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Statistical analysis of interval data
Troshkov, Kirill ; Antoch, Jaromír (advisor) ; Branda, Martin (referee)
Traditional statistical analysis starts with computing the basic statisti- cal characteristics such as the population mean E, population variance V , cova- riance and correlation. In computing these characteristics, it is usually assumed that the corresponding data values are known exactly. In real life there are many situations in which a more complete information can be achieved by describing a set of statistical units in terms of interval data. For example, daily tempera- tures registered as minimum and maximum values offer a more realistic view on the weather conditions variations with respect to the simple average values. In environmental analysis, we observe a pollution level x(t) in a lake at different mo- ments of time t, and we would like to estimate standard statistical characteristics such as mean, variance and correlation with other measurements. Another exam- ple can be given by financial series. The minimum and the maximum transaction prices recorded daily for a set of stocks represent a more relevant information for experts in order to evaluate the stocks tendency and volatility in the same day. We must therefore modify the existing statistical algorithms to process such interval data. In this work we will analyze algorithms and their modifications for computing various statistics under...
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Interval solver for nonlinear constraints
Garajová, Elif ; Hladík, Milan (advisor) ; Pergel, Martin (referee)
The thesis is focused on the Sivia algorithm (Set Inverter via Interval Ana- lysis) designed for solving a continuous constraint satisfaction problem using interval methods and propagation techniques. Basic properties of the algorithm are derived, including the correction of its presented complexity bound. Some improvements concerning the testing of constraint satisfaction and optimiza- tion of the number of interval boxes describing the solution are proposed. The thesis also introduces contractors used to enhance the effectivity of the Sivia algorithm by reducing the interval boxes processed. Presented algorithms were implemented in a solver for nonlinear constraints with a simple visualization of the result using the Matlab language. A comparison of basic contractors on specific examples is given.
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Interval solver for nonlinear constraints
Garajová, Elif ; Hladík, Milan (advisor) ; Pergel, Martin (referee)
The thesis is focused on the Sivia algorithm (Set Inverter via Interval Ana- lysis) designed for solving a continuous constraint satisfaction problem using interval methods and propagation techniques. Basic properties of the algorithm are derived, including the correction of its presented complexity bound. Some improvements concerning the testing of constraint satisfaction and optimiza- tion of the number of interval boxes describing the solution are proposed. The thesis also introduces contractors used to enhance the effectivity of the Sivia algorithm by reducing the interval boxes processed. Presented algorithms were implemented in a solver for nonlinear constraints with a simple visualization of the result using the Matlab language. A comparison of basic contractors on specific examples is given.
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Statistical analysis of interval data
Troshkov, Kirill ; Antoch, Jaromír (advisor) ; Branda, Martin (referee)
Traditional statistical analysis starts with computing the basic statisti- cal characteristics such as the population mean E, population variance V , cova- riance and correlation. In computing these characteristics, it is usually assumed that the corresponding data values are known exactly. In real life there are many situations in which a more complete information can be achieved by describing a set of statistical units in terms of interval data. For example, daily tempera- tures registered as minimum and maximum values offer a more realistic view on the weather conditions variations with respect to the simple average values. In environmental analysis, we observe a pollution level x(t) in a lake at different mo- ments of time t, and we would like to estimate standard statistical characteristics such as mean, variance and correlation with other measurements. Another exam- ple can be given by financial series. The minimum and the maximum transaction prices recorded daily for a set of stocks represent a more relevant information for experts in order to evaluate the stocks tendency and volatility in the same day. We must therefore modify the existing statistical algorithms to process such interval data. In this work we will analyze algorithms and their modifications for computing various statistics under...
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Interval data and sample variance: computational aspects
Sokol, Ondřej ; Černý, Michal (advisor) ; Rada, Miroslav (referee)
This thesis deals with the calculation of the upper limit of the sample variance when the exact data are not known but intervals which certainly contain them are available. Generally, finding the upper limit of the sample variance knowing only interval data is an NP-hard problem, but under certain conditions imposed on the input data an appropriate efficient algorithm can be used. In this work algorithms were modified so that, even at the cost of exponential complexity, one can always find the optimal solution. The goal of this thesis is to compare selected algorithms for calculating the upper limit of sample variance over interval data from the perspective of the average computational complexity on the generated data. Using simulations it is shown that if the data meets certain conditions, the complexity of the average case is polynomial.
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Application of Monte Carlo method on DEA models with interval characteristics
Ficl, Vít ; Jablonský, Josef (advisor) ; Charvát, Karel (referee)
To determine the efficiency of homogeneous decision-making units, DEA models were developed. By these models, the efficiency is assessed based on the given data obtained from past observations. To determine the efficiency in the forthcoming period, it is necessary to work with stochastic data. In this case, it is appropriate to specify optimistic and pessimistic estimates for data to build an interval in which the data could occur. Models with imprecise characteristics could either be solved in optimization way by IDEA models, or by Monte Carlo simulation. Within the simulation, the median and also the probability of reaching the efficient frontier may be determined. For the purpose of applying the Monte Carlo method for DEA models with interval data, a special computer application was created, which was also used to solve a sample example.
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