Matrix-variate distributions represent a natural way for modeling random matrices. Realizations from random matrices are generated by the simultaneous observation of variables in different situations or locations, and...
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Matrix-variate distributions represent a natural way for modeling random matrices. Realizations from random matrices are generated by the simultaneous observation of variables in different situations or locations, and are commonly arranged in three-way data structures. Among the matrix-variate distributions, the matrix normal density plays the same pivotal role as the multivariate normal distribution in the family of multivariate distributions. In this work we define and explore finite mixtures of matrix normals. An emalgorithm for the model estimation is developed and some useful properties are demonstrated. We finally show that the proposed mixture model can be a powerful tool for classifying three-way data both in supervised and unsupervised problems. A simulation study and some real examples are presented.
Skew scale mixtures of normal distributions are often used for statistical procedures involving asymmetric data and heavy-tailed. The main virtue of the members of this family of distributions is that they are easy to...
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Skew scale mixtures of normal distributions are often used for statistical procedures involving asymmetric data and heavy-tailed. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine expectation-maximization (em) algorithms for maximum likelihood estimation. In this paper, we extend the emalgorithm for linear regression models and we develop diagnostics analyses via local influence and generalized leverage, following Zhu and Lee's approach. This is because Cook's well-known approach cannot be used to obtain measures of local influence. The em-type algorithm has been discussed with an emphasis on the skew Student-t-normal, skew slash, skew-contaminated normal and skew power-exponential distributions. Finally, results obtained for a real data set are reported, illustrating the usefulness of the proposed method.
The analysis of finite mixture models for exponential repeated data is considered. The mixture components correspond to different unknown groups of the statistical units. Dependency and variability of repeated data ar...
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The analysis of finite mixture models for exponential repeated data is considered. The mixture components correspond to different unknown groups of the statistical units. Dependency and variability of repeated data are taken into account through random effects. For each component, an exponential mixed model is thus defined. When considering parameter estimation in this mixture of exponential mixed models, the em-algorithm cannot be directly used since the marginal distribution of each mixture component cannot be analytically derived. In this paper, we propose two parameter estimation methods. The first one uses a linearisation specific to the exponential distribution hypothesis within each component. The second approach uses a Metropolis-Hastings algorithm as a building block of a general MCem-algorithm. (C) 2009 Elsevier Inc. All rights reserved.
This paper considers a finite mixture model for longitudinal data, which can be used to study the dependency of the shape of the respective follow-up curves on treatments or other influential factors and to classify t...
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This paper considers a finite mixture model for longitudinal data, which can be used to study the dependency of the shape of the respective follow-up curves on treatments or other influential factors and to classify these curves. An em-algorithm to achieve the ml-estimate of the model is given. The potencies of the model are demonstrated using data of a clinical trial.
A recursive algorithm is proposed for estimation of parameters in mixture models, where the observations are governed by a hidden Markov chain. The performance of the algorithm is studied by simulations of a symmetric...
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A recursive algorithm is proposed for estimation of parameters in mixture models, where the observations are governed by a hidden Markov chain. The performance of the algorithm is studied by simulations of a symmetric normal mixture. The algorithm seems to be stable and produce approximately normally distributed estimates, provided the adaptive matrix is kept well conditioned.
In this paper, we introduce a flexible family of cure rate models, mainly motivated by the biological derivation of the classical promotion time cure rate model and assuming that a metastasis-competent tumor cell prod...
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In this paper, we introduce a flexible family of cure rate models, mainly motivated by the biological derivation of the classical promotion time cure rate model and assuming that a metastasis-competent tumor cell produces a detectable-tumor mass only when a specific number of distinct biological factors affect the cell. Special cases of the new model are, among others, the promotion time (proportional hazards), the geometric (proportional odds), and the negative binomial cure rate model. In addition, our model generalizes specific families of transformation cure rate models and some well-studied destructive cure rate models. Exact likelihood inference is carried out by the aid of the expectation-maximization algorithm;a profile likelihood approach is exploited for estimating the parameters of the model while model discrimination problem is analyzed by the aid of the likelihood ratio test. A simulation study demonstrates the accuracy of the proposed inferential method. Finally, as an illustration, we fit the proposed model to a cutaneous melanoma data-set. Copyright (C) 2017 John Wiley & Sons, Ltd.
