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Life tables analysis using selected multivariate statistical methods
Bršlíková, Jana ; Vilikus, Ondřej (advisor) ; Miskolczi, Martina (referee)
The mortality is historically one of the most important demographic indicator and definitely reflects the maturity of each country. The objective of this diploma thesis is the comparison of mortality rates in analyzed countries around the world over time and among each other using the principle component analysis that allows assessing data different way. The big advantage of this method is minimal loss of information and quite understandable interpretation of mortality in each country. This thesis offers several interesting graphical outputs, that for example confirm higher mortality rate in Eastern European countries compared to Western European countries and show that Czech republic is country where mortality has fallen most in context of post-communist countries between 1990 and 2010. Source of the data is Human Mortality Database and all data were processed in statistical tool SPSS.
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Comparisons of discriminant analysis and classification trees
Dlabač, Jaroslav ; Vilikus, Ondřej (advisor) ; Stecenková, Marina (referee)
This bachelor thesis compares two methods to discrimination and classification of data in multivariate statistics analysis. While discriminant analysis represents the classical statistical method for discrimination and subsequent classification data method, CART is a new procedure in data-minig, which uses artificial intelligence. The first half of this work is devoted to theoretical description and comparison of these two methods. The second half is the demonstration of both methods on practical example. At the end, the results of both methods are compared and evaluated.
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Classification and Regression Trees in R
Nemčíková, Lucia ; Bašta, Milan (advisor) ; Vilikus, Ondřej (referee)
Tree-based methods are a nice add-on to traditional statistical methods when solving classification and regression problems. The aim of this master thesis is not to judge which approach is better but rather bring the overview of these methods and apply them on the real data using R. Focus is made especially on the basic methodology of tree-based models and the application in specific software in order to provide wide range of tool for reader to be able to use these methods. One part of the thesis touches the advanced tree-based methods to provide full picture of possibilities.
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The use of statistical methods in data mining in predicting consumer behaviour for Internet purchases
Podzimková, Michaela ; Vilikus, Ondřej (advisor) ; Berka, Petr (referee)
Data mining is a new discipline that occurs with increasing amount of stored data and the increasing need to obtain the information hidden in them. It is focused on the mining of potentially useful information from large data sets and it lies at the intersection of statistics, machine learning, artificial intelligence, databases and other areas. The aim of this thesis is to present the process of data mining with an emphasis on its connection with statistics and to describe a selection of statistical methods widely used in this field and which were also used in the applied data mining problem in this thesis. Real data from purchases in the online store show that using different methods gives different results and interesting information about purchasing behavior, and also proves that not all methods are always applicable to all types of tasks.
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Bayesian statistical modelling
Vilikus, Ondřej ; Hebák, Petr (advisor) ; Berka, Petr (referee) ; Militký, Jiří (referee)
Conjoint analysis is a popular method in consumer preferences research. One of the factors that caused the increasing popularity of this method in recent years is wide use of hierarchical Bayesian models which has been found invaluable in solving the problem of how to obtain reliable estimates of individual preferences without need for overloading respondents with too many conjoint tasks. First goal of my dissertation was to confirm whether the use of Bayesian models is the best choice under all circumstances or whether there are some limitations of this approach. For this purpose I conducted a study based on simulated datasets. Algorithm used enabled generation of datasets that differed in several parameters of interest but which were most comparable in other aspects. Results show that hierarchical models represent choice leading to highest accuracy in predicting respondents' choices in holdout tasks. Use of hierarchical models is most beneficial in the situation of strongly heterogeneous population yet limited amount of available data. In these cases we are able to capture the structure of heterogeneity with significantly lower number of choice task necessary from each respondent. Second goal of the dissertation was to answer the question whether we can increase also the effectiveness of the questioning in conjoint analysis by adding several direct questions. Suggested hybrid choice-based conjoint method (HCBC) combines conjoint analysis tasks with direct questions regarding the preference of levels for each attribute. These are used during the estimation of the model and for increasing the effectiveness if the conjoint analysis tasks design. The HCBC was compared with traditional choice-based conjoint (CBC) and adaptive choice-based conjoint (ACBC) based on practical study involving 421 respondents randomly assigned in one of three test groups. Suggested method has been found as useful alternative that can help with reducing number of choice task needed and as a solution for some situations when diverse importance of the attributes tested does not allow for indirect estimation of preferences with respect to all attributes tested.
