Relevant bibliographies by topics / Likelihood ratio distributions

Academic literature on the topic 'Likelihood ratio distributions'

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Published: 10 March 2023

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Journal articles on the topic "Likelihood ratio distributions"

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Skolimowska, Magdalena, and Jarosław Bartoszewicz. "Weighting, likelihood ratio order and life distributions." Applicationes Mathematicae 33, no. 3-4 (2006): 283–91. http://dx.doi.org/10.4064/am33-3-4.

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Jiang, Tiefeng, and Yongcheng Qi. "Likelihood Ratio Tests for High-Dimensional Normal Distributions." Scandinavian Journal of Statistics 42, no. 4 (March 25, 2015): 988–1009. http://dx.doi.org/10.1111/sjos.12147.

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Krishnamoorthy, Kalimuthu, Meesook Lee, and Wang Xiao. "Likelihood ratio tests for comparing several gamma distributions." Environmetrics 26, no. 8 (August 31, 2015): 571–83. http://dx.doi.org/10.1002/env.2357.

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Huang, Kai, and Jie Mi. "APPLICATIONS OF LIKELIHOOD RATIO ORDER IN BAYESIAN INFERENCES." Probability in the Engineering and Informational Sciences 34, no. 1 (August 6, 2018): 1–13. http://dx.doi.org/10.1017/s026996481800027x.

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The present paper studies the likelihood ratio order of posterior distributions of parameter when the same order exists between the corresponding prior of the parameter, or when the observed values of the sufficient statistic for the parameter differ. The established likelihood order allows one to compare the Bayesian estimators associated with many common and general error loss functions analytically. It can also enable one to compare the Bayes factor in hypothesis testing without using numerical computation. Moreover, using the likelihood ratio (LR) order of the posterior distributions can yield the LR order between marginal predictive distributions, and posterior predictive distributions.
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Anderson, T. W., Huang Hsu, and Kai-Tai Fang. "Maximum-likelihood estimates and likelihood-ratio criteria for multivariate elliptically contoured distributions." Canadian Journal of Statistics 14, no. 1 (March 1986): 55–59. http://dx.doi.org/10.2307/3315036.

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Coelho, Carlos A., Barry C. Arnold, and Filipe J. Marques. "Near-Exact Distributions for Certain Likelihood Ratio Test Statistics." Journal of Statistical Theory and Practice 4, no. 4 (December 2010): 711–25. http://dx.doi.org/10.1080/15598608.2010.10412014.

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Vu, H. T. V., and R. A. Maller. "The Likelihood Ratio Test for Poisson versus Binomial Distributions." Journal of the American Statistical Association 91, no. 434 (June 1996): 818–24. http://dx.doi.org/10.1080/01621459.1996.10476949.

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Catana, Luigi-Ionut, and Vasile Preda. "A New Stochastic Order of Multivariate Distributions: Application in the Study of Reliability of Bridges Affected by Earthquakes." Mathematics 11, no. 1 (December 26, 2022): 102. http://dx.doi.org/10.3390/math11010102.

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In this article, we introduce and study a new stochastic order of multivariate distributions, namely, the conditional likelihood ratio order. The proposed order and other stochastic orders are analyzed in the case of a bivariate exponential distributions family. The theoretical results obtained are applied for studying the reliability of bridges affected by earthquakes. The conditional likelihood ratio order involves the multivariate stochastic ordering; it resembles the likelihood ratio order in the univariate case but is much easier to verify than the likelihood ratio order in the multivariate case. Additionally, the likelihood ratio order in the multivariate case implies this ordering. However, the conditional likelihood ratio order does not imply the weak hard rate order, and it is not an order relation on the multivariate distributions set. The new conditional likelihood ratio order, together with the likelihood ratio order and the weak hazard rate order, were studied in the case of the bivariate Marshall–Olkin exponential distributions family, which has a lack of memory type property. At the end of the paper, we also presented an application of the analyzed orderings for this bivariate distributions family to the study of the effects of earthquakes on bridges.
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Visscher, Peter M. "A Note on the Asymptotic Distribution of Likelihood Ratio Tests to Test Variance Components." Twin Research and Human Genetics 9, no. 4 (August 1, 2006): 490–95. http://dx.doi.org/10.1375/twin.9.4.490.

