Dissertationen: „Exponential Family of distribution“

1

Lai, Yanzhao. „Generalized method of moments exponential distribution family“. View electronic thesis (PDF), 2009. http://dl.uncw.edu/etd/2009-2/laiy/yanzhaolai.pdf.

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2

Hornik, Kurt, und Bettina Grün. „On standard conjugate families for natural exponential families with bounded natural parameter space“. Elsevier, 2014. http://dx.doi.org/10.1016/j.jmva.2014.01.003.

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Diaconis and Ylvisaker (1979) give necessary conditions for conjugate priors for distributions from the natural exponential family to be proper as well as to have the property of linear posterior expectation of the mean parameter of the family. Their conditions for propriety and linear posterior expectation are also sufficient if the natural parameter space is equal to the set of all d-dimensional real numbers. In this paper their results are extended to characterize when conjugate priors are proper if the natural parameter space is bounded. For the special case where the natural exponential family is through a spherical probability distribution n,we show that the proper conjugate priors can be characterized by the behavior of the moment generating function of n at the boundary of the natural parameter space, or the second-order tail behavior of n. In addition, we show that if these families are non-regular, then linear posterior expectation never holds. The results for this special case are also extended to natural exponential families through elliptical probability distributions.

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3

Wang, Zhizheng. „Hardware Utilization Measurement and Optimization: A Statistical Investigation and Simulation Study“. Thesis, Uppsala universitet, Statistiska institutionen, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-260070.

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It is essential for the managers to make investment on hardware based on the utilization information of the equipment. From December 2014, a pool of hardware and a scheduling and resource sharing system is implemented by one of the software testing sections in Ericsson. To monitor the efficiency of these equipment and the workflow, a model of non-homogeneous M/M/c queue is developed that successfully captures the main aspects of the system. The model is decomposed into arrival, service, failure and each part is estimated. Mixture exponential is estimated with EM algorithm and the impact of scheduling change is also examined. Finally a simulation of workflow is done with Python module and the optimized number of hardware is proposed based on this M/M/c queue system.

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4

Ruddy, Sean Matthew. „Shrinkage of dispersion parameters in the double exponential family of distributions, with applications to genomic sequencing“. Thesis, University of California, Berkeley, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3686002.

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The prevalence of sequencing experiments in genomics has led to an increased use of methods for count data in analyzing high-throughput genomic data to perform analyses. The importance of shrinkage methods in improving the performance of statistical methods remains. A common example is that of gene expression data, where the counts per gene are often modeled as some form of an overdispersed Poisson. In this case, shrinkage estimates of the per-gene dispersion parameter have lead to improved estimation of dispersion in the case of a small number of samples. We address a different count setting introduced by the use of sequencing data: comparing differential proportional usage via an overdispersed binomial model. Such a model can be useful for testing differential exon inclusion in mRNA-Seq experiments in addition to the typical differential gene expression analysis. In this setting, there are fewer such shrinkage methods for the dispersion parameter. We introduce a novel method that is developed by modeling the dispersion based on the double exponential family of distributions proposed by Efron (1986), also known as the exponential dispersion model (Jorgensen, 1987). Our methods (WEB-Seq and DEB-Seq) are empirical bayes strategies for producing a shrunken estimate of dispersion that can be applied to any double exponential dispersion family, though we focus on the binomial and poisson. These methods effectively detect differential proportional usage, and have close ties to the weighted likelihood strategy of edgeR developed for gene expression data (Robinson and Smyth, 2007; Robinson et al., 2010). We analyze their behavior on simulated data sets as well as real data for both differential exon usage and differential gene expression. In the exon usage case, we will demonstrate our methods' superior ability to control the FDR and detect truly different features compared to existing methods. In the gene expression setting, our methods fail to control the FDR; however, the rankings of the genes by p-value is among the top performers and proves to be robust to both changes in the probability distribution used to generate the counts and in low sample size situations. We provide implementation of our methods in the R package DoubleExpSeq available from the Comprehensive R Archive Network (CRAN).

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5

Ibukun, Michael Abimbola. „Modely s Touchardovým rozdělením“. Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445468.

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In 2018, Raul Matsushita, Donald Pianto, Bernardo B. De Andrade, Andre Cançado & Sergio Da Silva published a paper titled ”Touchard distribution”, which presented a model that is a two-parameter extension of the Poisson distribution. This model has its normalizing constant related to the Touchard polynomials, hence the name of this model. This diploma thesis is concerned with the properties of the Touchard distribution for which delta is known. Two asymptotic tests based on two different statistics were carried out for comparison in a Touchard model with two independent samples, supported by simulations in R.

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6

Okada, Daigo. „Decomposition of a set of distributions in extended exponential family form for distinguishing multiple oligo-dimensional marker expression profiles of single-cell populations and visualizing their dynamics“. Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263569.

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7

Sears, Timothy Dean, und tim sears@biogreenoil com. „Generalized Maximum Entropy, Convexity and Machine Learning“. The Australian National University. Research School of Information Sciences and Engineering, 2008. http://thesis.anu.edu.au./public/adt-ANU20090525.210315.

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This thesis identiﬁes and extends techniques that can be linked to the principle of maximum entropy (maxent) and applied to parameter estimation in machine learning and statistics. Entropy functions based on deformed logarithms are used to construct Bregman divergences, and together these represent a generalization of relative entropy. The framework is analyzed using convex analysis to charac- terize generalized forms of exponential family distributions. Various connections to the existing machine learning literature are discussed and the techniques are applied to the problem of non-negative matrix factorization (NMF).

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8

Gutierrez-Pena, Eduardo Arturo. „Bayesian topics relating to the exponential family“. Thesis, Imperial College London, 1995. http://hdl.handle.net/10044/1/8062.

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9

Kosmidis, Ioannis. „Bias reduction in exponential family nonlinear models“. Thesis, University of Warwick, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.492241.

