Analysis of Poisson count data using Geometric Process model

Wan, Wai-Yin; 溫慧妍,

doi:10.5353/th_b3783649

Cited by 2 publications

(8 citation statements)

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“…Chan and Leung (2010) initiated the binary GP model to study the trends of methadone treatment outcomes. And, Wan and Chan (2009) introduced the generalized mixture Poisson GP (GMPGP) model to analyze the new tumour counts of the bladder cancer patients which is extended from the PGP model initiated by Wan (2006).…”

Section: Geometric Process Modelmentioning

confidence: 99%

“…Following the framework of GP model, W it is assumed to follow a Poisson distribution f P (w it |x it ) with mean X it which forms a latent GP. Then, we further assume the stochastic process {Y it = a t−1 it X it } follows some lifetime distributions f (y it ), such as exponential distribution in Wan (2006) and gamma distribution in Wan and Chan (2009), with mean µ it , the resultant model is called Poisson geometric process (PGP) model.…”

Section: Robust Pgp Modelmentioning

confidence: 99%

“…, q a can describe a variety of trend patterns. Refer to Wan (2006) for more details. Apparently, by mixing the Poisson distribution with some heavy-tailed distributions, extra variability will be added to the Poisson distribution which enables the model to accommodate the enlarged variance caused by some extreme observations.…”

Section: Robust Pgp Modelmentioning

confidence: 99%

“…Meanwhile, the mixture effects in both mean and ratio functions can capture the population heterogeneity and overdispersion in the data. See Wan (2006) and Wan and Chan (2009) for more details. In this paper, we introduce a robust mixture Poisson geometric process (RMPGP) model using some heavy-tailed distributions in scale mixture representation.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions

Wan

Chan

2011

Computational Statistics & Data Analysis

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a b s t r a c tWe propose a robust Poisson geometric process model with heavy-tailed distributions to cope with the problem of outliers as it may lead to an overestimation of mean and variance resulting in inaccurate interpretations of the situations. Two heavy-tailed distributions namely Student's t and exponential power distributions with different tailednesses and kurtoses are used and they are represented in scale mixture of normal and scale mixture of uniform respectively. The proposed model is capable of describing the trend and meanwhile the mixing parameters in the scale mixture representations can detect the outlying observations. Simulations and real data analysis are performed to investigate the properties of the models.

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Section: Geometric Process Modelmentioning

confidence: 99%

Section: Robust Pgp Modelmentioning

confidence: 99%

Section: Robust Pgp Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions

Wan

Chan

2011

Computational Statistics & Data Analysis

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“…In this study, while treatment effect, placebo or thiopeta, on the new tumour counts is the main interest, the distinctive trend patterns displayed in the outcomes of the patients are also worthy of investigation. Therefore we apply the PGP model of Wan (2006) and Chan et al (2009) and extend it to include mixture effects, stochastic means for Poisson distribution and zero‐inflated modelling in order to handle population heterogeneity and excess zeros.…”

Section: Bladder Cancer Datamentioning

confidence: 99%

A New Approach for Handling Longitudinal Count Data with Zero‐Inflation and Overdispersion: Poisson Geometric Process Model

Wan

Chan

2009

Biometrical J

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For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).

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Analysis of Poisson count data using Geometric Process model

Cited by 2 publications

References 0 publications

Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions

Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions

A New Approach for Handling Longitudinal Count Data with Zero‐Inflation and Overdispersion: Poisson Geometric Process Model

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