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AbstractWhen using maximum likelihood methods to estimate genetic and environmental components of (co)variance, it is common to test hypotheses using likelihood ratio tests, since such tests have desirable asymptotic properties. In particular, the standard likelihood ratio test statistic is assumed asymptotically to follow a χ2 distribution with degrees of freedom equal to the number of parameters tested. Using the relationship between least squares and maximum likelihood estimators for balanced designs, it is shown why the asymptotic distribution of the likelihood ratio test for variance components does not follow a χ2 distribution with degrees of freedom equal to the number of parameters tested when the null hypothesis is true. Instead, the distribution of the likelihood ratio test is a mixture of χ2 distributions with different degrees of freedom. Implications for testing variance components in twin designs and for quantitative trait loci mapping are discussed. The appropriate distribution of the likelihood ratio test statistic should be used in hypothesis testing and model selection.
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Slooten, K. "Likelihood ratio distributions and the (ir)relevance of error rates." Forensic Science International: Genetics 44 (January 2020): 102173. http://dx.doi.org/10.1016/j.fsigen.2019.102173.

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Dissertations / Theses on the topic "Likelihood ratio distributions"

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Lynch, O'Neil. "Mixture distributions with application to microarray data analysis." Scholar Commons, 2009. http://scholarcommons.usf.edu/etd/2075.

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The main goal in analyzing microarray data is to determine the genes that are differentially expressed across two types of tissue samples or samples obtained under two experimental conditions. In this dissertation we proposed two methods to determine differentially expressed genes. For the penalized normal mixture model (PMMM) to determine genes that are differentially expressed, we penalized both the variance and the mixing proportion parameters simultaneously. The variance parameter was penalized so that the log-likelihood will be bounded, while the mixing proportion parameter was penalized so that its estimates are not on the boundary of its parametric space. The null distribution of the likelihood ratio test statistic (LRTS) was simulated so that we could perform a hypothesis test for the number of components of the penalized normal mixture model. In addition to simulating the null distribution of the LRTS for the penalized normal mixture model, we showed that the maximum likelihood estimates were asymptotically normal, which is a first step that is necessary to prove the asymptotic null distribution of the LRTS. This result is a significant contribution to field of normal mixture model. The modified p-value approach for detecting differentially expressed genes was also discussed in this dissertation. The modified p-value approach was implemented so that a hypothesis test for the number of components can be conducted by using the modified likelihood ratio test. In the modified p-value approach we penalized the mixing proportion so that the estimates of the mixing proportion are not on the boundary of its parametric space. The null distribution of the (LRTS) was simulated so that the number of components of the uniform beta mixture model can be determined. Finally, for both modified methods, the penalized normal mixture model and the modified p-value approach were applied to simulated and real data.
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Liang, Yi. "Likelihood ratio test for the presence of cured individuals : a simulation study /." Internet access available to MUN users only, 2002. http://collections.mun.ca/u?/theses,157472.

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Hornik, Kurt, and Bettina Grün. "On Maximum Likelihood Estimation of the Concentration Parameter of von Mises-Fisher Distributions." WU Vienna University of Economics and Business, 2012. http://epub.wu.ac.at/3669/1/Report120.pdf.

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Maximum likelihood estimation of the concentration parameter of von Mises-Fisher distributions involves inverting the ratio R_nu = I_{nu+1} / I_nu of modified Bessel functions. Computational issues when using approximative or iterative methods were discussed in Tanabe et al. (Comput Stat 22(1):145-157, 2007) and Sra (Comput Stat 27(1):177-190, 2012). In this paper we use Amos-type bounds for R_nu to deduce sharper bounds for the inverse function, determine the approximation error of these bounds, and use these to propose a new approximation for which the error tends to zero when the inverse of R is evaluated at values tending to 1 (from the left). We show that previously introduced rational bounds for R_nu which are invertible using quadratic equations cannot be used to improve these bounds.
Series: Research Report Series / Department of Statistics and Mathematics
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Pescim, Rodrigo Rossetto. "The new class of Kummer beta generalized distributions: theory and applications." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-30012014-112231/.