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The modified-score functions approach to bias reduction (Firth, 1993) is continually gaining in popularity (e.g. Mehrabi & Matthews, 1995; Pettitt et al., 1998; Heinze & Schemper, 2002; Bull et al., 2002; Zorn, 2005; Sartori, 2006; Bull et al., 2007), because of the superior properties of the bias-reduced estimator over the traditional maximum likelihood estimator, particularly in models for categorical responses. Most of the activity is noted for logistic regression, where the bias-reduction method neatly corresponds to penalization of the likelihood by Jeffreys prior and the bias-reduced estimates are always finite and beneficially shrink towards the origin. The recent applied and methodological interest in the bias-reduction method motivates the current thesis and the aim is to explore the nature and widen the applicability of the method, identifying cases where bias reduction is beneficial. Particularly, the current thesis focuses on the following three targets: i) To explore the nature of the bias-reducing modifications to the efficient scores and to obtain results that facilitate the application and the theoretical assessment of the bias-reduction method. ii) To establish theoretically that the bias-reduction method should be considered as an improvement over traditional ML for logistic regressions. iii) To deviate from the flat exponential family and explore the effect of bias reduction in some commonly used curved models for categorical responses.

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10

Silva, Michel Ferreira da. „Estimação e teste de hipótese baseados em verossimilhanças perfiladas“. Universidade de São Paulo, 2005. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-06122006-162733/.

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Tratar a função de verossimilhança perfilada como uma verossimilhança genuína pode levar a alguns problemas, como, por exemplo, inconsistência e ineficiência dos estimadores de máxima verossimilhança. Outro problema comum refere-se à aproximação usual da distribuição da estatística da razão de verossimilhanças pela distribuição qui-quadrado, que, dependendo da quantidade de parâmetros de perturbação, pode ser muito pobre. Desta forma, torna-se importante obter ajustes para tal função. Vários pesquisadores, incluindo Barndorff-Nielsen (1983,1994), Cox e Reid (1987,1992), McCullagh e Tibshirani (1990) e Stern (1997), propuseram modificações à função de verossimilhança perfilada. Tais ajustes consistem na incorporação de um termo à verossimilhança perfilada anteriormente à estimação e têm o efeito de diminuir os vieses da função escore e da informação. Este trabalho faz uma revisão desses ajustes e das aproximações para o ajuste de Barndorff-Nielsen (1983,1994) descritas em Severini (2000a). São apresentadas suas derivações, bem como suas propriedades. Para ilustrar suas aplicações, são derivados tais ajustes no contexto da família exponencial biparamétrica. Resultados de simulações de Monte Carlo são apresentados a fim de avaliar os desempenhos dos estimadores de máxima verossimilhança e dos testes da razão de verossimilhanças baseados em tais funções. Também são apresentadas aplicações dessas funções de verossimilhança em modelos não pertencentes à família exponencial biparamétrica, mais precisamente, na família de distribuições GA0(alfa,gama,L), usada para modelar dados de imagens de radar, e no modelo de Weibull, muito usado em aplicações da área da engenharia denominada confiabilidade, considerando dados completos e censurados. Aqui também foram obtidos resultados numéricos a fim de avaliar a qualidade dos ajustes sobre a verossimilhança perfilada, analogamente às simulações realizadas para a família exponencial biparamétrica. Vale mencionar que, no caso da família de distribuições GA0(alfa,gama,L), foi avaliada a aproximação da distribuição da estatística da razão de verossimilhanças sinalizada pela distribuição normal padrão. Além disso, no caso do modelo de Weibull, vale destacar que foram derivados resultados distribucionais relativos aos estimadores de máxima verossimilhança e às estatísticas da razão de verossimilhanças para dados completos e censurados, apresentados em apêndice.
The profile likelihood function is not genuine likelihood function, and profile maximum likelihood estimators are typically inefficient and inconsistent. Additionally, the null distribution of the likelihood ratio test statistic can be poorly approximated by the asymptotic chi-squared distribution in finite samples when there are nuisance parameters. It is thus important to obtain adjustments to the likelihood function. Several authors, including Barndorff-Nielsen (1983,1994), Cox and Reid (1987,1992), McCullagh and Tibshirani (1990) and Stern (1997), have proposed modifications to the profile likelihood function. They are defined in a such a way to reduce the score and information biases. In this dissertation, we review several profile likelihood adjustments and also approximations to the adjustments proposed by Barndorff-Nielsen (1983,1994), also described in Severini (2000a). We present derivations and the main properties of the different adjustments. We also obtain adjustments for likelihood-based inference in the two-parameter exponential family. Numerical results on estimation and testing are provided. We also consider models that do not belong to the two-parameter exponential family: the GA0(alfa,gama,L) family, which is commonly used to model image radar data, and the Weibull model, which is useful for reliability studies, the latter under both noncensored and censored data. Again, extensive numerical results are provided. It is noteworthy that, in the context of the GA0(alfa,gama,L) model, we have evaluated the approximation of the null distribution of the signalized likelihood ratio statistic by the standard normal distribution. Additionally, we have obtained distributional results for the Weibull case concerning the maximum likelihood estimators and the likelihood ratio statistic both for noncensored and censored data.

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11

Magalla, Champa Hemanthi. „Model adequacy tests for exponential family regression models“. Diss., Kansas State University, 2012. http://hdl.handle.net/2097/13640.

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Doctor of Philosophy
Department of Statistics
James Neill
The problem of testing for lack of fit in exponential family regression models is considered. Such nonlinear models are the natural extension of Normal nonlinear regression models and generalized linear models. As is usually the case, inadequately specified models have an adverse impact on statistical inference and scientific discovery. Models of interest are curved exponential families determined by a sequence of predictor settings and mean regression function, considered as a sub-manifold of the full exponential family. Constructed general alternative models are based on clusterings in the mean parameter components and allow likelihood ratio testing for lack of fit associated with the mean, equivalently natural parameter, for a proposed null model. A maximin clustering methodology is defined in this context to determine suitable clusterings for assessing lack of fit. In addition, a geometrically motivated goodness of fit test statistic for exponential family regression based on the information metric is introduced. This statistic is applied to the cases of logistic regression and Poisson regression, and in both cases it can be seen to be equal to a form of the Pearson chi[superscript]2 statistic. This same statement is true for multinomial regression. In addition, the problem of testing for equal means in a heteroscedastic Normal model is discussed. In particular, a saturated 3 parameter exponential family model is developed which allows for equal means testing with unequal variances. A simulation study was carried out for the logistic and Poisson regression models to investigate comparative performance of the likelihood ratio test, the deviance test and the goodness of fit test based on the information metric. For logistic regression, the Hosmer-Lemeshow test was also included in the simulations. Notably, the likelihood ratio test had comparable power with that of the Hosmer-Lemeshow test under both m- and n-asymptotics, with superior power for constructed alternatives. A distance function defined between densities and based on the information metric is also given. For logistic models, as the natural parameters go to plus or minus infinity, the densities become more and more deterministic and limits of this distance function are shown to play an important role in the lack of fit analysis. A further simulation study investigated the power of a likelihood ratio test and a geometrically derived test based on the information metric for testing equal means in heteroscedastic Normal models.

