context of predictive Data Mining. A GANN is a novel neural network implementation of a Generalized Additive Model. Originally GANNs were constructed interactively by considering partial residual plots. This methodology involves subjective human judgment, is time consuming, and can result in suboptimal results. The newly developed automated construction algorithm solves these difficulties by performing model selection based on an objective model selection criterion. Partial residual plots are only utilized after the best model is found to gain insight into the relationships between inputs and the target. Models are organized in a search tree with a greedy search procedure that identifies good models in a relatively short time. The automated construction algorithm, implemented in the powerful SAS® language, is nontrivial, effective, and comparable to other model selection methodologies found in the literature. This implementation, which is called AutoGANN, has a simple, intuitive, and user-friendly interface. The AutoGANN system is further extended with an approximation to Bayesian Model Averaging. This technique accounts for uncertainty about the variables that must be included in the model and uncertainty about the model structure. Model averaging utilizes in-sample model selection criteria and creates a combined model with better predictive ability than using any single model. In the field of Credit Scoring, the standard theory of scorecard building is not tampered with, but a pre-processing step is introduced to arrive at a more accurate scorecard that discriminates better between good and bad applicants. The pre-processing step exploits GANN models to achieve significant reductions in marginal and cumulative bad rates. The time it takes to develop a scorecard may be reduced by utilizing the automated construction algorithm. / Thesis (Ph.D. (Computer Science))--North-West University, Potchefstroom Campus, 2006.