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In this study, a new class of generalized distributions was developed, based on the Kummer beta distribution (NG; KOTZ, 1995), which contains as particular cases the exponentiated and beta generators of distributions. The main feature of the new family of distributions is to provide greater flexibility to the extremes of the density function and therefore, it becomes suitable for analyzing data sets with high degree of asymmetry and kurtosis. Also, two new distributions belonging to the new class of distributions, based on the Birnbaum-Saunders and generalized gamma distributions, that has as main characteristic the hazard function which assumes different forms (unimodal, bathtub shape, increase, decrease) were studied. In all studies, general mathematical properties such as ordinary and incomplete moments, generating function, mean deviations, reliability, entropies, order statistics and their moments were discussed. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis and the observed information matrix is derived. It is also considered the likelihood ratio statistics and formal goodness-of-fit tests to compare all the proposed distributions with some of its sub-models and non-nested models. The developed results for all studies were applied to six real data sets.
Neste trabalho, foi proposta uma nova classe de distribuições generalizadas, baseada na distribuição Kummer beta (NG; KOTZ, 1995), que contém como casos particulares os geradores exponencializado e beta de distribuições. A principal característica da nova família de distribuições é fornecer grande flexibilidade para as extremidades da função densidade e portanto, ela torna-se adequada para a análise de conjuntos de dados com alto grau de assimetria e curtose. Também foram estudadas duas novas distribuições que pertencem à nova família de distribuições, baseadas nas distribuições Birnbaum-Saunders e gama generalizada, que possuem função de taxas de falhas que assumem diferentes formas (unimodal, forma de banheira, crescente e decrescente). Em todas as pesquisas, propriedades matemáticas gerais como momentos ordinários e incompletos, função geradora, desvios médio, confiabilidade, entropias, estatísticas de ordem e seus momentos foram discutidas. A estimação dos parâmetros é abordada pelo método da máxima verossimilhança e pela análise bayesiana e a matriz de informação observada foi derivada. Considerou-se, também, a estatística de razão de verossimilhanças e testes formais de qualidade de ajuste para comparar todas as distribuições propostas com alguns de seus submodelos e modelos não encaixados. Os resultados desenvolvidos foram aplicados a seis conjuntos de dados.
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Dai, Xiaogang. "Score Test and Likelihood Ratio Test for Zero-Inflated Binomial Distribution and Geometric Distribution." TopSCHOLAR®, 2018. https://digitalcommons.wku.edu/theses/2447.

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The main purpose of this thesis is to compare the performance of the score test and the likelihood ratio test by computing type I errors and type II errors when the tests are applied to the geometric distribution and inflated binomial distribution. We first derive test statistics of the score test and the likelihood ratio test for both distributions. We then use the software package R to perform a simulation to study the behavior of the two tests. We derive the R codes to calculate the two types of error for each distribution. We create lots of samples to approximate the likelihood of type I error and type II error by changing the values of parameters. In the first chapter, we discuss the motivation behind the work presented in this thesis. Also, we introduce the definitions used throughout the paper. In the second chapter, we derive test statistics for the likelihood ratio test and the score test for the geometric distribution. For the score test, we consider the score test using both the observed information matrix and the expected information matrix, and obtain the score test statistic zO and zI . Chapter 3 discusses the likelihood ratio test and the score test for the inflated binomial distribution. The main parameter of interest is w, so p is a nuisance parameter in this case. We derive the likelihood ratio test statistics and the score test statistics to test w. In both tests, the nuisance parameter p is estimated using maximum likelihood estimator pˆ. We also consider the score test using both the observed and the expected information matrices. Chapter 4 focuses on the score test in the inflated binomial distribution. We generate data to follow the zero inflated binomial distribution by using the package R. We plot the graph of the ratio of the two score test statistics for the sample data, zI /zO , in terms of different values of n0, the number of zero values in the sample. In chapter 5, we discuss and compare the use of the score test using two types of information matrices. We perform a simulation study to estimate the two types of errors when applying the test to the geometric distribution and the inflated binomial distribution. We plot the percentage of the two errors by fixing different parameters, such as the probability p and the number of trials m. Finally, we conclude by briefly summarizing the results in chapter 6.
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Emberson, E. A. "The asymptotic distribution and robustness of the likelihood ratio and score test statistics." Thesis, University of St Andrews, 1995. http://hdl.handle.net/10023/13738.

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Cordeiro & Ferrari (1991) use the asymptotic expansion of Harris (1985) for the moment generating function of the score statistic to produce a generalization of Bartlett adjustment for application to the score statistic. It is shown here that Harris's expansion is not invariant under reparameterization and an invariant expansion is derived using a method based on the expected likelihood yoke. A necessary and sufficient condition for the existence of a generalized Bartlett adjustment for an arbitrary statistic is given in terms of its moment generating function. Generalized Bartlett adjustments to the likelihood ratio and score test statistics are derived in the case where the interest parameter is one-dimensional under the assumption of a mis-specified model, where the true distribution is not assumed to be that under the null hypothesis.
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Gottfridsson, Anneli. "Likelihood ratio tests of separable or double separable covariance structure, and the empirical null distribution." Thesis, Linköpings universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-69738.