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12

Tatman, Stacie E. „A bivariate distribution connected with poissonian maxima of exponential variables“. abstract and full text PDF (UNR users only), 2009. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1467770.

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13

Qeadan, Fares. „Bivariate distribution of n iid exponential random variables KPQ-EXP /“. abstract and full text PDF (UNR users only), 2008. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1456407.

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14

Wang, Zeyi. „Inference about Reliability Parameter with Underlying Gamma and Exponential Distribution“. FIU Digital Commons, 2011. http://digitalcommons.fiu.edu/etd/475.

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The statistical inference about the reliability parameter R involving independent gamma stress and exponential strength is considered. Assuming the shape parameter of gamma is a known arbitrary real number and the scale parameters of gamma and exponential are unknown, the UMVUE and MLE of R are obtained. A pivot is proposed. Some inference about R derived from this pivot is presented. It will be shown that the pivot can be used for testing hypothesis and constructing condence interval. A procedure of constructing the condence interval for R is derived. The performances of the UMVUE and MLE are compared numerically based on extensive Monte Carlo simulation. Simulation studies indicate that the performance of the two estimators is about the same. The MLE is preferred because of the simplicity of its computation.

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15

Hamza, Marwa. „Caractérisations des familles exponentielles naturelles cubiques : étude des lois Beta généralisées et de certaines lois de Kummer“. Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0036/document.

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Cette thèse contient deux parties différentes. Dans la première partie, nous nous sommes intéressés aux familles exponentielles naturelles cubiques dont la fonction variance est un polynôme de degré inférieur ou égal à 3. Nous donnons trois caractérisations de ces familles en se basant sur une approche Bayesienne. L’une de ces caractérisations repose sur le fait que la fonction cumulante vérifie une équation différentielle. La deuxième partie de notre travail est consacrée aux conséquences de la propriété d’indépendance de type « Matsumoto-Yor » qui a été développée par Koudou et Vallois. Cette propriété fait intervenir la famille de lois de Kummer de type 2 et les lois Beta généralisées. En se basant sur la méthode de conditionnement et sur la méthode de rejet, nous donnons des réalisations presque sûre de ces distributions de probabilités. D’autre part, nous caractérisons la famille de lois de Kummer de type 2 (resp. les lois Beta généralisées) par une équation algébrique impliquant des lois gamma (resp. les lois Beta)
This thesis has two different parts. In the first part we are interested in the real cubic natural exponential families such that their variance function is a polynomial of degree less than or equal to 3. We give three characterizations of such families using a Bayesian approach. One of these characterizations is based on a differential equation verified by the cumulant function. In a second part we study in depth the independence property of the type “Matsumoto-Yor” that was developed by Koudou and Vallois. This property involves the Kummer distribution of type 2 and the generalized beta ones. Using the conditioning and the rejection method, we give almost sure realization of these distributions. We characterize the family of Kummer distribution of type 2 with an algebraic equation involving the gamma ones. We proceed similarly with the generalized beta distributions

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16

Rauh, Johannes. „Finding the Maximizers of the Information Divergence from an Exponential Family“. Doctoral thesis, Universitätsbibliothek Leipzig, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-77355.

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The subject of this thesis is the maximization of the information divergence from an exponential family on a finite set, a problem first formulated by Nihat Ay. A special case is the maximization of the mutual information or the multiinformation between different parts of a composite system. My thesis contributes mainly to the mathematical aspects of the optimization problem. A reformulation is found that relates the maximization of the information divergence with the maximization of an entropic quantity, defined on the normal space of the exponential family. This reformulation simplifies calculations in concrete cases and gives theoretical insight about the general problem. A second emphasis of the thesis is on examples that demonstrate how the theoretical results can be applied in particular cases. Third, my thesis contain first results on the characterization of exponential families with a small maximum value of the information divergence.

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17

Possamai, Adriana Alvarez. „Modelos não lineares de família exponencial revisitados“. Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-05112009-103455/.

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O objetivo deste trabalho é fazer uma revisão dos modelos não lineares de família exponencial (Cordeiro & Paula (1989); Wei (1998)) para respostas independentes e apresentar possíveis extensões para o caso de dados correlacionados. Inicialmente são apresentados exemplos ilustrativos, alguns dos quais são reanalizados ao longo do texto. Em seguida são discutidos procedimentos de estimação e testes de hipóteses, tais como apresentação de um processo de estimação que pode ser adaptado ao processo iterativo usado na classe dos modelos lineares generalizados, e alguns resultados assintóticos. Técnicas usuais de diagnóstico, como pontos de alavanca, análise de resíduos e diagnóstico de influência são adaptados para a classe dos modelos não lineares de família exponencial. Extensões para a classe dos modelos não lineares com resposta binomial negativa são também apresentadas. Finalmente, são consideradas duas possíveis extensões dos modelos não lineares de família exponencial para dados correlacionados, através de equações de estimação generalizadas e através de modelagem mista em que efeitos aleatórios em forma linear são adicionados ao componente não linear da parte sistemática do modelo conforme sugerido recentemente por Tang et al. (2006a).
The aim of this work is to present a review of the exponential family nonlinear models (Cordeiro & Paula (1989); Wei (1998)) for independent responses and to present possible extensions for the case of correlated data. Firstly, ilustrative examples are presented with some of them being reanalyzed along the text. Then, estimation and hypothesis testing procedures, such as the presentation of an iterative process adapted from the one of generalized linear models, and some asymptotic results are discussed. Useful diagnostic techniques, as calculation of leverage measures, residual analysis and influence diagnostics are adapted for the class of exponential family nonlinear models. Extensions to nonlinear negative binomial models are also presented. Finally, two possible extensions for correlated data are considered, by using generalized estimating equations and mixed modeling in which linear random effects are added into the systematic component together with the nonlinear function, as suggested by Tang et al. (2006a).

