Attention allows us to monitor objects or regions of visual space and extract information from them to use for report or storage. Classical theories of attention assumed a single focus of selection but many everyday activities, such as playing video games, suggest otherwise. Nonetheless, the underlying mechanism which can explain the ability to divide attention has not been well established. Numerous attempts have been made in order to clarify divided attention, including analytical strategies as well as methods working with visual phenomena, even more sophisticated predictors incorporating information about past selection decisions. Virtually all the attempts approach this problem by constructing a simplified model of attention. In this study, we develop a version of the existing Bayesian framework to propose such models, and evaluate their ability to generate eye movement trajectories. For the comparison of models, we use the eye movement trajectories generated by several analytical strategies. We measure the similarity between...

Attention allows us to monitor objects or regions of visual space and extract information from them to use for report or storage. Classical theories of attention assumed a single focus of selection but many everyday activities, such as playing video games, suggest otherwise. Nonetheless, the underlying mechanism which can explain the ability to divide attention has not been well established. Numerous attempts have been made in order to clarify divided attention, including analytical strategies as well as methods working with visual phenomena, even more sophisticated predictors incorporating information about past selection decisions. Virtually all the attempts approach this problem by constructing a simplified model of attention. In this study, we develop a version of the existing Bayesian framework to propose such models, and evaluate their ability to generate eye movement trajectories. For the comparison of models, we use the eye movement trajectories generated by several analytical strategies. We measure the...

The goal of this thesis was to implement a practical tool for optimizing hy- perparameters of neural networks using Bayesian optimization. We show the theoretical foundations of Bayesian optimization, including the necessary math- ematical background for Gaussian Process regression, and some extensions to Bayesian optimization. In order to evaluate the performance of Bayesian op- timization, we performed multiple real-world experiments with different neural network architectures. In our comparison to a random search, Bayesian opti- mization usually obtained a higher objective function value, and achieved lower variance in repeated experiments. Furthermore, in three out of four experi- ments, the hyperparameters discovered by Bayesian optimization outperformed the manually designed ones. We also show how the underlying Gaussian Process regression can be a useful tool for visualizing the effects of each hyperparameter, as well as possible relationships between multiple hyperparameters. 1

Bayesian factor analysis - abstract Factor analysis is a method which enables high-dimensional random vector of measurements to be approximated by linear combinations of much lower number of hidden factors. Classical estimation procedure of this model lies on the cho- ice of the number of factors, the decomposition of variance matrix while keeping identification conditions satisfied and on the appropriate choice of rotation for better interpretation of the model. This model will be transferred into bayesian framework which offers the usage of prior information unlike the classical appro- ach. The number of hidden factors can be considered as a random parameter and the dependency of each measurement on at most one factor can be forced by suitable specification of prior distribution. Estimates of model parameters are based on posterior distribution which is approximated by Monte Carlo Markov Chain methods. Bayesian approach solves the problem of selection of the num- ber of factors, the model estimation and the ensuring of the identifiability and the interpretability at the same time. The ability to estimate the real number of hidden factors is tested in a simulation study. 1

The purpose of this thesis is to find how we can use Bayesian statistics in analysis of sociological data and to compare outcomes of frequentist and Bayesian approach. Bayesian statistics uses probability distributions on statistical parameters. In the beginning of the analysis in Bayesian approach a prior probability (that is chosen on the basis of relevant information) is attached to the parameters. After combining prior probability and our observed data, posterior probability is computed. Because of the posterior probability we can make statistical conclusions. Comparison of approaches was made from the view of theoretical foundations and procedures and also by means of analysis of sociological data. Point estimates, interval estimates, hypothesis testing (on the example of two-sample t-test) and multiple linear regression analysis were compared. The outcome of this thesis is that considering its philosophy and thanks to the interpretational simplicity the Bayesian analysis is more suitable for sociological data analysis than common frequentist approach. Comparison showed that there is no difference between outcomes of frequentist and objective Bayesian analysis regardless of the sample size. For hypothesis testing we can use Bayesian credible intervals. Using subjective Bayesian analysis on...

