This dissertation presents a Bayesian hierarchical model to combine two-resolution metrology data for inspecting the geometric quality of manufactured parts. The high- resolution data points are scarce, and thus scatter over the surface being measured, while the low-resolution data are pervasive, but less accurate or less precise. Combining the two datasets could supposedly make a better prediction of the geometric surface of a manufactured part than using a single dataset. One challenge in combining the metrology datasets is the misalignment which exists between the low- and high-resolution data points. This dissertation attempts to provide a Bayesian hierarchical model that can handle such misaligned datasets, and includes the following components: (a) a Gaussian process for modeling metrology data at the low-resolution level; (b) a heuristic matching and alignment method that produces a pool of candidate matches and transformations between the two datasets; (c) a linkage model, conditioned on a given match and its associated transformation, that connects a high-resolution data point to a set of low-resolution data points in its neighborhood and makes a combined prediction; and finally (d) Bayesian model averaging of the predictive models in (c) over the pool of candidate matches found in (b). This Bayesian model averaging procedure assigns weights to different matches according to how much they support the observed data, and then produces the final combined prediction of the surface based on the data of both resolutions. The proposed method improves upon the methods of using a single dataset as well as a combined prediction without addressing the misalignment problem. This dissertation demonstrates the improvements over alternative methods using both simulated data and the datasets from a milled sine-wave part, measured by two coordinate measuring machines of different resolutions, respectively.

<p>The expected equity premium is an important parameter in many financial models, especially within portfolio optimization. A good forecast of the future equity premium is therefore of great interest. In this thesis we seek to forecast the equity premium, use it in portfolio optimization and then give evidence on how sensitive the results are to estimation errors and how the impact of these can be minimized.</p><p>Linear prediction models are commonly used by practitioners to forecast the expected equity premium, this with mixed results. To only choose the model that performs the best in-sample for forecasting, does not take model uncertainty into account. Our approach is to still use linear prediction models, but also taking model uncertainty into consideration by applying Bayesian model averaging. The predictions are used in the optimization of a portfolio with risky assets to investigate how sensitive portfolio optimization is to estimation errors in the mean vector and covariance matrix. This is performed by using a Monte Carlo based heuristic called portfolio resampling.</p><p>The results show that the predictive ability of linear models is not substantially improved by taking model uncertainty into consideration. This could mean that the main problem with linear models is not model uncertainty, but rather too low predictive ability. However, we find that our approach gives better forecasts than just using the historical average as an estimate. Furthermore, we find some predictive ability in the the GDP, the short term spread and the volatility for the five years to come. Portfolio resampling proves to be useful when the input parameters in a portfolio optimization problem is suffering from vast uncertainty. </p>

<p>With the development of modern data collection approaches, researchers may collect hundreds to millions of variables, yet may not need to utilize all explanatory variables available in predictive models. Hence, choosing models that consist of a subset of variables often becomes a crucial step. In linear regression, variable selection not only reduces model complexity, but also prevents over-fitting. From a Bayesian perspective, prior specification of model parameters plays an important role in model selection as well as parameter estimation, and often prevents over-fitting through shrinkage and model averaging.</p><p>We develop two novel hierarchical priors for selection and model averaging, for Generalized Linear Models (GLMs) and normal linear regression, respectively. They can be considered as "spike-and-slab" prior distributions or more appropriately "spike- and-bell" distributions. Under these priors we achieve dimension reduction, since their point masses at zero allow predictors to be excluded with positive posterior probability. In addition, these hierarchical priors have heavy tails to provide robust- ness when MLE's are far from zero.</p><p>Zellner's g-prior is widely used in linear models. It preserves correlation structure among predictors in its prior covariance, and yields closed-form marginal likelihoods which leads to huge computational savings by avoiding sampling in the parameter space. Mixtures of g-priors avoid fixing g in advance, and can resolve consistency problems that arise with fixed g. For GLMs, we show that the mixture of g-priors using a Compound Confluent Hypergeometric distribution unifies existing choices in the literature and maintains their good properties such as tractable (approximate) marginal likelihoods and asymptotic consistency for model selection and parameter estimation under specific values of the hyper parameters.</p><p>While the g-prior is invariant under rotation within a model, a potential problem with the g-prior is that it inherits the instability of ordinary least squares (OLS) estimates when predictors are highly correlated. We build a hierarchical prior based on scale mixtures of independent normals, which incorporates invariance under rotations within models like ridge regression and the g-prior, but has heavy tails like the Zeller-Siow Cauchy prior. We find this method out-performs the gold standard mixture of g-priors and other methods in the case of highly correlated predictors in Gaussian linear models. We incorporate a non-parametric structure, the Dirichlet Process (DP) as a hyper prior, to allow more flexibility and adaptivity to the data.</p> / Dissertation