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18

Meyer, Christine Siegwarth. „Income distribution and family structure“. Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/11899.

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19

Zhi, Tianchen. „Maximum Likelihood Estimation of Parameters in Exponential Power Distribution with Upper Record Values“. FIU Digital Commons, 2017. http://digitalcommons.fiu.edu/etd/3211.

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The exponential power (EP) distribution is a very important distribution that was used by survival analysis and related with asymmetrical EP distribution. Many researchers have discussed statistical inference about the parameters in EP distribution using i.i.d random samples. However, sometimes available data might contain only record values, or it is more convenient for researchers to collect record values. We aim to resolve this problem. We estimated two parameters of the EP distribution by MLE using upper record values. According to simulation study, we used the Bias and MSE of the estimators for studying the efficiency of the proposed estimation method. Then, we discussed the prediction on the next upper record value by known upper record values. The study concluded that MLEs of EP distribution parameters by upper record values has satisfactory performance. Also, prediction of the next upper record value performed well

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20

Choi, Sujung. „On two-sample data analysis by exponential model“. Texas A&M University, 2005. http://hdl.handle.net/1969.1/2653.

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We discuss two-sample problems and the implementation of a new two-sample data analysis procedure. The proposed procedure is based on the concepts of mid-distribution, design of score functions, components, comparison distribution, comparison density and exponential model. Assume that we have a random sample X1, . . . ,Xm from a continuous distribution F(y) = P(Xi y), i = 1, . . . ,m and a random sample Y1, . . . ,Yn from a continuous distribution G(y) = P(Yi y), i = 1, . . . ,n. Also assume independence of the two samples. The two-sample problem tests homogeneity of two samples and formally can be stated as H0 : F = G. To solve the two-sample problem, a number of tests have been proposed by statisticians in various contexts. Two typical tests are the two-sample t?test and the Wilcoxon's rank sum test. However, since they are testing differences in locations, they do not extract more information from the data as well as a test of the homogeneity of the distribution functions. Even though the Kolmogorov-Smirnov test statistic or Anderson-Darling tests can be used for the test of H0 : F = G, those statistics give no indication of the actual relation of F to G when H0 : F = G is rejected. Our goal is to learn why it was rejected. Our approach gives an answer using graphical tools which is a main property of our approach. Our approach is functional in the sense that the parameters to be estimated are probability density functions. Compared with other statistical tools for two-sample problems such as the t-test or the Wilcoxon rank-sum test, density estimation makes us understand the data more fully, which is essential in data analysis. Our approach to density estimation works with small sample sizes, too. Also our methodology makes almost no assumptions on two continuous distributions F and G. In that sense, our approach is nonparametric. Our approach gives graphical elements in two-sample problem where exist not many graphical elements typically. Furthermore, our procedure will help researchers to make a conclusion as to why two populations are different when H0 is rejected and to give an explanation to describe the relation between F and G in a graphical way.

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21

Rauh, Johannes [Verfasser], Nihat [Akademischer Betreuer] Ay, Jürgen [Akademischer Betreuer] Jost, Jürgen [Gutachter] Jost und Andreas [Gutachter] Knauf. „Finding the Maximizers of the Information Divergence from an Exponential Family : Finding the Maximizersof the Information Divergencefrom an Exponential Family / Johannes Rauh ; Gutachter: Jürgen Jost, Andreas Knauf ; Nihat Ay, Jürgen Jost“. Leipzig : Universitätsbibliothek Leipzig, 2011. http://d-nb.info/1237895499/34.

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22

Ma, Yimin. „Bayesian and empirical Bayesian analysis for the truncation parameter distribution families /“. *McMaster only, 1998.

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23

Fang, Youjian Carleton University Dissertation Mathematics and Statistics. „TES/GI/1 queues: exponential bounding techniques for the delay (distribution) and stability issues“. Ottawa, 1995.

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24

Ozdem, Mehmet. „Video Distribution Over Ip Networks“. Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608187/index.pdf.

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As applications like IPTV and VoD (Video on demand) are gaining popularity, it is becoming more important to study the behavior of video signals in the Internet access infrastructures such as ADSL and cable networks. Average delay, average jitter and packet loss in these networks affect the quality of service, hence transmission and access speeds need to be determined such that these parameters are minimized. In this study the behavior of the above mentioned IP networks under variable bit rate (VBR) video traffic is investigated. ns-2 simulator is used for this purpose and actual as well as artificially generated signals are applied to the networks under test. Variable bit rate (VBR) traffic is generated synthetically using ON/OFF sources with ON/OFF times taken from exponential or Pareto distributions. As VBR video shows long range dependence with a Hurst parameter between 0.5 and 1, this parameter was used as a metric to measure the accuracy of the synthetic sources. Two different topologies were simulated in this study: one similar to ADSL access networks and the other behaving like cable distribution network. The performance of the networks (delay, jitter and packet loss) under VBR video traffic and different access speeds were measured. According to the obtained results, minimum access speeds in order achieve acceptable quality video delivery to the customers were suggested.

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25

Wang, Rui. „Generalizing Multistage Partition Procedures for Two-parameter Exponential Populations“. ScholarWorks@UNO, 2018. https://scholarworks.uno.edu/td/2510.

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ANOVA analysis is a classic tool for multiple comparisons and has been widely used in numerous disciplines due to its simplicity and convenience. The ANOVA procedure is designed to test if a number of different populations are all different. This is followed by usual multiple comparison tests to rank the populations. However, the probability of selecting the best population via ANOVA procedure does not guarantee the probability to be larger than some desired prespecified level. This lack of desirability of the ANOVA procedure was overcome by researchers in early 1950's by designing experiments with the goal of selecting the best population. In this dissertation, a single-stage procedure is introduced to partition k treatments into "good" and "bad" groups with respect to a control population assuming some key parameters are known. Next, the proposed partition procedure is genaralized for the case when the parameters are unknown and a purely-sequential procedure and a two-stage procedure are derived. Theoretical asymptotic properties, such as first order and second order properties, of the proposed procedures are derived to document the efficiency of the proposed procedures. These theoretical properties are studied via Monte Carlo simulations to document the performance of the procedures for small and moderate sample sizes.

