Pharmacometric model-based analysis using nonlinear mixed-effects models (NLMEM) has to date mainly been applied to learning activities in drug development. However, such analyses can also serve as the primary analysis in confirmatory studies, which is expected to bring higher power than traditional analysis methods, among other advantages. Because of the high expertise in designing and interpreting confirmatory studies with other types of analyses and because of a number of unresolved uncertainties regarding the magnitude of potential gains and risks, pharmacometric analyses are traditionally not used as primary analysis in confirmatory trials. The aim of this thesis was to address current hurdles hampering the use of pharmacometric model-based analysis in confirmatory settings by developing strategies to increase model compliance to distributional assumptions regarding the residual error, to improve the quantification of parameter uncertainty and to enable model prespecification. A dynamic transform-both-sides approach capable of handling skewed and/or heteroscedastic residuals and a t-distribution approach allowing for symmetric heavy tails were developed and proved relevant tools to increase model compliance to distributional assumptions regarding the residual error. A diagnostic capable of assessing the appropriateness of parameter uncertainty distributions was developed, showing that currently used uncertainty methods such as bootstrap have limitations for NLMEM. A method based on sampling importance resampling (SIR) was thus proposed, which could provide parameter uncertainty in many situations where other methods fail such as with small datasets, highly nonlinear models or meta-analysis. SIR was successfully applied to predict the uncertainty in human plasma concentrations for the antibiotic colistin and its prodrug colistin methanesulfonate based on an interspecies whole-body physiologically based pharmacokinetic model. Lastly, strategies based on model-averaging were proposed to enable full model prespecification and proved to be valid alternatives to standard methodologies for studies assessing the QT prolongation potential of a drug and for phase III trials in rheumatoid arthritis. In conclusion, improved methods for handling residual error, parameter uncertainty and model uncertainty in NLMEM were successfully developed. As confirmatory trials are among the most demanding in terms of patient-participation, cost and time in drug development, allowing (some of) these trials to be analyzed with pharmacometric model-based methods will help improve the safety and efficiency of drug development.

This paper uses Bayesian Model Averaging (BMA) to find robust determinants of economic growth in a new dataset of 255 European regions between 1995 and 2005. The paper finds that income convergence between countries is dominated by the catching-up of regions in new member states in Central and Eastern Europe (CEE), whereas convergence within countries is driven by regions in old EU member states. Regions containing capital cities are growing faster, particularly in CEE countries, as do regions with a large share of workers with higher education. The results are robust to allowing for spatial spillovers among European regions.

Understanding the determinants of aggregated default probabilities (PDs) has attracted substantial research over the past decades. This study addresses two major difficulties in understanding the determinants of aggregate PDs: Model uncertainty and multicollinearity among the regressors. We present Bayesian Model Averaging (BMA) as a powerful tool that overcomes model uncertainty. Furthermore, we supplement BMA with ridge regression to mitigate multicollinearity. We apply our approach to an Austrian dataset. Our findings suggest that factor prices like short term interest rates and energy prices constitute major drivers of default rates, while firms' profits reduce the expected number of failures. Finally, we show that the results of our baseline model are fairly robust to the choice of the prior model size. / Series: Research Report Series / Department of Statistics and Mathematics

The spread between interest rate and sovereign bond rate is commonly used in- dicator for country's probability to default. Existing literature proposes many different potential spread determinants but fails to agree on which of them are important. As a result, there is a considerable uncertainty about the cor- rect model explaining the spread. We address this uncertainty by employing Bayesian Model Averaging method (BMA). The BMA technique attempts to consider all the possible combinations of variables and averages them using a model fit measure as weights. For this empirical exercise, we consider 20 different explanatory variables for a panel of 47 countries for the 1980-2010 period. Most of the previously suggested determinants were attributed high inclusion probabilities. Only the "foreign exchange reserves growth" and the "exports growth" scored low by their inclusion probabilities. We also find a role of variables previously not included in the literature's spread determinants - "openness" and "unemployment" which rank high by the inclusion probability. These results are robust to a wide range of both parameter and model priors. JEL Classification C6, C8, C11, C51, E43 Keywords Sovereign Spread Determinants, Model Uncer- tainty, Bayesian Model Averaging Author's e-mail semanv()gmail()com...

Inflation is one of the often used monetary indicators in conducting monetary policy. Even though money supply is an essential determinant of inflation, it is not used in inflation modeling. Currently, output gap is considered as most predicative variable. This thesis brings the empirical evidence on the hypothesis of money supply carrying more information on estimating inflation than the output gap. It is provided on the case of 16 developed European economies using Bayesian Model Averaging (BMA). BMA is a comprehensive approach that deals with the model uncertainty and thus solves the variable selection problem. The results of analysis confirmed that money supply includes more information of inflation than the output gap and thus should be used in inflation modeling. These outcomes are robust towards prior selection and high correlation of some variables.