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The focus in this thesis is on the calculations of an empirical null distributionfor likelihood ratio tests testing either separable or double separable covariancematrix structures versus an unstructured covariance matrix. These calculationshave been performed for various dimensions and sample sizes, and are comparedwith the asymptotic χ2-distribution that is commonly used as an approximative distribution. Tests of separable structures are of particular interest in cases when data iscollected such that more than one relation between the components of the observationis suspected. For instance, if there are both a spatial and a temporalaspect, a hypothesis of two covariance matrices, one for each aspect, is reasonable.
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Ngunkeng, Grace. "Statistical Analysis of Skew Normal Distribution and its Applications." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1370958073.

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Tao, Jinxin. "Comparison Between Confidence Intervals of Multiple Linear Regression Model with or without Constraints." Digital WPI, 2017. https://digitalcommons.wpi.edu/etd-theses/404.

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Regression analysis is one of the most applied statistical techniques. The sta- tistical inference of a linear regression model with a monotone constraint had been discussed in early analysis. A natural question arises when it comes to the difference between the cases of with and without the constraint. Although the comparison be- tween confidence intervals of linear regression models with and without restriction for one predictor variable had been considered, this discussion for multiple regres- sion is required. In this thesis, I discuss the comparison of the confidence intervals between a multiple linear regression model with and without constraints.
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Osaka, Haruki. "Asymptotics of Mixture Model Selection." Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/27230.

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In this thesis, we consider the likelihood ratio test (LRT) when testing for homogeneity in a three component normal mixture model. It is well-known that the LRT in this setting exhibits non-standard asymptotic behaviour, due to non-identifiability of the model parameters and possible degeneracy of Fisher Information matrix. In fact, Liu and Shao (2004) showed that for the test of homogeneity in a two component normal mixture model with a single fixed component, the limiting distribution is an extreme value Gumbel distribution under the null hypothesis, rather than the usual chi-squared distribution in regular parametric models for which the classical Wilks' theorem applies. We wish to generalise this result to a three component normal mixture to show that similar non-standard asymptotics also occurs for this model. Our approach follows closely to that of Bickel and Chernoff (1993), where the relevant asymptotics of the LRT statistic were studied indirectly by first considering a certain Gaussian process associated with the testing problem. The equivalence between the process studied by Bickel and Chernoff (1993) and the LRT was later proved by Liu and Shao (2004). Consequently, they verified that the LRT statistic for this problem diverges to infinity at the rate of loglog n; a statement that was first conjectured in Hartigan (1985). In a similar spirit, we consider the limiting distribution of the supremum of a certain quadratic form. More precisely, the quadratic form we consider is the score statistic for the test for homogeneity in the sub-model where the mean parameters are assumed fixed. The supremum of this quadratic form is shown to have a limiting distribution of extreme value type, again with a divergence rate of loglog n. Finally, we show that the LRT statistic for the three component normal mixture model can be uniformly approximated by this quadratic form, thereby proving that that the two statistics share the same limiting distribution.
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Books on the topic "Likelihood ratio distributions"

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Srivastava, M. S. Saddlepoint method for obtaining tail probability of Wilk's likelihood ratio test. Toronto: University of Toronto, Dept. of Statistics, 1988.

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Jandaghi, Gholamreza. Monte Carlo estimation of the distributions of the pedigree likelihood, the score statistic and the likelihood ratio statistic using the Gibbs Sampler. 1994.

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Alexander, Peter D. G., and Malachy O. Columb. Presentation and handling of data, descriptive and inferential statistics. Edited by Jonathan G. Hardman. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780199642045.003.0028.

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The need for any doctor to comprehend, assimilate, analyse, and form an opinion on data cannot be overestimated. This chapter examines the presentation and handling of such data and its subsequent statistical analysis. It covers the organization and description of data, measures of central tendency such as mean, median, and mode, measures of dispersion (standard deviation), and the problems of missing data. Theoretical distributions, such as the Gaussian distribution, are examined and the possibility of data transformation discussed. Inferential statistics are used as a means of comparing groups, and the rationale and use of parametric and non-parametric tests and confidence intervals is outlined. The analysis of categorical variables using the chi-squared test and assessing the value of diagnostic tests using sensitivity, specificity, positive and negative predictive values, and a likelihood ratio are discussed. Measures of association are covered, namely linear regression, as is time-to-event analysis using the Kaplan–Meier method. Finally, the chapter discusses the statistical analysis used when comparing clinical measurements—the Bland and Altman method. Illustrative examples, relevant to the practice of anaesthesia, are used throughout and it is hoped that this will provide the reader with an outline of the methodologies employed and encourage further reading where necessary.
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Book chapters on the topic "Likelihood ratio distributions"

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Basmann, R. L., and Hae-Shin Hwang. "A Monte Carlo Study of Structural Estimator Distributions After Performance of Likelihood Ratio Pre-Tests." In Contributions to Econometric Theory and Application, 132–59. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4613-9016-9_5.

