The lowland Maya site of Ceibal, Guatemala, had a long history of occupation, spanning from the Middle Preclassic Period through the Terminal Classic (1000 BC to AD 950). The Ceibal-Petexbatun Archaeological Project has been conducting archaeological investigations at this site since 2005 and has obtained 154 radiocarbon dates, which represent the largest collection of radiocarbon assays from a single Maya site. The Bayesian analysis of these dates, combined with a detailed study of ceramics, allowed us to develop a high-precision chronology for Ceibal. Through this chronology, we traced the trajectories of the Preclassic collapse around AD 150–300 and the Classic collapse around AD 800–950, revealing similar patterns in the two cases. Social instability started with the intensification of warfare around 75 BC and AD 735, respectively, followed by the fall of multiple centers across the Maya lowlands around AD 150 and 810. The population of Ceibal persisted for some time in both cases, but the center eventually experienced major decline around AD 300 and 900. Despite these similarities in their diachronic trajectories, the outcomes of these collapses were different, with the former associated with the development of dynasties centered on divine rulership and the latter leading to their downfalls. The Ceibal dynasty emerged during the period of low population after the Preclassic collapse, suggesting that this dynasty was placed under the influence from, or by the direct intervention of, an external power.

Social networks constitute a major channel for the diffusion of information and the formation of attitudes in a society. Introducing a dynamic model of social learning, the first part of this thesis studies the emergence of socially influential individuals and groups, and identifies the characteristics that make them influential. The second part uses a Bayesian network game to analyse the role of social interaction and conformism in the making of decisions whose returns or costs are ex ante uncertain.

We present a two-country New Open Economy Macro model of the Austrian economy within the European Union's Economic & Monetary Union (EMU). The model includes both nominal and real frictions that have proven to be important in matching business cycle facts, and that allows for an investigation of the effects and cross-country transmission of a number of structural shocks: shocks to technologies, shocks to preferences, cost-push type shocks and policy shocks. The model is estimated using Bayesian methods on quarterly data covering the period of 1976:Q1- 2005:Q1. In addition to the assessment of the relative importance of various shocks, the model also allows to investigate effects of the monetary regime switch with the final stage of the EMU and investigates in how far this has altered macroeconomic transmission. We find that Austria's economy appears to react stronger to demand shocks, while in the rest of the Euro Area supply shocks have a stronger impact. Comparing the estimations on pre-EMU and EMU subsamples we find that the contribution of (rest of the) Euro Area shocks to Austria's business cycle fluctuations has increased significantly. (author´s abstract) / Series: EI Working Papers / Europainstitut

Tropospheric ozone is one of the six criteria pollutants regulated by the United States Environmental Protection Agency under the Clean Air Act and has been linked with several adverse health effects, including mortality. Due to the strong dependence on weather conditions, ozone may be sensitive to climate change and there is great interest in studying the potential effect of climate change on ozone, and how this change may affect public health. In this paper we develop a Bayesian spatial model to predict ozone under different meteorological conditions, and use this model to study spatial and temporal trends and to forecast ozone concentrations under different climate scenarios. We develop a spatial quantile regression model that does not assume normality and allows the covariates to affect the entire conditional distribution, rather than just the mean. The conditional distribution is allowed to vary from site-to-site and is smoothed with a spatial prior. For extremely large datasets our model is computationally infeasible, and we develop an approximate method. We apply the approximate version of our model to summer ozone from 1997-2005 in the Eastern U.S., and use deterministic climate models to project ozone under future climate conditions. Our analysis suggests that holding all other factors fixed, an increase in daily average temperature will lead to the largest increase in ozone in the Industrial Midwest and Northeast. / Dissertation

System identification deals with the estimation of mathematical models from experimental data. As mathematical models are built for specific purposes, ensuring that the estimated model represents the system with sufficient accuracy is a relevant aspect in system identification. Factors affecting the accuracy of the estimated model include the experimental data, the manner in which the estimation method accounts for prior knowledge about the system, and the uncertainties arising when designing the experiment and initializing the search of the estimation method. As the accuracy of the estimated model depends on factors that can be affected by the user, it is of importance to guarantee that the user decisions are optimal. Hence, it is of interest to explore how to optimally perform an experiment in the system, how to account for prior knowledge about the system and how to deal with uncertainties that can potentially degrade the model accuracy. This thesis is divided into three topics. The first contribution concerns an input design framework for the identification of nonlinear dynamical models. The method designs an input as a realization of a stationary Markov process. As the true system description is uncertain, the resulting optimization problem takes the uncertainty on the true value of the parameters into account. The stationary distribution of the Markov process is designed over a prescribed set of marginal cumulative distribution functions associated with stationary processes. By restricting the input alphabet to be a finite set, the parametrization of the feasible set can be done using graph theoretical tools. Based on the graph theoretical framework, the problem formulation turns out to be convex in the decision variables. The method is then illustrated by an application to model estimation of systems with quantized measurements. The second contribution of this thesis is on Bayesian techniques for input design and estimation of dynamical models. In regards of input design, we explore the application of Bayesian optimization methods to input design for identification of nonlinear dynamical models. By imposing a Gaussian process prior over the scalar cost function of the Fisher information matrix, the method iteratively computes the predictive posterior distribution based on samples of the feasible set. To drive the exploration of this set, a user defined acquisition function computes at every iteration the sample for updating the predictive posterior distribution. In this sense, the method tries to explore the feasible space only on those regions where an improvement in the cost function is expected. Regarding the estimation of dynamical models, this thesis discusses a Bayesian framework to account for prior information about the model parameters when estimating linear time-invariant dynamical models. Specifically, we discuss how to encode information about the model complexity by a prior distribution over the Hankel singular values of the model. Given the prior distribution and the likelihood function, the posterior distribution is approximated by the use of a Metropolis-Hastings sampler. Finally, the existence of the posterior distribution and the correctness of the Metropolis-Hastings sampler is analyzed and established. As the last contribution of this thesis, we study the problem of uncertainty in system identification, with special focus in input design. By adopting a risk theoretical perspective, we show how the uncertainty can be handled in the problems arising in input design. In particular, we introduce the notion of coherent measure of risk and its use in the input design formulation to account for the uncertainty on the true system description. The discussion also introduces the conditional value at risk, which is a risk coherent measure accounting for the mean behavior of the cost function on the undesired cases. The use of risk coherent measures is also employed in application oriented input design, where the input is designed to achieve a prescribed performance in the intended model application. / <p>QC 20161216</p>

