불충분한 반응에서의 이변수 포아송 회귀의 베이지안 추론
- 불충분한 반응에서의 이변수 포아송 회귀의 베이지안 추론
- Other Titles
- Bayesian Inference for Bivariate Poisson Regression with Underreported Responses
- Issue Date
- Shankar et al., 1997
Washington et al., 2003). These models are motivated by the fact that traditional applications of PRM and NBRM do not address the possibility of zero-inflated counting processes. Zero-inflation can be explained by the existence of a dual-state process for accident data generation (cf. Shankar et al., 1997
Carson and Mannering, 2001
Lee and Mannering, 2002). Zero-inflated models are characterized in the following manner. Some roadway segments could have accidents, but the corresponding probabilities are too low to be measured over some time periods.
Subsequently, these segments are often regarded as safe spots with a zero-accident state. Other roadway segments may follow a standard count process (PRM or NBRM) for which the number of accidents with non- negative integers is a possible outcome over a specified time period.
The rest of thesis is organized as follows. In Chapter 2, we extensively describe the models including zero-inflated Poisson regression models and multivariate Poisson distributions. In Chapter 3, we present prior specifi- cations and Bayesian computation algorithms. In Chapter 4, general full conditional distributions are derived. Experimental results are presented in Chapter 5. We finish this thesis with brief concluding remarks.
Multivariate Poisson distributions are useful tools in applications involving multivariate discrete data. A number of techniques has been proposed to deal with the computational problems of the multivariate Poisson distribution.
In connection with bivariate Poisson distributions such estimation techniques have been proposed by Papageorgiou and Loukas (1988). Trivariate distributions have been discussed in detail by Kawamura (1976). For additional references see Tsionas (1999).
The purpose of this paper is to consider Bayesian inference in bivariate Poisson regression models using the methods previously proposed by Tsionas (1999). The statistical framework is that of a bivariate Poisson distribution whose parameters depend on exogenous variables just like the parameter of the univariate Poisson distribution depends on certain variables in order to arrive at the univariate Poisson regression model. As the maximum likelihood estimation is prohibitive for the bivariate Poisson distribution, the same holds true for the proposed bivariate Poisson regression model.
However based on the data augmentation method of Tsionas (1999), it is possible to analyze bivariate Poisson regression models using computational Bayesian methods organized around Gibbs sampling.
We often encounter situations where these count data have a tendency to contain a large portion of zero observations. For instance, according to Lambert (1992) the portion of defective items could be at least 80% provided a manufacturing process is near perfectly executed. We call these zero-inflated data if a number of zeros is greater than expected when using the standard PRM or NBRM. As a result, the zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) regression models have received considerable attention when used in roadway safety studies (cf. Miaou, 1994
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