Over‐and Underdispersion Models

Kokonendji, Célestin C.

doi:10.1002/9781118596333.ch30

Cited by 26 publications

(15 citation statements)

References 111 publications

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“…GLM allows choosing the suitable model fit on the basis of dispersion parameters and model fit criteria. The procedures of model fitting are 1) model selection 2) parameter estimation and 3) prediction of future values (McCullagh & Nelder, 1989;Kokonendji, 2014). Journal of Geoscience and Environment Protection…”

Section: Generalized Linear Modelsmentioning

confidence: 99%

Estimating the Probability of Earthquake Occurrence and Return Period Using Generalized Linear Models

Shrestha¹

2019

GEP

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In this paper, the frequency of an earthquake occurrence and magnitude relationship has been modeled with generalized linear models for the set of earthquake data of Nepal. A goodness of fit of a statistical model is applied for generalized linear models and considering the model selection information criterion, Akaike information criterion and Bayesian information criterion, generalized Poisson regression model has been selected as a suitable model for the study. The objective of this study is to determine the parameters (a and b values), estimate the probability of an earthquake occurrence and its return period using a Poisson regression model and compared with the Gutenberg-Richter model. The study suggests that the probabilities of earthquake occurrences and return periods estimated by both the models are relatively close to each other. The return periods from the generalized Poisson regression model are comparatively smaller than the Gutenberg-Richter model.

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Section: Generalized Linear Modelsmentioning

confidence: 99%

Estimating the Probability of Earthquake Occurrence and Return Period Using Generalized Linear Models

Shrestha¹

2019

GEP

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“…The Poisson parametric part in (2) is generally retained because of its equidispersion property with respect to over-and underdispersion phenomenon in the family of count distributions (Kokonendji 2014).…”

Section: Estimator and Cross-validation Proceduresmentioning

confidence: 99%

Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data

2015

Self Cite

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This work takes advantage of semiparametric modelling which improves significantly in many situations the estimation accuracy of the purely nonparametric approach. Herein for semiparametric estimations of probability mass function (pmf) of count data, and an unknown count regression function (crf), the kernel used is a binomial one and the bandiwdth selection is investigated by developing Bayesian approaches. About the latter, Bayes local and global bandwidth approaches are used to establish data-driven selection procedures in semiparametric framework. From conjugate beta prior distributions of the smoothing parameter and under the squared errors loss function, Bayes estimate for pmf is obtained in closed form. This is not available for the crf which is computed by the Markov Chain Monte Carlo technique. Simulation studies demonstrate that both proposed methods perform better than the classical cross-validation procedures, in particular the smoothing quality and execution times are optimized. All applications are made on real data sets. B Nabil Zougab

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“…25,26 Consequently, many techniques have been proposed to optimize data representation for more efficient and accurate clustering, 27 such as log-normalizing counts to reduce the impact of burstiness on the likelihood of a document, 28 or proposing other suitable distributions, such as zero-inflated Poisson or negative multinomial distributions. [29][30][31] The most successful results, however, were reached by introducing Dirichlet distribution as a prior to the multinomial, which is the classic approach to multinomial estimation, owing to Dirichlet being a natural conjugate to the multinomial. 32 This model, known as the Dirichlet compound multinomial, 26 has led to better clustering results that are comparable to the ones obtained with multiple heuristic changes to the multinomial model.…”

Section: Introductionmentioning

confidence: 99%

Mixture‐based clustering for count data using approximated Fisher Scoring and Minorization–Maximization approaches

Bregu

Zamzami

Bouguila

2020

Computational Intelligence

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The multinomial distribution has been widely used to model count data. To increase clustering efficiency, we use an approximation to the Fisher scoring algorithm, which is more robust regarding the choice of initial parameter values. Then, we use a novel approach to estimate the optimal number of components, based on minimum message length criterion. Moreover, we consider a generalization of the multinomial model obtained by introducing the Dirichlet as prior, yielding the Dirichlet Compound Multinomial (DCM). Even though DCM can address the burstiness phenomenon of count data, the presence of Gamma function in its density function usually leads to undesired complications. In this article, we use two alternative representations of DCM distribution to perform clustering based on finite mixture models, where the mixture parameters are estimated using the minorization-maximization framework. To evaluate and compare the performance of our proposed models, we have considered three challenging real-world applications that involve high-dimensional count vectors, namely, sentiment analysis, facial expression recognition, and human action recognition. The results show that the proposed algorithms increase the clustering efficiency of their respective models remarkably, and the best results are achieved by the second parametrization of DCM, which can accommodate over-dispersed count data.

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Over‐and Underdispersion Models

Cited by 26 publications

References 111 publications

Estimating the Probability of Earthquake Occurrence and Return Period Using Generalized Linear Models

Estimating the Probability of Earthquake Occurrence and Return Period Using Generalized Linear Models

Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data

Mixture‐based clustering for count data using approximated Fisher Scoring and Minorization–Maximization approaches

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