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26

Gillan, Catherine C. „Using the piecewise exponential distribution to model the length of stay in a manpower planning system“. Thesis, University of Ulster, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338317.

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27

Lee, Gunhee. „Noninformative priors for some models useful in reliability and survival analysis /“. free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9720544.

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28

Jansen, van Rensburg Helena Maria. „Goodness-of-fit tests based on new characterizations of the exponential distribution / Helena Maria Jansen van Rensburg“. Thesis, North-West University, 2006. http://hdl.handle.net/10394/1095.

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The exponential density is probably one of the most widely used distributions in practice. Due to its importance, many goodness-of-fit tests for exponentiality have been proposed in the literature. The objectives of this research are as follow: 0 to study the importance of the exponential distribution in practical problems, 0 to investigate alternative classes of distributions to the exponential distribution, 0 to present an overview of existing characterizations of the exponential distribution, 0 to evaluate existing goodness-of-fit tests for exponentiality, 0 to develop new goodness-of-fit tests for exponentiality, and 0 to compare the proposed goodness-of-fit tests to existing tests by means of relative efficiencies and simulation studies of the power of the tests. To achieve these objectives, we begin with a brief discussion of the exponential distribution and other parametric families of life distributions, followed by a summary of six well-known nonparametric classes of alternative distributions. A comprehensive literature study of existing characterizations of the exponential distribution and existing goodness-of fit tests for exponentiality are presented. We then propose and prove two new characterizations of the exponential distribution in the class of NBUE life distributions based on properties of order statistics. These characterizations are used to develop a new class of goodness-of-fit tests for exponentiality. The tests are shown to be consistent and the limiting distributions under the null and alternative hypotheses are derived. We show that the new class of test statistics includes two statistics which arc equivalent to the well-known Gini test statistic (Gail and Gastwirth 1978a) and the coefficient of variation test statistic (Borges, Proschan and Rodrigucs 1984). The newly proposed tests are compared to existing goodness-of-fit tests by means of Pitman and approximate Bahadur relative efficiencies. Monte Carlo studies are conducted to compare the various tests with regard to power for small and moderate sample sizes against a wide range of alternative distributions. We recommend three members of the class of test statistics as being very effective testing procedures for exponentiality. In conclusion, practical examples based on real-life data are presented.
Thesis (Ph.D. (Statistics))--North-West University, Potchefstroom Campus, 2007.

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Gautham, Smitha. „An Efficient Implementation of an Exponential Random Number Generator in a Field Programmable Gate Array (FPGA)“. VCU Scholars Compass, 2010. http://scholarscompass.vcu.edu/etd/2173.

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Many physical, biological, ecological and behavioral events occur at times and rates that are exponentially distributed. Modeling these systems requires simulators that can accurately generate a large quantity of exponentially distributed random numbers, which is a computationally intensive task. To improve the performance of these simulators, one approach is to move portions of the computationally inefficient simulation tasks from software to custom hardware implemented in Field Programmable Gate Arrays (FPGAs). In this work, we study efficient FPGA implementations of exponentially distributed random number generators to improve simulator performance. Our approach is to generate uniformly distributed random numbers using standard techniques and scale them using the inverse cumulative distribution function (CDF). Scaling is implemented by curve fitting piecewise linear, quadratic, cubic, and higher order functions to solve for the inverse CDF. As the complexity of the scaling function increases (in terms of order and the number of pieces), number accuracy increases and additional FPGA resources (logic cells and block RAMs) are consumed. We analyze these tradeoffs and show how a designer with particular accuracy requirements and FPGA resource constraints can implement an accurate and efficient exponentially distributed random number generator.

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Crumer, Angela Maria. „Comparison between Weibull and Cox proportional hazards models“. Kansas State University, 2011. http://hdl.handle.net/2097/8787.

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Master of Science
Department of Statistics
James J. Higgins
The time for an event to take place in an individual is called a survival time. Examples include the time that an individual survives after being diagnosed with a terminal illness or the time that an electronic component functions before failing. A popular parametric model for this type of data is the Weibull model, which is a flexible model that allows for the inclusion of covariates of the survival times. If distributional assumptions are not met or cannot be verified, researchers may turn to the semi-parametric Cox proportional hazards model. This model also allows for the inclusion of covariates of survival times but with less restrictive assumptions. This report compares estimates of the slope of the covariate in the proportional hazards model using the parametric Weibull model and the semi-parametric Cox proportional hazards model to estimate the slope. Properties of these models are discussed in Chapter 1. Numerical examples and a comparison of the mean square errors of the estimates of the slope of the covariate for various sample sizes and for uncensored and censored data are discussed in Chapter 2. When the shape parameter is known, the Weibull model far out performs the Cox proportional hazards model, but when the shape parameter is unknown, the Cox proportional hazards model and the Weibull model give comparable results.

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Majumder, M. Mahbubul A. „On Tukey's gh family of distributions“. Virtual Press, 2007. http://liblink.bsu.edu/uhtbin/catkey/1371472.

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Skewness and elongation are two factors that directly determine the shape of a probability distribution. Thus, to obtain a flexible distribution it is always desirable that the parameters of the distribution directly determine the skewness and elongation. To meet this purpose, Tukey (1977) introduced a family of distributions called g-and-h family (gh family) based on a transformation of the standard normal variable where g and h determine the skewness and the elongation, respectively. The gh family of distributions was extensively studied by Hoaglin (1985) and Martinez and Iglewicz (1984). For its flexibility in shape He and Raghunathan (2006) have used this distribution for multiple imputations. Because of the complex nature of this family of distributions, it is not possible to have an explicit mathematical form of the density function and the estimates of the parameters g and h fully depend on extensive numerical computations.In this study, we have developed algorithms to numerically compute the density functions. We present algorithms to obtain the estimates of g and h using method of moments, quantile method and maximum likelihood method. We analyze the performance of each method and compare them using simulation technique. Finally, we study some special cases of gh family and their properties.
Department of Mathematical Sciences

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Gaonkar, Chetan Chandrakant. „Diversity, distribution and evolution of the planktonic diatom family Chaetocerotaceae“. Thesis, Open University, 2017. http://oro.open.ac.uk/50352/.