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Srovnání bayesovského a četnostního přístupu
Ageyeva, Anna ; Hebák, Petr (advisor) ; Vilikus, Ondřej (referee)
The thesis deals with Bayesian approach to statistics and its comparison to frequentist approach. The main aim of the thesis is to compare frequentist and Bayesian approaches to statistics by analyzing statistical inferences, examining the question of subjectivity and objectivity in statistics. Another goal of the thesis is to draw attention to the importance and necessity to teach Bayesian statistics at our University more profound. The thesis includes three chapters. The first chapter presents a Bayesian approach to statistics and its main notions and principles. Statistical inferences are treated in the second chapter. The third chapter deals with comparing Bayesian and frequentist approaches. The final chapter concerns the place of Bayesian approach nowadays in science. Appendix concludes the list of Bayesian textbooks and Bayesian free software.
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History of bayesian statistics
Karel, Tomáš ; Hebák, Petr (advisor) ; Vilikus, Ondřej (referee)
The historical development of statistical theories contains a particular combat between Clasical (frequentist) and Bayessian School. This thesis brings near the history of this development, elaborates on possibilities about future applicability of Bayessian approach into other scientific areas and usability in teaching basic courses of statistics. The thesis summarizes important contributors and their significant contributions in Bayessian field. Their work helped to spread these methodes within scientific community. We briefly describe the differences between frequentist and bayesian approach. These are further demonstrated on two motivation examples. The same is carried on demostration of the differences between subjective approach and objective approach in probabilistic understanding and its influence on conducting the result. This work is aimed as the short introductory text for future students with the same for Bayessians as I posses.
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Frequentist and Bayesian inference
Shykhmanter, Dmytro ; Vilikus, Ondřej (advisor) ; Hebák, Petr (referee)
The thesis provides both theoretical and practical comparison of frequentist and Bayesian methods of statistical inference. Comparing of these two concepts begins with describing the philosophy of probability theory. Also is introduced the problem of determinism as well as three main probability interpretations. Statistical inference is a process of making general conclusions based on a given evidence. The frequentist statistics uses the observed data as an only evidence for its conclusions, while the Bayesian one is based on an idea that the subjective degree of belief can be also used for these purposes. Why should one disregard to his experience, knowledge or even intuition? Often happens that results of statistical data analysis are useless in sense that they come out not as it is expected. This situation is illustrated when there are a number of ski resorts which are graded on five star scale. If we look to the top ten, we will find that some of those should not belong there, though the data says they do. Generally the top positions are occupied by the objects with fewer reviews, while those with more reviews get lower average score. Bayesian data analysis methods enable to eliminate this kind of problem. Based on a prior information about the whole data set, every ski resort would get a fair score and as the result, the model would better represent the quality of the each resort based on the respondents' reviews.
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Market segmentation and cluster analysis
Zuzák, Jaroslav ; Vilikus, Ondřej (advisor) ; Hebák, Petr (referee)
This bachelor thesis deals with possibilities of statistic-analytical tools in market segmentation (i.e. a marketing concept), which is introduced as well. The theoretical part focuses on cluster analysis and its best-known algorithms, their assumptions and from those following possible usefulness and potential limitations. In the practical part a segmentation study of gallery and museum visitors is conducted on the basis of lifestyle and leasuretime activities variables. The resulting segments are profiled using other variables to create a more real-life image of the visitors and nonvisitors of galleries and museums.
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