The presented thesis investigates the identification of burst locations in water distribution systems (WDS) by analysis of field and simulation experimental data. This required the development of a new hybrid method of burst detection and sizing, and also a burst location identification algorithm. Generally, existing practice relies on a combination of some simple procedure and experience of the involved staff and cannot be easily automated. The practical methods are based on direct manifestation of burst on the surface or on systematically surveying suspected areas e.g. by using listening sticks, such methods are very time consuming. The proposed burst location algorithm is based on comparing data by means of statistical analysis of field data with results of water network simulation. An extended network hydraulic simulator is used to model pressure dependent leakage terms. The presence of a burst changes the flow pattern and also pressure at network nodes which may be used to estimate the burst size and its location. The influence of such random factors as demand flows and background leakage on the process of burst detection is also considered. The field data is from a generalised fixed area and variable area (FAVOR) test where inlet pressure is being stepped up and down and the following variables are measured: inlet flow, inlet pressure (head) and pressure at a number of selected sensitive nodes. The method has three stages and uses two different models, one is inlet flow model (IFM) to represent the total inlet flow and another is the extended hydraulic model to simulate different burst locations. Initially the presence of a potential burst is investigated. If this is confirmed precise values of the demand, background leakage flow and burst flow in IFM are subsequently estimated. They are used to identify the burst site at the third stage of the method. The method can be easily adapted for practical use. It requires data from experiments carried out at night between 1am and 5am and involves placing typically about 20 temporary loggers to collect the measurements during this period. It also requires the availability of a hydraulic model which normally is in the possession of a water company. The program has been implemented in the Matlab package and is easy to use. The current methodology is tuned to identify a single burst but can be generalised to identify locations of multiple bursts.

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Statistically more test samples obtained from a single chip would give a better picture of the various noise processes present. Increasing the number of samples while testing one chip would however lead to an increase in the testing time, decreasing the overall throughput. The aim of this report is to investigate the detection of non-Gaussian noise (burst noise) in a random set of data with a small number of samples. In order to determine whether a given set of noise samples has non-Gaussian noise processes present, a Chi-Squared ‘Goodness of Fit’ test on a modeled set of random data is presented. A discussion of test methodologies using a single test measurement pass as well as two passes is presented from the obtained simulation results. / text

Pagrindinis šio darbo tikslas susipažinti su steganografijos mokslu bei statistiniais stegoanalizės metodais, kurių dėka slepiama ir atrandama informacija įvairiuose failuose. Šitame magistro darbe išnagrinėti, aprašyti bei įgyvendinti du steganografijos ir du stegoanalizės metodai. Visi metodai realizuoti JAVA programavimo kalba, daliai matematiniams skaičiavimams atlikti panaudota MAPLE programa. Darbo pabaigoje pateikta metodų analizė. / The main goal of the thesis is to review the methods of steganography and steganalysis and to experiment with them. Steganography helps to embed hidden messages in such way that anyone except the intended recipient is unaware of the existence of the message but with the use of statistical steganalysis methods those hidden messages can be detected. This thesis consists of two steganography (LSB and LSBH) and two steganalysis methods (RS and PoV) description and implementation. All methods were implemented with JAVA code. Thesis is concluded with a comparison of these methods' quality.

This study was designed to determine whether chis-quared based tests for independence give reliable estimates (as compared to the exact values provided by Fisher's exact probabilities test) of the probability of a relationship between the variables in 3 X 3, 3 X 4 , and 3 X 5 contingency tables when the sample size is 10, 20, or 30. In addition to the classical (uncorrected) chi-squared test, four methods for continuity correction were compared to Fisher's exact probabilities test. The four methods were Yates' correction, two corrections attributed to Cochran, and Mantel's correction. The study was modeled after a similar comparison conducted on 2 X 2 contingency tables and published by Michael Haber.