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The number and abundance of diatom species in environmental samples are counted traditionally by means of light microscopy (LM). However, recognizing –let alone, counting- species is often challenging because of the existence of cryptic species and intraspecific phenotypic plasticity. Proper characterization requires isolation of cells, growing them into monoclonal cultures, and characterizing the cultures genetically and morphologically. However, not all species grow in culture, featureless ones are less likely to be isolated, and the procedure is laborious. High-throughput sequencing (HTS) metabarcoding bypasses morphology; DNA is collected from environmental samples, a particular marker sequenced, and the resulting sequences sorted into clusters or terminal clades assumed to represent species. Yet, reference barcodes of taxonomically validated species are needed to identify these clades. This exercise is the main aim of my thesis. Since it is impossible to do this for all the diversity within a PhD thesis project, we selected Chaetocerotaceae, an abundant and diverse family of marine planktonic diatoms, containing two genera: Chaetoceros and Bacteriastrum. Its members uniquely share setae; thin siliceous tubes emerging from the valve corners, facilitating detection in samples. Strains were obtained from the Gulf of Naples (GoN), from Central Chile and Roscoff – at sites for which LTER time series data are available. A total of 270 strains were obtained from these sites, and their 18S- and partial 28S rDNA sequences and morphological information gathered. The strains grouped into 60 genetically distinct species, thus providing a dataset of validated Chaetocerotacean 18S reference barcodes. Inferred molecular phylogenies showed monophyletic Chaetocerotaceae as well as monophyletic Bacteriastrum inside paraphyletic Chaetoceros, and the presence of cryptic diversity. To start with taxonomic updates, the species C. sporotruncatus and C. dichatoensis were described within the C. socialis species-complex based on spore morphology and sequence differences. Several rDNA sequences contained spliceosomal introns (ca. 100bp) and/or group-I introns (ca. 400bp). Phylogenies inferred from the introns did not corroborate rDNA phylogenies, suggesting horizontal gene transfer. Presence/absence of introns in conspecific strains sampled in different seasons suggests population differentiation between these seasons. A HTS dataset consisting of V4-sequences (part of 18S) from 48 seawater samples taken over the seasons in the GoN revealed 76 terminal clades of which 46 grouped with a reference barcode. Some of these species occur year-round whereas most others are seasonal. Surprisingly, of the 30 clades belonging to unknown Chaetocerotacean species, two appear to be among the most abundant in the GoN.

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Lima, Stênio Rodrigues. „The half-normal generalized family and Kumaraswamy Nadarajah-Haghighi distribution“. Universidade Federal de Pernambuco, 2015. https://repositorio.ufpe.br/handle/123456789/14917.

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CAPES
As distribuições generalizadas têm sido amplamente estudadas na Estatística e diversos autores têm investigado novas distribuições de sobrevivência devido a sua flexibilidade para ajustar dados. Neste trabalho um novo método de compor distribuições é proposto: a família Half-Normal-G, em que G e chamada distribuição baseline. Demostramos que as funções densidades das distribuiçõess propostas podem ser expressas como combinação linear de funções densidades das respectivas exponencializadas-G. Diversas propriedades dessa família são estudadas. Apresentamos também uma nova distribuição de probabilidade baseado na Família de Distribuições Generalizadas Kumaraswamy (kw- G), j a conhecida na literatura. Escolhemos como baseline a distribuição Nadarajah- Haghighi, recentemente estudada por Nadarajah e Haghighi (2011) e que desenvolveram algumas propriedades interessantes. Estudamos várias propriedades da nova distribuição Kumaraswamu-Nadarajah-Haghighi (Kw-NH) e fizemos duas aplicações de bancos de dados mostrando empiricamente a flexibilidade do modelo.

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Azevedo, João Rolando Brás. „Geographic information systems applied to patient distribution for Family Health Teams“. Dissertação, Faculdade de Medicina da Universidade do Porto, 2011. http://hdl.handle.net/10216/62217.

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Karki, Shanta. „Distribution, proliferation, and transposition of mPing family transposons in genus Oryza“. Kyoto University, 2009. http://hdl.handle.net/2433/123996.

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Kyoto University (京都大学)
0048
新制・課程博士
博士(農学)
甲第14684号
農博第1766号
新制||農||970(附属図書館)
学位論文||H21||N4457(農学部図書室)
UT51-2009-D396
京都大学大学院農学研究科農学専攻
(主査)教授谷坂隆俊, 教授遠藤隆, 教授冨永達
学位規則第4条第1項該当

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Azevedo, João Rolando Brás. „Geographic information systems applied to patient distribution for Family Health Teams“. Master's thesis, Faculdade de Medicina da Universidade do Porto, 2011. http://hdl.handle.net/10216/62217.

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Nixon, Valerie. „Valuation and distribution of pension benefits under the Family Law Act, 1986“. Thesis, University of Ottawa (Canada), 1991. http://hdl.handle.net/10393/7538.

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Starvaggi, Patrick William. „Exact Distributions of Sequential Probability Ratio Tests“. Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1397042380.

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Tchouta, Romual Eloge. „Estimating the Difference of Percentiles from Two Independent Populations“. Digital Commons @ East Tennessee State University, 2008. https://dc.etsu.edu/etd/1981.

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We first consider confidence intervals for a normal percentile, an exponential percentile and a uniform percentile. Then we develop confidence intervals for a difference of percentiles from two independent normal populations, two independent exponential populations and two independent uniform populations. In our study, we mainly focus on the maximum likelihood to develop our confidence intervals. The efficiency of this method is examined via coverage rates obtained in a simulation study done with the statistical software R.

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Kubrycht, Pavel. „Analýza síly testů hypotéz“. Master's thesis, Vysoká škola ekonomická v Praze, 2016. http://www.nusl.cz/ntk/nusl-264617.

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This Thesis deals with the power of a statistical test and the associated problem of determining the appropriate sample size. It should be large enough to meet the requirements of the probabilities of errors of both the first and second kind. The aim of this Thesis is to demonstrate theoretical methods that result in derivation of formulas for minimum sample size determination. For this Thesis, three important probability distributions have been chosen: Normal, Bernoulli, and Exponential.