This thesis studies the relationship between GDP and Social Progress Index, components of social progress model and their dimensions. Using the dataset of 49 countries and Bayesian Model Averaging (BMA) and clustering analysis we found that there is not straight relationship between GDP and SPI. By testing 15 different models for each of 3 dimension (Basic Human Needs, Foundations of Wellbeing and Opportunity) of SPI we have found that the best variation of components would be to include all of them for each dimension. By using BMA approach we have found that the best model of SPI out of 12 components includes only intercept, tolerance and inclusion variables. The rest of components show quite low probability of inclusion, however, none of them showed 0 posterior probability. JEL Classification A13, C11, E01, I30, Keywords Kuznets, progress, SPI, GDP, BMA Author's e-mail valeria.e.efimenko@gmail.com Supervisor's e-mail daniel.vach@gmail.com

We propose the use of Latent Class Analysis methods to analyze the covariate inclusion patterns across specifications resulting from Bayesian model averaging exercises. Using Dirichlet Process clustering, we are able to identify and describe dependency structures among variables in terms of inclusion in the specifications that compose the model space. We apply the method to two datasets of potential determinants of economic growth. Clustering the posterior covariate inclusion structure of the model space formed by linear regression models reveals interesting patterns of complementarity and substitutability across economic growth determinants.

The Sahel region located in Western Africa is well known for its high rainfall variability. Severe and recurring droughts have plagued the region during the last three decades of the 20th century, while heavy precipitation events (with return periods of up to 1,200 years) were reported between 2007 and 2014. Vulnerability to extreme events is partly due to the fact that people are not prepared to cope with them. It would be of great benefit to farmers if information about the magnitudes of precipitation and streamflow in the upcoming rainy season were available a few months before; they could then switch to more adapted crops and farm management systems if required. Such information would also be useful for other sectors of the economy, such as hydropower production, domestic/industrial water consumption, fishing and navigation. A logical solution to the above problem would be seasonal rainfall and streamflow forecasting, which would allow to generate knowledge about the upcoming rainy season based on information available before it's beginning. The research in this thesis sought to improve seasonal rainfall and streamflow forecasting in the Sahel by developing statistical rainfall and streamflow seasonal forecasting models. Sea surface temperature (SST) were used as pools of predictor. The developed method allowed for a systematic search of the best period to calculate the predictor before it was used to predict average rainfall or streamflow over the upcoming rainy season. Eight statistical models consisted of various statistical methods including linear and polynomial regressions were developed in this study. Two main approaches for seasonal streamflow forecasting were developed here: 1) A two steps streamflow forecasting approach (called the indirect method) which first linked the average SST over a period prior to the date of forecast to average rainfall amount in the upcoming rainy season using the eight statistical models, then linked the rainfall amount to streamflow using a rainfall-runoff model (Soil and Water Assessment Tool (SWAT)). In this approach, the forecasted rainfall was disaggregated to daily time step using a simple approach (the fragment method) before being fed into SWAT. 2) A one step streamflow forecasting approach (called as the direct method) which linked the average SST over a period prior to the date of forecast to the average streamflow in the upcoming rainy season using the eight statistical models. To decrease the uncertainty due to model selection, Bayesian Model Averaging (BMA) was also applied. This method is able to explore the possibility of combining all available potential predictors (instead of selecting one based on an arbitrary criterion). The BMA is also capability to produce the probability density of the forecast which allows end-users to visualize the density of expected value and assess the level of uncertainty of the generated forecast. Finally, the economic value of forecast system was estimated using a simple economic approach (the cost/loss ratio method). Each developed method was evaluated using three well known model efficiency criteria: the Nash-Sutcliffe coefficient (Ef), the coefficient of determination (R2) and the Hit score (H). The proposed models showed equivalent or better rainfall forecasting skills than most research conducted in the Sahel region. The linear model driven by the Pacific SST produced the best rainfall forecasts (Ef = 0.82, R2 = 0.83, and H = 82%) at a lead time of up to 12 months. The rainfall forecasting model based on polynomial regression and forced by the Atlantic ocean SST can be used using a lead time of up to 5 months and had a slightly lower performance (Ef = 0.80, R2 = 0.81, and H = 82%). Despite the fact that the natural relationship between rainfall and SST is nonlinear, this study found that good results can be achieved using linear models. For streamflow forecasting, the direct method using polynomial regression performed slightly better than the indirect method (Ef = 0.74, R2 = 0.76, and H = 84% for the direct method; Ef = 0.70, R2 = 0.69, and H = 77% for the indirect method). The direct method was driven by the Pacific SST and had five months lead time. The indirect method was driven by the Atlantic SST and had six months lead time. No significant difference was found in terms of performance between BMA and the linear regression models based on a single predictor for streamflow forecasting. However, BMA was able to provide a probabilistic forecast that accounts for model selection uncertainty, while the linear regression model had a longer lead time. The economic value of forecasts developed using the direct and indirect methods were estimated using the cost/loss ratio method. It was found that the direct method had a better value than the indirect method. The value of the forecast declined with higher return periods for all methods. Results also showed that for the particular watershed under investigation, the direct method provided a better information for flood protection. This research has demonstrated the possibility of decent seasonal streamflow forecasting in the Sirba watershed, using the tropical Pacific and Atlantic SSTs as predictors.The findings of this study can be used to improve the performance of seasonal streamflow forecasting in the Sahel. A package implementing the statistical models developed in this study was developed so that end users can apply them for seasonal rainfall or streamflow forecasting in any region they are interested in, and using any predictor they may want to try.

