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31	隨機森林分類方法於基因組顯著性檢定上之應用 / Assessing the significance of a Gene Set 卓達瑋 Unknown Date (has links) 在現今生物醫學領域中，一重要課題為透過基因實驗所獲得的量化資料，來研究與分析基因與外顯表型變數(phenotype)的相關性。已知多數已發展的方法皆屬於單基因分析法，無法適當的考慮基因之間的相關性。本研究主要針對基因組分析(gene set analysis)問題，提出統計檢定方法來驗證特定基因組的顯著性。為了能盡其所能的捕捉整體基因組與外顯表型變數的關係，我們結合了傳統的檢定方法與分類方法，提出以隨機森林分類方法(Random Forests)的測試組分類誤差值(test error)作為檢定統計量(test statistic)，並以其排列顯著值(permutation-based p-value)來獲得統計結論。我們透過模擬研究將本研究方法和其他七種基因組分析方法做比較，可發現本方法在型一誤差率(type I error rate)和檢定力(power)上皆有優異表現。最後，我們運用本方法在數個實際基因資料組的分析上，並深入探討所獲得結果。 / Nowadays microarray data analysis has become an important issue in biomedical research. One major goal is to explore the relationship between gene expressions and some specific phenotypes. So far in literatures many developed methods are single gene-based methods, which use solely the information of individual genes and cannot appropriately take into account the relationship among genes. This research focuses on the gene set analysis, which carries out the statistical test for the significance of a set of genes to a phenotype. In order to capture the relationship between a gene set and the phenotype, we propose the use of performance of a complex classifier in the statistical test: The test error rate of a Random Forests classification is adopted as the test statistic, and the statistical conclusion is drawn according to its permutation-based p-value. We compare our test with other seven existing gene set analyses through simulation studies. It’s found that our method has leading performance in terms of having a controlled type I error rate and a high power. Finally, this method is applied in several real examples and brief discussions on the results are provided. 外顯表型變數基因組分析隨機森林分類方法排列顯著值 phenotypes gene set analysis Random Forests permutation-based p-value
32	Matematické modelování kurzu koruny / Mathematical modelling of crown rate UHLÍŘOVÁ, Žaneta January 2015 (has links) This thesis is focused on mathematical modelling of exchange rate CZK/USD in 1991 - 2014. Time series was divided into 5 parts. First Box-Jenkins methodology models were examined, especially ARIMA model. Unfortunately, the model could not be used because none of the time series showed correlation. The time series is considered as a white noise. The data appear to be completely random and unpredictable. The time series have not constant variance neither normal distribution and therefore GARCH volatility model was used as the second model. It is better not to divide time series when using model of volatility. Volatility model contributes to more accurate prediction than the standard deviation. Results were calculated in RStudio software and MS Excel.
33	Bayesian Methods Under Unknown Prior Distributions with Applications to The Analysis of Gene Expression Data Rahal, Abbas 14 July 2021 (has links) The local false discovery rate (LFDR) is one of many existing statistical methods that analyze multiple hypothesis testing. As a Bayesian quantity, the LFDR is based on the prior probability of the null hypothesis and a mixture distribution of null and non-null hypothesis. In practice, the LFDR is unknown and needs to be estimated. The empirical Bayes approach can be used to estimate that mixture distribution. Empirical Bayes does not require complete information about the prior and hyper prior distributions as in hierarchical Bayes. When we do not have enough information at the prior level, and instead of placing a distribution at the hyper prior level in the hierarchical Bayes model, empirical Bayes estimates the prior parameters using the data via, often, the marginal distribution. In this research, we developed new Bayesian methods under unknown prior distribution. A set of adequate prior distributions maybe defined using Bayesian model checking by setting a threshold on the posterior predictive p-value, prior predictive p-value, calibrated p-value, Bayes factor, or integrated likelihood. We derive a set of adequate posterior distributions from that set. In order to obtain a single posterior distribution instead of a set of adequate posterior distributions, we used a blended distribution, which minimizes the relative entropy of a set of adequate prior (or posterior) distributions to a "benchmark" prior (or posterior) distribution. We present two approaches to generate a blended posterior distribution, namely, updating-before-blending and blending-before-updating. The blended posterior distribution can be used to estimate the LFDR by considering the nonlocal false discovery rate as a benchmark and the different LFDR estimators as an adequate set. The likelihood ratio can often be misleading in multiple testing, unless it is supplemented by adjusted p-values or posterior probabilities based on sufficiently strong prior distributions. In case of unknown prior distributions, they can be estimated by empirical Bayes methods or blended distributions. We propose a general framework for applying the laws of likelihood to problems involving multiple hypotheses by bringing together multiple statistical models. We have applied the proposed framework to data sets from genomics, COVID-19 and other data. Robust Bayesian statistics Imprecise probability Bayesian model checking Blended inference Posterior predictive p-value Local false discovery rate Empirical Bayes Multiple testing Bayesian false discovery rate Measure of evidence Direct likelihood inference Likelihoodism