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Berggren, Erik. „Improvement of Automotive Article Placement and Workload Distribution in Warehousing“. Thesis, Högskolan i Jönköping, Tekniska Högskolan, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-31171.

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Purpose – The purpose is to: Improve the efficiency of warehouses operations as well as reduce its workload imbalances by altering the warehouse layout and work zones at a storage area. This was done by answering the following research questions: What is the current state of the sites efficiency and workload imbalances? How can the warehouse layout be designed to increase the efficiency? How can warehouse work zones be altered to reduce workload imbalances? Method – The purpose was achieved through a case study at a vehicle manufacturing facility. By studying established methods of efficiency, layout designs and workload imbalances, ways of improving the operations was discovered. The effects of these methods were then tested through the case. Findings –There are two categories improving efficiency, namely increasing output or decreasing input. The study also provides examples of ways to do both, and verifies them at the case company. The focus of both methods is a decrease in travel distance which proved to be a reliable way of increasing efficiency. Workload imbalances can be decreased by sharing workload between the resources. The case shows the result of two different resources with unequal workload and discusses the trade-off between efficiency and workload equality. Implications – The practical implications of the study is guidelines for how efficiency can be increased and how workload imbalances can be decreased. The academic implications are verifications of the used theories. Limitations – This study focuses on a restricted part of the storage process, namely traveling. There are more processes which could be included to further benefit the overall efficiency, these have however been excluded to limit the scope. The study also uses a heuristic approach based on prior research which means that the optimal solution might still be unknown. Keywords – Efficiency, workload imbalances, storage management, family grouping

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Fincher, Jayla Eileen. „Siblings and Inheritances: A Phenomenological Study Exploring the Relational Outcomes Following the Inheritance Distribution Process“. Thesis, Virginia Tech, 2016. http://hdl.handle.net/10919/71695.

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The purpose of this study was to contribute to a more complete understanding of the family inheritance experience by exploring the perspectives of beneficiaries. This qualitative study aimed to describe and discuss how individuals' sibling relationships were impacted following the distribution process of an inheritance that was intended to be equally distributed. Eight individuals participated in semi-structured interviews, with areas of inquiry covering perceptions of challenges and benefits of the distribution process, fairness of the outcome of distribution among siblings, and the impact the process has had on their sibling relationships. The data was analyzed using transcendental phenomenology. Findings suggest families experience varying degrees of conflict during inheritance distributions, but not all conflict was devastating to the relationships following the distributions. Specific relational aspects were identified in contributing to the level of satisfaction of the distribution, which subsequently affected their relationships afterward. Additionally, the handling of conflict and efforts to repair relational strains significantly contribute to relational outcomes following the distribution. The majority of participants reported stronger relationships following the inheritance distribution. The findings provide a foundation for further research to explore beneficiary's experiences of receiving an inheritance within multi-child families.
Master of Science

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Manrique, Luis. „The impact of inflation on family money income distribution in Venezuela during the 1980s“. Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1995. http://handle.dtic.mil/100.2/ADA311420.

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Thesis (M.S. in Management) Naval Postgraduate School, June 1995.
Thesis advisor(s) Katsuaki L. Terasawa, David R. Henderson. "June 1995." Includes bibliographical references. Also available online.

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Braga, Altemir da Silva. „Extensions of the normal distribution using the odd log-logistic family: theory and applications“. Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-02102017-092313/.

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In this study we propose three new distributions and a study with longitudinal data. The first was the Odd log-logistic normal distribution: theory and applications in analysis of experiments, the second was Odd log-logistic t Student: theory and applications, the third was the Odd log-logistic skew normal: the new distribution skew-bimodal with applications in analysis of experiments and the fourth regression model with random effect of the Odd log-logistic skew normal distribution: an application in longitudinal data. Some have been demonstrated such as symmetry, quantile function, some expansions, ordinary incomplete moments, mean deviation and the moment generating function. The estimation of the model parameters were approached by the method of maximum likelihood. In applications were used regression models to data from a completely randomized design (CRD) or designs completely randomized in blocks (DBC). Thus, the models can be used in practical situations for as a completely randomized designs or completely randomized blocks designs, mainly, with evidence of asymmetry, kurtosis and bimodality.
A distribuição normal é uma das mais importantes na área de estatística. Porém, não é adequada para ajustar dados que apresentam características de assimetria ou de bimodalidade, uma vez que tal distribuição possui apenas os dois primeiros momentos, diferentes de zero, ou seja, a média e o desvio-padrão. Por isso, muitos estudos são realizados com a finalidade de criar novas famílias de distribuições que possam modelar ou a assimetria ou a curtose ou a bimodalidade dos dados. Neste sentido, é importante que estas novas distribuições tenham boas propriedades matemáticas e, também, a distribuição normal como um submodelo. Porém, ainda, são poucas as classes de distribuições que incluem a distribuição normal como um modelo encaixado. Dentre essas propostas destacam-se: a skew-normal, a beta-normal, a Kumarassuamy-normal e a gama-normal. Em 2013 foi proposta a nova família X de distribuições Odd log-logística-G com o objetivo de criar novas distribuições de probabildade. Assim, utilizando as distribuições normal e a skew-normal como função base foram propostas três novas distribuições e um quarto estudo com dados longitudinais. A primeira, foi a distribuição Odd log-logística normal: teoria e aplicações em dados de ensaios experimentais; a segunda foi a distribuição Odd log-logística t Student: teoria e aplicações; a terceira foi a distribuição Odd log-logística skew-bimodal com aplicações em dados de ensaios experimentais e o quarto estudo foi o modelo de regressão com efeito aleatório para a distribuição distribuição Odd log-logística skew-bimodal: uma aplicação em dados longitudinais. Estas distribuições apresentam boas propriedades tais como: assimetria, curtose e bimodalidade. Algumas delas foram demonstradas como: simetria, função quantílica, algumas expansões, os momentos incompletos ordinários, desvios médios e a função geradora de momentos. A flexibilidade das novas distrições foram comparada com os modelos: skew-normal, beta-normal, Kumarassuamy-normal e gama-normal. A estimativas dos parâmetros dos modelos foram obtidas pelo método da máxima verossimilhança. Nas aplicações foram utilizados modelos de regressão para dados provenientes de delineamentos inteiramente casualizados (DIC) ou delineamentos casualizados em blocos (DBC). Além disso, para os novos modelos, foram realizados estudos de simulação para verificar as propriedades assintóticas das estimativas de parâmetros. Para verificar a presença de valores extremos e a qualidade dos ajustes foram propostos os resíduos quantílicos e a análise de sensibilidade. Portanto, os novos modelos estão fundamentados em propriedades matemáticas, estudos de simulação computacional e com aplicações para dados de delineamentos experimentais. Podem ser utilizados em ensaios inteiramente casualizados ou em blocos casualizados, principalmente, com dados que apresentem evidências de assimetria, curtose e bimodalidade.