In recent years, there has been a growing need for causal analysis in many modern stream applications such as web page click monitoring, patient health care monitoring, stock market prediction, electric grid monitoring, and network intrusion detection systems. The detection and prediction of causal relationships help in monitoring, planning, decision making, and prevention of unwanted consequences. An event stream is a continuous unbounded sequence of event instances. The availability of a large amount of continuous data along with high data throughput poses new challenges related to causal modeling over event streams, such as (1) the need for incremental causal inference for the unbounded data, (2) the need for fast causal inference for the high throughput data, and (3) the need for real-time prediction of effects from the events seen so far in the continuous event streams. This dissertation research addresses these three problems by focusing on utilizing temporal precedence information which is readily available in event streams: (1) an incremental causal model to update the causal network incrementally with the arrival of a new batch of events instead of storing the complete set of events seen so far and building the causal network from scratch with those stored events, (2) a fast causal model to speed up the causal network inference time, and (3) a real-time top-k predictive query processing mechanism to find the most probable k effects with the highest scores by proposing a run-time causal inference mechanism which addresses cyclic causal relationships. In this dissertation, the motivation, related work, proposed approaches, and the results are presented in each of the three problems.

We propose a method to deal simultaneously with model uncertainty and correlated regressors in linear regression models by combining elastic net specifications with a spike and slab prior. The estimation method nests ridge regression and the LASSO estimator and thus allows for a more flexible modelling framework than existing model averaging procedures. In particular, the proposed technique has clear advantages when dealing with datasets of (potentially highly) correlated regressors, a pervasive characteristic of the model averaging datasets used hitherto in the econometric literature. We apply our method to the dataset of economic growth determinants by Sala-i-Martin et al. (Sala-i-Martin, X., Doppelhofer, G., and Miller, R. I. (2004). Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach. American Economic Review, 94: 813-835) and show that our procedure has superior out-of-sample predictive abilities as compared to the standard Bayesian model averaging methods currently used in the literature. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics

The article offers a dynamic approach for predicting the outcomes of NFL games using the NFL games from 2002-2005. A logistic regression model is used to predict the probability that one team defeats another. The parameters of this model are the strengths of the teams and a home field advantage factor. Since it assumed that a team's strength is time dependent, the strength parameters were assigned a seasonal time series process. The best model was selected using all the data from 2002 through the first seven weeks of 2005. The last weeks of 2005 were used for prediction estimates.

The path of steepest ascent can used to optimize a response in an experiment, but problems can occur with multiple responses. Past approaches to this issue such as Del Castillo’s overlap of confidence cones and Mee and Xiao’s Pareto Optimality, have not considered the correlations of the responses or parameter uncertainty. We propose a new method using the Bayesian reliability to calculate this direction. We utilize this method with four examples: a 2 factor, 2-response experiment where the paths of steepest ascent are similar, ensuring our results match Del Castillo’s and Mee and Xiao’s; a 2 factor, 2-response experiment with disparate paths of steepest ascent illustrating the importance of the Bayesian reliability; two simulation examples, showing parameter uncertainty is considered; and a 5 factor, 2-response experiment proving this method is not dimensional limited. With a Bayesian reliable point, a direction in multivariate steepest ascent can be found.

Performance of stock markets is determined by three classes of variables: macroeconomic indicators, industry & firm heterogeneity and third country effects. When assessing performance of a stock market index, impact of industry & firm heterogeneity is marginal as it is already embedded in the index through its constituent companies. This paper will therefore focus on the other two. Chinese stock market was selected as an application as their performance compared to other domestic indicators (mainly GDP growth) is considered inferior by many researchers. Using econometric framework for panel data and a Bayesian extension, the paper estimates multiple models of Chinese stock market performance examining individual determinants of it. Subsequently, it predicts development of theoretical prices of two main Chinese stock indices on two time samples until 2013. The paper then demonstrates underperformance of Chinese stock market by comparing the modeled prices to actual prices realized on the market. JEL Classification C23, C51, C53, G15, G17 Keywords underperformance, panel data, fixed effects model, Bayesian Model Averaging Author's e-mail roman_kovac@ymail.com Supervisor's e-mail karel.bata@seznam.cz