Bayesian Generalized Nonlinear Models (BGNLM) offer a flexible alternative to GLM while still providing better interpretability than machine learning techniques such as neural networks. In BGNLM, the methods of Bayesian Variable Selection and Model Averaging are applied in an extended GLM setting. Models are fitted to data using MCMC within a genetic framework in an algorithm called GMJMCMC. In this thesis, we present a new implementation of the algorithm as a package in the programming language R. We also present a novel algorithm called S-IRLS-SGD for estimating the MLE of a GLM by subsampling the data. Finally, we present some theory combining the novel algorithm with GMJMCMC/MJMCMC/MCMC and a number of experiments demonstrating the performance of the contributed algorithm.

This thesis serves to investigate the varying effects of public health-care expenditure and private health-care expenditure on economic growth in developed and developing countries. I have contributed to the literature by using an expansive geographical dataset, lagged variables to address endogeneity, and model averaging techniques. I do so by first addressing the issue of model uncertainty, which is inherent in growth studies, by using Bayesian Model Averaging as the method of analysis in the thesis. Examination of 126 countries (32 developed and 94 developing) in the period 2000-2018 reveals that there is no variation in the impact of public health expenditure on economic growth between developed and developing countries. Contrary to public health expenditure, private health expenditure has a varying impact on both developed and developing countries. My analysis also reveals that the results hold when lagged variables are used in the model. Public health expenditure has unanimously a negative effect on economic growth in both developed and developing countries. Private health expenditure, on the other hand, has a positive impact on economic growth in developed and developing countries. Furthermore, I found that the results are robust to different model specifications. JEL Classification I15, O11,...

The current literature on international migration is diverse, and there is an ongoing debate as to the size and magnitude of the development-migration nexus, and no consensus about this effect has been reached. In this thesis, I explore quantitatively the effect of GDP (as a measure of development) on migration using a meta-analysis approach by synthesizing the empirical findings on this effect, adjusting for the biases, and controlling for the design of the studies. To examine the phenomenon in a systematic way, I collected 179 regression coefficients from 40 different articles, where the results suggest a weak presence of publication selection. Nevertheless, when correcting for publication bias, the effect of development on migration is rather small. Additionally, to explain the inherent model uncertainty, the Bayesian model averaging (BMA) was conducted. The results suggest that studies controlling for the variables of direct foreign investment and age results in a larger effect of development on migration and that the presence of country- level differences boosts migration inflows, particularly in OECD countries.

Using an early warning system (EWS) methodology, this thesis analyses the predictability of stock market crises from the perspective of behavioural fnance. Specifcally, in our EWS based on the multinomial logit model, we consider in- vestor sentiment as one of the potential crisis indicators. Identifcation of the relevant crisis indicators is based on Bayesian model averaging. The empir- ical results reveal that price-earnings ratio, short-term interest rate, current account, credit growth, as well as investor sentiment proxies are the most rele- vant indicators for anticipating stock market crises within a one-year horizon. Our thesis hence provides evidence that investor sentiment proxies should be a part of the routinely considered variables in the EWS literature. In general, the predictive power of our EWS model as evaluated by both in-sample and out-of-sample performance is promising. JEL Classifcation G01, G02, G17, G41 Keywords Stock market crises, Early warning system, In- vestor sentiment, Crisis prediction, Bayesian model averaging Title Predicting stock market crises using investor sentiment indicators