Generating Random Vectors Using Transformation with Multiple Roots and its Applications

An approach is proposed to generate random vectors using transformation with multiple roots. This approach generalizes the one-dimensional inverse transformation with multiple roots method to higher dimensions, i.e., to random vectors with or without densities. In this approach, multiple roots of the transformation and probabilities of selecting each of the roots are derived. The strategies for constructing such a transformation are discussed and several examples are presented to motivate this simulation approach

[[alternative]]Stochastic Estimation Model for Uncertain Cost Elements

計畫編號：NSC94-2211-E032-020研究期間：200508~200607研究經費：350,000[[abstract]]本研究將提出以蒙地卡羅方法從事不確定性營建專案估價之模式。研究方法為應用多變量隨機亂數產生法中之高斯關連結構來處理具相關特性之成本項目。為求突破其他模式之限制，本研究提出之模式將處理：(1)成本項目具有不同的統計分佈型式(有些為連續分佈、有些為間斷分佈；有些為對稱分佈、有些為偏態分佈)；(2)相關特性可以用傳統線性或等級相關係數加以描述；(3)成本項目具有複雜的相關情況；(4)自動化近似非半正定性相關值矩陣以滿足數學理論要求。主要研究步驟為：首先近似相關值矩陣；再就可行之相關性調整具高斯分佈之隨機亂數；依據各式分佈之反函數將高斯隨機亂數轉換為各式成本項目之估計值；最後就所有估計值進行不確定性營建專案估價。本研究提出之模式將尋求應用於實務案例，並就結果之統計相關性與原先設定加以比較驗證。模擬結果將可實證指出成本項目之相關特性對專案成本造成之顯著影響。 關鍵詞：專案估價、風險評估、蒙地卡羅方法、高斯關連結構、統計分析[[sponsorship]]行政院國家科學委員

Independently Controlling Stochastic Field Realization Magnitude and Phase Statistics for the Construction of Novel Partially Coherent Sources

In this paper, we present a method to independently control the field and irradiance statistics of a partially coherent beam. Prior techniques focus on generating optical field realizations whose ensemble-averaged autocorrelation matches a specified second-order field moment known as the cross-spectral density (CSD) function. Since optical field realizations are assumed to obey Gaussian statistics, these methods do not consider the irradiance moments, as they, by the Gaussian moment theorem, are completely determined by the field’s first and second moments. Our work, by including control over the irradiance statistics (in addition to the CSD function), expands existing synthesis approaches and allows for the design, modeling, and simulation of new partially coherent beams, whose underlying field realizations are not Gaussian distributed. We start with our model for a random optical field realization and then derive expressions relating the ensemble moments of our fields to those of the desired partially coherent beam. We describe in detail how to generate random optical field realizations with the proper statistics. We lastly generate two example partially coherent beams using our method and compare the simulated field and irradiance moments theory to validate our technique

Influence Diagnostics for Generalized Estimating Equations Applied to Correlated Categorical Data

Influence diagnostics in regression analysis allow analysts to identify observations that have a strong influence on model fitted probabilities and parameter estimates. The most common influence diagnostics, such as Cook’s Distance for linear regression, are based on a deletion approach where the results of a model with and without observations of interest are compared. Here, deletion-based influence diagnostics are proposed for generalized estimating equations (GEE) for correlated, or clustered, nominal multinomial responses. The proposed influence diagnostics focus on GEEs with the baseline-category logit link function and a local odds ratio parameterization of the association structure. Formulas for both observation- and cluster-deletion diagnostics are provided which are multivariate extensions of the current one-step approximation approaches used for GEEs with univariate marginal responses. Simulation studies were conducted to evaluate the accuracies of the one-step diagnostics in multinomial GEE as well as in other commonly used categorical response models. Applications are presented on 2017-2018 English Premier League shot-outcome data and on a cohort study on small renal mass histologic subtype distributions

Generating non-normal distributions : methods and effects

Many inferential statistical tests require that the observed variables have a normal distribution. Monte Carlo simulations are used to investigate the effect of violating this assumption and require an algorithm that generates samples from non-normal distributions, thereby controlling correlations among random variables, the marginal distributions, and the multivariate distribution. Most previously used algorithms only allow control over the correlations and the marginals, but recent results show that the robustness of certain methods depends on the multivariate distribution as well. In my thesis, I suggest a new method to generate samples from non-normal distributions that allows manipulations of all three parameters simultaneously. The algorithm jointly controls the correlation matrix, central moments of the marginals, and the multivariate distribution. Additionally, I also show that the multivariate distribution has a distinct impact on the robustness of a structural equation model, whereas extraction criteria for exploratory factor analysis are unaffected by the underlying distribution

On Compositional Data Modeling and Its Biomedical Applications

Compositional data occur naturally in biomedical studies which investigate changes in the proportions of various components of a combined medical measurement. The statistical method to analyze this type of data is underdeveloped. Currently the multivariate logitnormal model seems to be the only model routinely used in analyzing compositional data, and its application is mainly in geology and has yet to be known to the biomedical elds. In this dissertation, we propose the multivariate simplex model as an alternative method of modeling compositional data, either cross-sectional or longitudinal and develop statistical methods to analyze such data. We suggest three approaches to making a fair comparison between the multivariate simplex models and the multivariate logit-normal models. The simulations indicate that our proposed multivariate simplex models often outperform the multivariate logit-normal models

SHALLOW-WATER SENSOR PLACEMENT

Placing acoustic sensors allows for remote detection of vessels in areas of interest. We study the problem of placing only a few sensors to effectively monitor signals at many locations. Though our approach applies to sensor placement problems generally, we focus on placing hydrophones to efficiently monitor acoustic signals over a large region. Our starting point is the mutual information criterion for sensor placement, which despite being theoretically attractive has not been widely adopted because of its computational difficulty. To remedy these computational challenges, we introduce a novel branch and bound algorithm that relies upon a new semidefinite programming relaxation of the mutual information problem. Our contributions allow practitioners to solve sensor placement problems to global optimality while exploring only a fraction of the solution space required by brute force. Our work has been made open source at https://github.com/rbassett3/mutual_info_sensor_placement.Arlington, VA, 22203Outstanding ThesisLieutenant, United States NavyApproved for public release. Distribution is unlimited