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Janžura, Martin. "Asymptotic Behaviour of the Error Probabilities in the Pseudo-Likelihood Ratio Test for Gibbs-Markov Distributions." In Asymptotic Statistics, 285–96. Heidelberg: Physica-Verlag HD, 1994. http://dx.doi.org/10.1007/978-3-642-57984-4_23.

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Coelho, Carlos A., and Barry C. Arnold. "MathematicaⓇ, Maxima, and R Packages to Implement the Likelihood Ratio Tests and Compute the Distributions in the Previous Chapter." In Finite Form Representations for Meijer G and Fox H Functions, 453–90. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28790-0_6.

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Nagar, A. L., and Charu Chandrika. "Edgeworth Approximations to the Distributions of the Likelihood Ratio and F Statistics in the Null and Non-null Cases." In Contributions to Consumer Demand and Econometrics, 189–221. London: Palgrave Macmillan UK, 1992. http://dx.doi.org/10.1007/978-1-349-12221-9_11.

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Ferguson, Thomas S. "Asymptotic Distribution of the Likelihood Ratio Test Statistic." In A Course in Large Sample Theory, 144–50. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-4549-5_22.

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Krauth, J. "Distribution of a Likelihood Ratio Statistic for Spatial Disease Clusters." In Classification and Knowledge Organization, 153–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59051-1_16.

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Holmquist, Björn, Anna Sjöström, and Sultana Nasrin. "Approximating Noncentral Chi-Squared to the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit." In Recent Developments in Multivariate and Random Matrix Analysis, 175–98. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56773-6_11.

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Coelho, Carlos A., and Barry C. Arnold. "Application of the Finite Form Representations of Meijer G and Fox H Functions to the Distribution of Several Likelihood Ratio Test Statistics." In Finite Form Representations for Meijer G and Fox H Functions, 71–452. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28790-0_5.

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Greenhouse, Samuel W., and Joseph L. Gastwirth. "The Joint Asymptotic Distribution of the Maximum Likelihood and Mantel-Haenszel Estimators of the Common Odds Ratio in k 2 x 2 Tables." In Modelling and Prediction Honoring Seymour Geisser, 264–73. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-2414-3_16.

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"A New Approach to Asymptotic Distributions of Maximum Likelihood Ratio Statistics." In Statistical Sciences and Data Analysis, 325–36. De Gruyter, 1993. http://dx.doi.org/10.1515/9783112318867-031.

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Conference papers on the topic "Likelihood ratio distributions"

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Coelho, Carlos A., and Filipe J. Marques. "Near-exact distributions for the block equicorrelation and equivariance likelihood ratio test statistic." In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4823950.

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Ramos-Castro, Daniel, Joaquin Gonzalez-Rodriguez, Alberto Montero-Asenjo, and Javier Ortega-Garcia. "Suspect-Adapted MAP Estimation of Within-Source Distributions in Generative Likelihood Ratio Estimation." In 2006 IEEE Odyssey - The Speaker and Language Recognition Workshop. IEEE, 2006. http://dx.doi.org/10.1109/odyssey.2006.248090.

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Coelho, Carlos A., Filipe J. Marques, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "On the Exact, Asymptotic and Near-exact Distributions for the Likelihood Ratio Statistics to Test Equality of Several Exponential Distributions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637902.

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Williams, O. R., K. Bennett, R. Much, V. Schönfelder, J. J. Blom, and J. Ryan. "Statistical analysis of COMPTEL maximum likelihood-ratio distributions: evidence for a signal from previously undetected AGN." In The fourth compton symposium. AIP, 1997. http://dx.doi.org/10.1063/1.54040.

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Marques, Filipe J., Carlos A. Coelho, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "The Exact and Near-Exact Distributions of the Likelihood Ratio Statistic for the Block Sphericity Test." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3497907.

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Grilo, Luís M., and Carlos A. Coelho. "Near-exact distributions for the likelihood ratio statistic used to test the reality of a covariance matrix." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825615.