To investigate in detail the effect of infection or vaccination on the human immune system, ELISpot assays are used to simultaneously test the immune response to a large number of peptides of interest. Scientists comm...
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To investigate in detail the effect of infection or vaccination on the human immune system, ELISpot assays are used to simultaneously test the immune response to a large number of peptides of interest. Scientists commonly use "peptide pools", where, instead of an individual peptide, a test well contains a group of peptides. Since the response from a well may be due to any or many of the peptides in the pool, pooled assays usually need to be followed by confirmatory assays of a number of individual peptides. We present a statistical method that enables estimation of individual peptide responses from pool responses using the Expectation Maximization (em) algorithm for "incomplete data". We demonstrate the accuracy and precision of these estimates in simulation studies of ELISpot plates with 90 pools of 6 or 7 peptides arranged in three dimensions and three Mock wells for the estimation of background. In analysis of real pooled data from 6 subjects in a HIV-1 vaccine trial, where 199 peptides were arranged in 80 pools if size 9 or 10, our estimates were in very good agreement with the results from individual-peptide confirmatory assays. Compared to the classical approach, we could identify almost all the same peptides with high or moderate response, with less than half the number of confirmatory tests. Our method facilitates efficient use of the information available in pooled ELISpot data to avoid or reduce the need for confirmatory testing. We provide an easy-to-use free online application for implementing the method, where on uploading two spreadsheets with the pool design and pool responses, the user obtains the estimates of the individual peptide responses. (C) 2016 Elsevier B.V. All rights reserved.
Partially linear models (PLMs) are an important tool in modelling economic and biometric data and are considered as a flexible generalization of the linear model by including a nonparametric component of some covariat...
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Partially linear models (PLMs) are an important tool in modelling economic and biometric data and are considered as a flexible generalization of the linear model by including a nonparametric component of some covariate into the linear predictor. Usually, the error component is assumed to follow a normal distribution. However, the theory and application (through simulation or experimentation) often generate a great amount of data sets that are skewed. The objective of this paper is to extend the PLMs allowing the errors to follow a skew-normal distribution [A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171-178], increasing the flexibility of the model. In particular, we develop the expectation-maximization (em) algorithm for linear regression models and diagnostic analysis via local influence as well as generalized leverage, following [H. Zhu and S. Lee, Local influence for incomplete-data models, J. R. Stat. Soc. Ser. B 63 (2001), pp. 111-126]. A simulation study is also conducted to evaluate the efficiency of the emalgorithm. Finally, a suitable transformation is applied in a data set on ragweed pollen concentration in order to fit PLMs under asymmetric distributions. An illustrative comparison is performed between normal and skew-normal errors.
Non-negative matrix factorisation (NMF) is an increasingly popular unsupervised learning method. However, parameter estimation in the NMF model is a difficult high-dimensional optimisation problem. We consider algorit...
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Non-negative matrix factorisation (NMF) is an increasingly popular unsupervised learning method. However, parameter estimation in the NMF model is a difficult high-dimensional optimisation problem. We consider algorithms of the alternating least squares type. Solutions to the least squares problem fall in two categories. The first category is iterative algorithms, which include algorithms such as the majorise-minimise (MM) algorithm, coordinate descent, gradient descent and the Fevotte-Cemgil expectation-maximisation (FC-em) algorithm. We introduce a new family of iterative updates based on a generalisation of the FC-emalgorithm. The coordinate descent, gradient descent and FC-emalgorithms are special cases of this new em family of iterative procedures. Curiously, we show that the MM algorithm is never a member of our general emalgorithm. The second category is based on cone projection. We describe and prove a cone projection algorithm tailored to the non-negative least square problem. We compare the algorithms on a test case and on the problem of identifying mutational signatures in human cancer. We generally find that cone projection is an attractive choice. Furthermore, in the cancer application, we find that a mix-and-match strategy performs better than running each algorithm in isolation.
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