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Chua, Kim Chyang, und 蔡金強. „Simulation Study on Bayes Sequential Estimation for a Particular Exponential Family of Distributions“. Thesis, 2011. http://ndltd.ncl.edu.tw/handle/02673925730739216159.

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46

Tseng, Chung-Hung, und 曾仲宏. „Simulation Study of a Two-stage Procedure for a Particular Exponential Family of Distributions“. Thesis, 2012. http://ndltd.ncl.edu.tw/handle/34179284488514862204.

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47

Wen-Feng, Ou, und 歐文峰. „Second Order Approximation on Bayes Sequential Estimation for a Particular Exponential Family of Distributions“. Thesis, 2013. http://ndltd.ncl.edu.tw/handle/49433115702113337270.

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Wu, Chia-Ying, und 吳佳穎. „A New Approach for Deriving Better Confidence Intervals Supplemented with Point Estimators for Parameters of Some Most Used Discrete Exponential Family Distributions“. Thesis, 2011. http://ndltd.ncl.edu.tw/handle/34634787578603201117.

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碩士
國立東華大學
應用數學系
99
Interval estimation of a binomial proportion p is a basic and important problem. The poor and unreliable behavior, in coverage probabilities, of the popular Wald interval has been widely discussed in the literature. Among other existing works in the last decade, in this study, we try a different route, central limit theorem (CLT) plus the δ-method in short, to construct the confidence interval, CITW, for p, then we consider the center of CITW be its supplemental point estimator for CITW. For comparisons, we choose, from the literature, those with good performance in coverage probabilities to compare with our proposed CITW and Wald interval in terms of coverage probabilities and average lengths. We also examine the performance of the point estimator, center of each interval, supplemented with each selected interval by mean square error and integrated mean square error (IMSE) when comparing to the classical maximum likelihood estimator of p. By the results of simulation and numerical calculations, has very satisfactory coverage probabilities, reasonable average length and its supplemental point estimator has good consistent property and acceptable IMSE. Thus, our proposed intervals CITW and their supplemental point estimators, in pair, are strongly recommendable for inferring both in statistical viewpoint and practical purpose. Our studies also indicate that the same approach works for other two important discrete exponential distributions: Poisson and negative binomial distributions. Our research illustrate that our approach gives better confidence intervals with acceptable supplemental point estimators for the parameter, comparing to those obtained by using CLT directly.

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Sebatjane, Phuti. „Understanding patterns of aggregation in count data“. Diss., 2016. http://hdl.handle.net/10500/22067.

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The term aggregation refers to overdispersion and both are used interchangeably in this thesis. In addressing the problem of prevalence of infectious parasite species faced by most rural livestock farmers, we model the distribution of faecal egg counts of 15 parasite species (13 internal parasites and 2 ticks) common in sheep and goats. Aggregation and excess zeroes is addressed through the use of generalised linear models. The abundance of each species was modelled using six different distributions: the Poisson, negative binomial (NB), zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), zero-altered Poisson (ZAP) and zero-altered negative binomial (ZANB) and their fit was later compared. Excess zero models (ZIP, ZINB, ZAP and ZANB) were found to be a better fit compared to standard count models (Poisson and negative binomial) in all 15 cases. We further investigated how distributional assumption a↵ects aggregation and zero inflation. Aggregation and zero inflation (measured by the dispersion parameter k and the zero inflation probability) were found to vary greatly with distributional assumption; this in turn changed the fixed-effects structure. Serial autocorrelation between adjacent observations was later taken into account by fitting observation driven time series models to the data. Simultaneously taking into account autocorrelation, overdispersion and zero inflation proved to be successful as zero inflated autoregressive models performed better than zero inflated models in most cases. Apart from contribution to the knowledge of science, predictability of parasite burden will help farmers with effective disease management interventions. Researchers confronted with the task of analysing count data with excess zeroes can use the findings of this illustrative study as a guideline irrespective of their research discipline. Statistical methods from model selection, quantifying of zero inflation through to accounting for serial autocorrelation are described and illustrated.
Statistics
M.Sc. (Statistics)

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50

Rudolph, Maja. „Exponential Family Embeddings“. Thesis, 2018. https://doi.org/10.7916/D8NZ9RHT.

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Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. Exponential family embeddings extend the idea of word embeddings to other types of high-dimensional data. Exponential family embeddings have three ingredients; embeddings as latent variables, a predefined conditioning set for each observation called the context and a conditional likelihood from the exponential family. The embeddings are inferred with a scalable algorithm. This thesis highlights three advantages of the exponential family embeddings model class: (A) The approximations used for existing methods such as word2vec can be understood as a biased stochastic gradients procedure on a specific type of exponential family embedding model --- the Bernoulli embedding. (B) By choosing different likelihoods from the exponential family we can generalize the task of learning distributed representations to different application domains. For example, we can learn embeddings of grocery items from shopping data, embeddings of movies from click data, or embeddings of neurons from recordings of zebrafish brains. On all three applications, we find exponential family embedding models to be more effective than other types of dimensionality reduction. They better reconstruct held-out data and find interesting qualitative structure. (C) Finally, the probabilistic modeling perspective allows us to incorporate structure and domain knowledge in the embedding space. We develop models for studying how language varies over time, differs between related groups of data, and how word usage differs between languages. Key to the success of these methods is that the embeddings share statistical information through hierarchical priors or neural networks. We demonstrate the benefits of this approach in empirical studies of Senate speeches, scientific abstracts, and shopping baskets.

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