The recent popularity of Bayesian inference is due to the practical advantages of the Bayesian approach. The Bayesian analysis makes it possible to reflect ones prior beliefs into the analysis. In this thesis, we explore some asymptotic results in Bayesian nonparametric inference for restricted and unrestricted space of distributions. This thesis is divided into two parts. In the first part, we employ the Dirichlet process in a hypothesis testing framework to propose a Bayesian nonparametric chi-squared goodness-of-fit test. Our suggested method corresponds to Lo's Bayesian bootstrap procedure for chi-squared goodness-of-fit test. Indeed, our bootstrap rectifies some shortcomings of regular bootstrap which only counts number of observations falling in each bin in contingency tables. We consider the Dirichlet process as the prior for the distribution of data and carry out the test based on the Kullback-Leibler distance between the Dirichlet process posterior and the hypothesized distribution. We prove that this distance asymptotically converges to the same chi-squared distribution as the classical frequentist's chi-squared test. Moreover, the results are generalized to the chi-squared test of independence for contingency tables. In the second part, our main focus is on Bayesian nonparametric inference for a restricted group of distributions called spherically symmetric distributions. We describe a Bayesian nonparametric approach to perform an inference for a bivariate spherically symmetric distribution. We place a Dirichlet invariant process prior on the set of all bivariate spherically symmetric distributions and derive the Dirichlet invariant process posterior. Indeed, our approach is an extension of the Dirichlet invariant process for the symmetric distributions on the real line to bivariate spherically symmetric distribution where the underlying distribution is invariant under a finite group of rotations. Further, we obtain the Dirichlet invariant process posterior for the infinite transformation group and we prove that it approaches a certain Dirichlet process. Finally, we develop our approach to obtain the Bayesian nonparametric posterior distribution for functionals of the distribution's support when the support satisfies certain symmetry conditions. When symmetry holds with respect to the parallel lines of axes (for example, in two dimensional space x = a and y = b) we employ our approach to approximate the distribution of certain functionals such as area and perimeter for the support of the distribution. This suggests a Bayesian nonparametric bootstrapping scheme. The estimates can be derived based on posterior averaging. Then, our simulation results demonstrate that our suggested bootstrapping technique improves the accuracy of the estimates.

The human cytomegalovirus (CMV) is one of the viruses which extensively infect in the world. In order to grow and reproduce, the CMV invades designated cellular lives and influences their behavior. The origin of replication (also called the replication origin) is a particular sequence in the CMV DNA genome at which replication is initiated. In this study, we develop some statistical tests of complementary palindromes, which can be applied to narrow the search for replication origin of the CMV DNA sequence. Let X_(2k) be the number of complementary palindromes with length 2k and Y_(2k) be the number of non-covered complementary palindromes with length 2k inside a given DNA sequence. Consider the null hypothesis that the marginal probabilities of the four nucleotides remain the same (1/4) over the given sequence versus the alternative hypothesis that the marginal probabilities are different. The likelihood ratio test based on the joint distributions of Y_(18) and Y_(2k) | (Y_(2(k+1)), ...,Y_(18)), where k=1, ..., 8, under the null and the alternative hypotheses are derived. The null distribution of the test statistic is approximated by a scaled chi-squared distribution. The scale parameter and the degree of freedom are estimated by the method of moments. The Pearson's chi-squared test based on the marginal distributions of X_(2k), where k=1, ..., 9. The null distribution of the test statistic is also approximated by a scaled chi-squared distribution. There is an another focus about ratios statistics X_(2k)/X_(2(k+1)) and Y_(2k)/Y_(2(k+1)), which approximate a specific value under the null hypotheses. Simulation studies are performed to confirm the theoretical findings.

For this project, a historical statistical analysis of the Amplitude of Mass Fluctuations ($\sigma_8$) and Hubble's Constant ($H_0$) parameters in the Standard Cosmological Model was carried out to determine whether or not the given error bars truly represent the dispersion of values. It was found through analysis of the Chi-Squared ($\chi^2$) values of the data that for $\sigma_8$ (60 data points and $\chi^2$ between 183.167 and 189.037) that the associated probability Q is extremely low, with $Q = 1.5597*10^{-15}$ for the weighted average and $Q = 1.2107*10^{-14}$ for the best fit of the data. This was also the case for the $\chi^2$ values (163 data points and $\chi^2$ between 484.3977 and 575.655) of $H_0$, where $Q = 4.2176*10^{-34}$ for the linear fit of the data and $Q = 1.0342*10^{-47}$ for the weighted average of the data. Through further analysis, it is shown in question, a linear fit is a better estimate of the data than the weighted average. The general conclusion is that the statistical error bars have been underestimated (in around 20\% of the measurements), or the systematic errors were not properly taken into account.

Taiwan Security Market is a typical order-driven market, and the business transactions are matched through the electronic trading system since 1988. In this work, we study the joint distributions of tick size changes of bid price and ask price, bid volume, and ask volume¡@for each matching order in Taiwan Stock Exchange (TSEC). Exponentially weighted moving average (EWMA) method is adopted to update the joint distribution of the incoming order variables aforementioned. Here we propose five methods to determine the update timing and consider three different initial matrices of the joint distributions. In empirical study, the daily matching data of two enterprises Uni-president Enterprises Corporation and Formosa Plastics Corporation in April, 2005 are considered. The goodness of fit for the joint distributions are determined by Chi-square Goodness of Fit Test. The results show that EWMA method provide good fit for most of the daily transaction data.

Master's thesis is focused on solution of the statistical problem to find a probability distribution of a discrete random variable on the basis of the observed data. These estimates are obtained by minimizing pseudo-quasinorm which is introduced here.The thesis further focuses on atributes of this pseudo-quasinorm. It also contains practical application of these methods.