Mixed Poisson Distributions

Karlis, Dimitris; Xekalaki, Evdokia

doi:10.1111/j.1751-5823.2005.tb00250.x

Cited by 258 publications

(210 citation statements)

References 138 publications

(141 reference statements)

Supporting

Mentioning

205

Contrasting

Unclassified

Order By: Relevance

“…After specifying the model, we can devise strategies to find a statistically optimal estimator. If we select the mean squared error (MSE) as the criterion to minimize, then we arrive at the minimum mean squared error (MMSE) estimator also termed posterior mean estimator [23] and is given by (1) which can be written, by applying Bayes' rule, as 2 (2) The marginal distribution of the noisy image appearing in the denominator of (2) belongs to the mixed Poisson distribution family [24]; parameter estimation for an interesting subclass of this family is discussed in [25]. The Bayesian framework is attractive for our problem, but poses two challenges: One is the specification of an appropriate multivariate prior distribution for the intensity image, the other is the solution of the estimation problem in a multidimensional space which can be a formidable task.…”

Section: A Problem Formulationmentioning

confidence: 99%

“…Using the identity (can be easily verified by direct substitution) (22) where the Polya distribution [29] (also called Dirichlet-multinomial) is defined in Table I, we can write the posterior factors as mixtures of Dirichlet densities (23) Here indicates which mixture component is responsible for generating the observation and the corresponding posterior mixture assignment weights equal (24) Note that the expressions (23) and (24) also cover the separable model, in which case the Dirichlet reduces to beta distribution.…”

Section: A Multiscale Posterior Factorizationmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising

Lefkimmiatis

Maragos

Papandreou

2009

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

Abstract-We present an improved statistical model for analyzing Poisson processes, with applications to photon-limited imaging. We build on previous work, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities (rates) in adjacent scales are modeled as mixtures of conjugate parametric distributions. Our main contributions include: 1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the noisy observed Poisson data (counts); 2) extension of the method to work under a multiscale hidden Markov tree model (HMT) which couples the mixture label assignments in consecutive scales, thus modeling interscale coefficient dependencies in the vicinity of image edges; 3) exploration of a 2-D recursive quad-tree image representation, involving Dirichlet-mixture rate-ratio densities, instead of the conventional separable binary-tree image representation involving beta-mixture rate-ratio densities; and 4) a novel multiscale image representation, which we term Poisson-Haar decomposition, that better models the image edge structure, thus yielding improved performance. Experimental results on standard images with artificially simulated Poisson noise and on real photon-limited images demonstrate the effectiveness of the proposed techniques.

show abstract

Section: A Problem Formulationmentioning

confidence: 99%

Section: A Multiscale Posterior Factorizationmentioning

confidence: 99%

Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising

Lefkimmiatis

Maragos

Papandreou

2009

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

show abstract

“…The main condition for using the Poisson model is the equivalence of mean and variance of the response variable. If this condition is not present, the generalized Poisson distribution model will be appropriate (24)(25)(26). Discrete-count data sometimes show excessive dispersion and cannot be explained by a simple model such as binomial or Poisson.…”

Section: Discussionmentioning

confidence: 99%

Efficiency of Zero-Inflated Generalized Poisson Regression Model on Hospital Length of Stay Using Real Data and Simulation Study

Hassankiadeh

Kazemnejad

Fesharaki

et al. 2018

CJHR

View full text Add to dashboard Cite

Background: An important feature of Poisson distribution is the equality of mean and variance. However, additional zeroes in the data may cause over-dispersion in most cases, in which zero-inflated models are recommended. In this study, we aimed to evaluate the efficacy of zero-inflated models to predict hospital length of stay (LOS) using real data and simulated study. Methods: This study was conducted on patients admitted at Shariati hospital, Tehran, Iran. Zero inflated Poisson (ZIP), zero inflated negative binomials (ZINB) and zero inflated generalized Poisson (ZIGP) models were fitted on patient's length of stay. The fitted models were compared using the Akaike information criterion (AIC). The simulated data was generated using a model with the lowest AIC. Different models were then compared using the AIC. Data analysis was performed in R statistical software. Results:The results of both real data and simulation study showed lower AIC for ZIGP model compared to ZIP and ZINB model. Conclusion: Given the high dispersion and Zero Inflation in hospital LOS, the zero-inflated generalized Poisson regression model is the most suitable model to predict determinants of LOS. Keywords: Computer Simulation, Hospital, Length of Stay, Poisson Distribution Citation: Farhadi Hassankiadeh R, Kazemnejad A, Gholami Fesharaki M, Kargar Jahromi S. Efficiency of zero-inflated generalized poisson regression model on hospital length of stay using real data and simulation study.

show abstract

“…Since it is a mixed Poisson distribution then it is overdispersed. The probability of observing a zero value is higher than under a Poisson distribution with the same mean, termed zero inflated phenomenon, (see Karlis & Xekalaki, 2005 and references therein). Furthermore, for mean values under 2.4, which includes practically all the real data cases, it is straightforward to prove the termed one-deflated phenomenon, i.e., f PL (1; θ 1 ) < f P (1;…”

Section: The Modelmentioning

confidence: 99%

The Bayes Premium in an Aggregate Loss Poisson-Lindley Model with Structure Function STSP

Hernández-Bastida¹,

Fernández-Sánchez²

2013

IJSP

View full text Add to dashboard Cite

Many premium calculating problems in actuarial science consider the number of claims, denoted as K, as the variable risk. Traditionally, this random variable is modelled by the Poisson distribution. However, it is well known that automobile insurance portfolios are characterized by zero-inflation (high percentage of zero values in the sample) and overdispersion (the variance is greater than the mean), and the Poisson distribution does not properly reflect the last phenomenon. In this paper we determine the Bayes premium considering that K follows a PoissonLindley distribution, with parameter θ 1 in [0, 1], which is a potential alternative to describe these situations. As the structure function for θ 1 we elicit the standardized two-sided power distribution, which is a reasonable alternative to the usual beta distribution. In addition, an aggregate loss model is considered with primary distribution given by the Poisson-Lindley distribution. A Bayesian analysis is developed to obtain the Bayes premium. The conclusion is that the STSP is not an adequate alternative in the problem in question because it is more informative and less dispersed than the Beta distribution.

show abstract

Mixed Poisson Distributions

Cited by 258 publications

References 138 publications

Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising

Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising

Efficiency of Zero-Inflated Generalized Poisson Regression Model on Hospital Length of Stay Using Real Data and Simulation Study

The Bayes Premium in an Aggregate Loss Poisson-Lindley Model with Structure Function STSP

Contact Info

Product

Resources

About