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Gold, Erica, Peter French, and Philip Harrison. "Examining long-term formant distributions as a discriminant in forensic speaker comparisons under a likelihood ratio framework." In ICA 2013 Montreal. ASA, 2013. http://dx.doi.org/10.1121/1.4800285.

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Krause, Oswin, Asja Fischer, and Christian Igel. "Algorithms for Estimating the Partition Function of Restricted Boltzmann Machines (Extended Abstract)." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/704.

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Estimating the normalization constants (partition functions) of energy-based probabilistic models (Markov random fields) with a high accuracy is required for measuring performance, monitoring the training progress of adaptive models, and conducting likelihood ratio tests. We devised a unifying theoretical framework for algorithms for estimating the partition function, including Annealed Importance Sampling (AIS) and Bennett's Acceptance Ratio method (BAR). The unification reveals conceptual similarities of and differences between different approaches and suggests new algorithms. The framework is based on a generalized form of Crooks' equality, which links the expectation over a distribution of samples generated by a transition operator to the expectation over the distribution induced by the reversed operator. Different ways of sampling, such as parallel tempering and path sampling, are covered by the framework. We performed experiments in which we estimated the partition function of restricted Boltzmann machines (RBMs) and Ising models. We found that BAR using parallel tempering worked well with a small number of bridging distributions, while path sampling based AIS performed best with many bridging distributions. The normalization constant is measured w.r.t.~a reference distribution, and the choice of this distribution turned out to be very important in our experiments. Overall, BAR gave the best empirical results, outperforming AIS.
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Draayer, Bret, Gary W. Carhart, and Michael K. Giles. "Optical recognition via Bayesian classification: system performance." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.thaa2.

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Given a collection of training images (TIs) to be recognized and a set of filters designed to represent the TIs, a recognition system based on the Bayes likelihood ratio test typically requires a calibration data set to provide an estimate of each probability distribution residing in the signal space. In order to make use of all the correlations evaluated, the dimension of the signal space should be set equal to the product of the number of filters (N f ) and the number of components required by the correlation metric (N m ). Responses are thus N-dimensional vectors (where N = N f N m ), and characterizing the response distributions (one per TI) by an N-dimensional variance analysis allows an unknown sample to be classified by correlating its response with each of the distributions. The calibration data not only provides descriptions of the distributions (used for classification), but also implicitly locates the boundaries between classification regions. Knowledge of the boundaries permits an evaluation of system performance by integrating classification errors over the entire signal space. A recognition system using the procedure outlined above was constructed and calibrated. Expected performance was calculated and compared to observed performance.
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10

Peng, Yijie, Michael C. Fu, and Jian-Qiang Hu. "Estimating distribution sensitivity using generalized likelihood ratio method." In 2016 13th International Workshop on Discrete Event Systems (WODES). IEEE, 2016. http://dx.doi.org/10.1109/wodes.2016.7497836.

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Reports on the topic "Likelihood ratio distributions"

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Anderson, T. W., and H. Hsu. Invariant Tests and Likelihood Ratio Tests for Multivariate Elliptically Contoured Distributions. Fort Belvoir, VA: Defense Technical Information Center, June 1985. http://dx.doi.org/10.21236/ada155844.

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Chernoff, Herman, and Eric Lander. Asymptotic Distribution of the Likelihood Ratio Test That a Mixture of Two Binomials is a Single Binomial. Fort Belvoir, VA: Defense Technical Information Center, May 1991. http://dx.doi.org/10.21236/ada236714.

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3

Amengual, Dante, Xinyue Bei, Marine Carrasco, and Enrique Sentana. Score-type tests for normal mixtures. CIRANO, January 2023. http://dx.doi.org/10.54932/uxsg1990.

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Testing normality against discrete normal mixtures is complex because some parameters turn increasingly underidentified along alternative ways of approaching the null, others are inequality constrained, and several higher-order derivatives become identically 0. These problems make the maximum of the alternative model log-likelihood function numerically unreliable. We propose score-type tests asymptotically equivalent to the likelihood ratio as the largest of two simple intuitive statistics that only require estimation under the null. One novelty of our approach is that we treat symmetrically both ways of writing the null hypothesis without excluding any region of the parameter space. We derive the asymptotic distribution of our tests under the null and sequences of local alternatives. We also show that their asymptotic distribution is the same whether applied to observations or standardized residuals from heteroskedastic regression models. Finally, we study their power in simulations and apply them to the residuals of Mincer earnings functions.
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