The model uncertainty is a phenomenon where general consensus about the form of specific model is unclear. Stock returns perfectly meet this condition, as extensive literature offers diverse methods and potential drivers without a clear winner among them. Relatively recently, averaging techniques emerged as a possible solution to such scenarios. The two major averaging branches, Bayesian (BMA) and Frequentist (FMA) averaging, naturally deal with uncertainty by averaging over all model candidates rather than choosing the "best" one of them. We focus on FMA and apply this method to our data from U.S. market about S&P 500 index, that I help to explain with the set of eleven explanatory variables chosen in accordance with related literature. To preserve a real-world applicability, I use rolling window scheme to regularly update data in the fitting model for quarterly based re- estimation. Consequently, predictions are obtained with the use of most recent data. Firstly, we find out that simple historical average model can be beaten with a standard model selection approach based on AIC value, with variables as Dividend Yield, Earnings ratio, and Book-to-Market value proving consistently as most significant across quarterly models. With FMA techniques, I was not able to consistently beat the benchmark...

In this paper, we examine the determinants of outward FDI from four major OECD investors, namely, the US, Germany, France, and the Netherlands, to 129 developing countries classified under five regions over the period 1995-2008. Our goal is to distinguish whether the motivation for FDI differs among these investors in developing countries. Rather than relying on specific theories of FDI determinants, we examine them all simultaneously by employing Bayesian model averaging (BMA). This approach permits us to select the most appropriate model (or combination of models) that governs FDI allocation and to distinguish robust FDI determinants. We find that no single theory governs the decision of OECD FDI in developing countries but a combination of theories. In particular, OECD investors search for destinations with whom they have established intensive trade relations and that offer a qualified labor force. Low wages and attractive tax rates are robust investment criteria too, and a considerable share of FDI is still resource-driven. Overall, investors show fairly similar strategies in the five developing regions.

Topic of mergers and acquisitions (M&A) is popular both in academia and financial circles and press. A great deal of research has been focused on the value creation side of M&A deals, nonetheless factors influencing the particular method of payment used in M&A transactions are equally interesting. This thesis focuses on number of factors influencing the choice of medium of exchange in M&A deals with European Union domiciled bidders. Using Bayesian model averaging and a relatively new dataset of transactions announced between 2010 and 2018, the analysis finds several bidder, target and deal specific characteristics to be of a provable effect on the choice of payment. Finally, several enhancements and research questions for a further research are identified.

This manuscript consists of two papers that formulate novel methodologies pertaining to time series analysis in the state-space framework. In Chapter 1, we introduce an innovative time series forecasting procedure that relies on model-based clustering and model averaging. The clustering algorithm employs a state-space model comprised of three latent structures: a long-term trend component; a seasonal component, to capture recurring global patterns; and an anomaly component, to reflect local perturbations. A two-step clustering algorithm is applied to identify series that are both globally and locally correlated, based on the corresponding smoothed latent structures. For each series in a particular cluster, a set of forecasting models is fit, using covariate series from the same cluster. To fully utilize the cluster information and to improve forecasting for a series of interest, multi-model averaging is employed. We illustrate the proposed technique in an application that involves a collection of monthly disease incidence series. In Chapter 2, to effectively characterize a count time series that arises from a zero-inflated binomial (ZIB) distribution, we propose two classes of statistical models: a class of observation-driven ZIB (ODZIB) models, and a class of parameter-driven ZIB (PDZIB) models. The ODZIB model is formulated in the partial likelihood framework. Common iterative algorithms (Newton-Raphson, Fisher Scoring, and Expectation Maximization) can be used to obtain the maximum partial likelihood estimators (MPLEs). The PDZIB model is formulated in the state-space framework. For parameter estimation, we devise a Monte Carlo Expectation Maximization (MCEM) algorithm, using particle methods to approximate the intractable conditional expectations in the E-step of the algorithm. We investigate the efficacy of the proposed methodology in a simulation study, and illustrate its utility in a practical application pertaining to disease coding.

This thesis concerns the phylogenetic relationships and the evolution of the gall-inducing wasps belonging to the family Cynipidae. Several previous studies have used morphological data to reconstruct the evolution of the family. DNA sequences from several mitochondrial and nuclear genes where obtained and the first molecular, and combined molecular and morphological, analyses of higher-level relationships in the Cynipidae is presented. A Bayesian approach to data analysis is adopted, and models allowing combined analysis of heterogeneous data, such as multiple DNA data sets and morphology, are developed. The performance of these models is evaluated using methods that allow the estimation of posterior model probabilities, thus allowing selection of most probable models for the use in phylogenetics. The use of Bayesian model averaging in phylogenetics, as opposed to model selection, is also discussed. It is shown that Bayesian MCMC analysis deals efficiently with complex models and that morphology can influence combined-data analyses, despite being outnumbered by DNA data. This emphasizes the utility and potential importance of using morphological data in statistical analyses of phylogeny. The DNA-based and combined-data analyses of cynipid relationships differ from previous studies in two important respects. First, it was previously believed that there was a monophyletic clade of woody rosid gallers but the new results place the non-oak gallers in this assemblage (tribes Pediaspidini, Diplolepidini, and Eschatocerini) outside the rest of the Cynipidae. Second, earlier studies have lent strong support to the monophyly of the inquilines (tribe Synergini), gall wasps that develop inside the galls of other species. The new analyses suggest that the inquilines either originated several times independently, or that some inquilines secondarily regained the ability to induce galls. Possible reasons for the incongruence between morphological and DNA data is discussed in terms of heterogeneity in evolutionary rates among lineages, and convergent evolution of morphological characters.