We present an innovative Bayesian method for estimation of statistical parameters of time series data. This method works by comparing coefficients of Karhunen-Lo\`{e}ve expansion of observed and synthetic data with known parameters. We show one new method for generating synthetic data with prescribed properties and we demonstrate on a numerical example how this method can be used for estimation of physically interesting features in power spectra calculated from observed light curves of some X-ray sources.

This master's thesis deals with possible applications of Bayesian networks. The theoretical part is mainly of mathematical nature. At first, we focus on general probability theory and later we move on to the theory of Bayesian networks and discuss approaches to inference and to model learning while providing explanations of pros and cons of these techniques. The practical part focuses on applications that demand learning a Bayesian network, both in terms of network parameters as well as structure. These applications include general benchmarks, usage of Bayesian networks for knowledge discovery regarding the causes of criminality and exploration of the possibility of using a Bayesian network as a spam filter.

We have performed 3D ambient noise tomography of the Bohemian Massif. We invert adopted inter-station dispersion curves of both Love and Rayleigh waves in periods 4-20 s, which were extracted from ambient noise cross-correlations, using a two-step approach. In the first step, the inter-station dispersion curves are localized for each period into the so-called dispersion maps. To account for finite-frequency effects, gradient method employing Fréchet kernels is used. Assuming membrane wave approximation of the surface wave propagation at each period, the kernels were calculated using the adjoint method. To reduce the effect of data noise, the kernels were regularized by Gaussian smoothing. The proper level of regularization is assessed on synthetic tests. In the second step, the phase-velocity dispersion maps are inverted into a 3D S-wave velocity model using the Bayesian approach. The posterior probability density function describing the solution is sampled by more than one million models obtained by Monte-Carlo approach (parallel tempering). The calculated variance of the model shows that the well resolved part corresponds to the upper crust (i.e., upper 20 km). The mean velocity model contains mainly large scale structures that show good correlation with the main geologic domains of the Bohemian...

Do investors make bad decisions following the clock change? If so, there would be traces of such anomaly in market data. In this thesis, we investigate these traces focusing on the stock markets of the Visegrad Group, known to be pre- vailingly illiquid. We combine the most recent financial data with the ARIMA- GARCH framework while employing brand-new Bayesian techniques. Using several robustness checks, we show that such e ect cannot be traced in these markets. While we do not claim to challenge the seminal works in this field, we do support the evidence that the e ects of daylight saving policy do not pertain to less liquid markets. JEL Classification C11, G12, G14, G41 Keywords daylight saving time, market anomaly, Visegrad Group, Bayesian analysis Title Daylight Saving Time and Stock Market Re- turns: Evidence from the Visegrad Group

Community ecology from the perspective of classic and Bayesian statistics Ekologie společenstev z hlediska klasické a Bayesovské statistiky Řešitel: Adam Klimeš Vedoucí práce: Mgr. Petr Keil, Ph.D. Abstract Quantitative evaluation of evidence through statistics is a central part of present-day science. Bayesian approach represents an emerging but rapidly developing enrichment of statistical analysis. The approach differs in its foundations from the classic methods. These differences, such as the different interpretation of probability, are often seen as obstacles for acceptance of Bayesian approach. In this thesis I outline ways to deal with the assumptions of Bayesian approach, and I address the main objections against it. I present Bayesian approach as a new way to handle data to answer scientific questions. I do this from a standpoint of community ecology: I illustrate the novelty that Bayesian approach brings to data analysis of typical community ecology data, specifically, the analysis of multivariate datasets. I focus on principal component analysis, one of the typical and frequently used analytical techniques. I execute Bayesian analyses that are analogical to the classic principal components analysis, I report the advantages of the Bayesian version, such as the possibility of working with...