34	Modelling and controlling risk in energy systems Gonzalez, Jhonny January 2015 (has links) The Autonomic Power System (APS) grand challenge was a multi-disciplinary EPSRC-funded research project that examined novel techniques that would enable the transition between today's and 2050's highly uncertain and complex energy network. Being part of the APS, this thesis reports on the sub-project 'RR2: Avoiding High-Impact Low Probability events'. The goal of RR2 is to develop new algorithms for controlling risk exposure to high-impact low probability (Hi-Lo) events through the provision of appropriate risk-sensitive control strategies. Additionally, RR2 is concerned with new techniques for identifying and modelling risk in future energy networks, in particular, the risk of Hi-Lo events. In this context, this thesis investigates two distinct problems arising from energy risk management. On the one hand, we examine the problem of finding managerial strategies for exercising the operational flexibility of energy assets. We look at this problem from a risk perspective taking into account non-linear risk preferences of energy asset managers. Our main contribution is the development of a risk-sensitive approach to the class of optimal switching problems. By recasting the problem as an iterative optimal stopping problem, we are able to characterise the optimal risk-sensitive switching strategies. As byproduct, we obtain a multiplicative dynamic programming equation for the value function, upon which we propose a numerical algorithm based on least squares Monte Carlo regression. On the other hand, we develop tools to identify and model the risk factors faced by energy asset managers. For this, we consider a class of models consisting of superposition of Gaussian and non-Gaussian Ornstein-Uhlenbeck processes. Our main contribution is the development of a Bayesian methodology based on Markov chain Monte Carlo (MCMC) algorithms to make inference into this class of models. On extensive simulations, we demonstrate the robustness and efficiency of the algorithms to different data features. Furthermore, we construct a diagnostic tool based on Bayesian p-values to check goodness-of-fit of the models on a Bayesian framework. We apply this tool to MCMC results from fitting historical electricity and gas spot price data- sets corresponding to the UK and German energy markets. Our analysis demonstrates that the MCMC-estimated models are able to capture not only long- and short-lived positive price spikes, but also short-lived negative price spikes which are typical of UK gas prices and German electricity prices. Combining together the solutions to the two problems above, we strive to capture the interplay between risk, uncertainty, flexibility and performance in various applications to energy systems. In these applications, which include power stations, energy storage and district energy systems, we consistently show that our risk management methodology offers a tradeoff between maximising average performance and minimising risk, while accounting for the jump dynamics of energy prices. Moreover, the tradeoff is achieved in such way that the benefits in terms of risk reduction outweigh the loss in average performance. 510
35	IMPACT BEHAVIOR OF AMMONIUM PERCHLORATE (AP) - HYDROXYL-TERMINATED POLYBUTADIENE (HTPB) COMPOSITE MATERIAL Saranya Ravva (15353902) 25 April 2023 (has links) <p>This work investigated the effects of varying the crystal sizes of ammonium perchlorate (AP) when embedded with a polymeric binder, hydroxyl-terminated polybutadiene (HTPB) on impact-induced temperature behavior. AP and HTPB are the most used oxidizers and fuel binders in the aerospace solid rocket design industry. In this study, samples of 200 µm and 400µm coarse AP crystals in HTPB were constructed using a conventional hand-mixing method. Using a parametric optimization technique such as the Taguchi method, direct-ink-writing as the additive manufacturing process was used for achieving the required shape fidelity in printing HTPB and by introducing ultraviolet polymers to decrease the curing time.</p> <p>A drop hammer experiment in conjunction with an infrared camera was used to study the impact-induced behavior in the conventionally made AP-HTPB samples. The thermal images obtained from the camera at millisecond resolution are invaluable and provide information about distribution across the sample surface, and the evolution of temperature rise observed in the samples which are complex and not easily understood otherwise and therefore help in improving and attaining desired propellant performance. A two-sample t-Test has been utilized to infer the results and statistical nonsignificance has been observed in the highest temperature rises among 200 µm and 400 µm AP-HTPB sample conditions but a difference in temperature distribution has been observed. A much uniform distribution of temperature over the sample surface on impact is observed in thermal images of 200 µm AP-HTPB sample condition compared to 400 µm AP-HTPB sample condition.</p> Aerospace materials Aerospace structures Additive manufacturing Composite and hybrid materials Ammonium Perchlorate (AP) Hydroxyl-Terminated Polybutadiene (HTPB) Impact Testing Aerospace Engineering Additive Manufacturing Direct Ink Writing Parametric Optimization Taguchi Method Drop Hammer Impact IR camera Solid Rocket Propellant APCP T-test p-value Aerospace Materials
36	Statistical Inference Chou, Pei-Hsin 26 June 2008 (has links) In this paper, we will investigate the important properties of three major parts of statistical inference: point estimation, interval estimation and hypothesis testing. For point estimation, we consider the two methods of finding estimators: moment estimators and maximum likelihood estimators, and three methods of evaluating estimators: mean squared error, best unbiased estimators and sufficiency and unbiasedness. For interval estimation, we consider the the general confidence interval, confidence interval in one sample, confidence interval in two samples, sample sizes and finite population correction factors. In hypothesis testing, we consider the theory of testing of hypotheses, testing in one sample, testing in two samples, and the three methods of finding tests: uniformly most powerful test, likelihood ratio test and goodness of fit test. Many examples are used to illustrate their applications. finite population correction factor statistical hypothesis type I error composite hypothesis power Central limit theorem Basu theorem critical value goodness of fit test likelihood ratio test Lehmann-Scheffe theorem complete statistic ancillary statistic P-value type II error Rao-Blackwell theorem simple hypothesis one-sided test two-sided test significance level sufficient statistic alternative hypothesis testing hypothesis null hypothesis rejection region confidence interval confidence level minimum variance unbiased estimator interval estimation uniformly most powerful test Cramer-Rao inequality likelihood function mean square error moment estimator error of estimation point estimation maximum likelihood estimator bias consistent estimator minimal sufficient statistic factorization theorem unbiased estimator statistic most powerful test test statistics Neyman-Pearson lemma decision rule

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