تحليل بيزي رگرسيون چندكي براي داده هاي شمارشي صفرآماسيده

چكيده انگليسي :

Bayesian analysis of quantile regression for zero inflated count data MINA AZIZI KOOHANESTANI m azizi@math iut ac ir October 20 2020 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Zahra Saberi z saberi@iut ac irAdvisor Dr Reyhaneh Rikhtehgaran r rikhtehgaran@iut ac ir2000 MSC 62G08 62E20 62F15Keywords Asymmetric Laplace distribution Bayesian quantile regression Count data Hurdle model Marcov chainMonte Carlo Two part model Zero inflatedAbstract This M Sc thesis is based on the following papers Gibbs sampling methods for bayesian quantile regression Journal K H K G of statistical computation and simulation 81 11 2011 1565 1578 J A bayesian two part quantile regression model for count data with excess K C S J zeros Statistical Modelling 2018 p 1471082X18799919Regression models are a good tool for examining the relationship between response variable and one or more ex planatory variables that have a special place in statistics A widely used regression model is quantile regression that allows for the examination of explanatory variables effects across an entire response distribution and offer afuller picture of the relationship between independent and dependent variables than that obtained by mean regressionincluding ordinary least squares OLS Quantile regression estimators are not sensitive to outliers unlike OLS estimators In other hand quantile regressionmodel does not require to specific hypothesis of OLS regression model such as the normality of the response variabledistribution and homogeneity of variance Quantile regression is considered from both classical and Bayesian approach Classical quantile regression is a non parametric method in which no assumptions are made for model error distribution but in the Bayesian framework placing an asymmetric Laplace distribution on the error terms has attracted much attention In order to easily imple ment Bayesian methods to obtain parameter estimation the Marcov chain Monte Carlo methods are used to generatethe samples from the posterior distribution In particular we apply normal priors on regression parameters and deve lope a Gibbs sampling algorithm based on a location scale mixture representation of the asymmetric Laplace distri bution Bayesian approach presents significantly narrower parameter intervals than classical approach particularlyat the smallest sample size Quantile regression methods have been almost exclusively applied to continuous response variables When the re sponse variable is count jittering transformation on the response variable is proposed After this transformation log linear quantile regression is used In modeling count data it is common in many fields including business epidemiology and ecology to encounter alarge number of zeros When the number of zeros in response variable is greater than expected under a standard countdistribution such as Poisson or negative binomial with a fixed mean the data are said to be zero inflated Modelsthat ignore this phenomenon lead to biased or even altogether misspecified parameter estimates Two popular models for addressing excess zeros in count data are the hurdle model and a class of zero inflated mod els The zero inflated models assume that some of the zeros ara sampling zeros realizations from a standard countdistribution while the rest are structural zeros arising from a separate data generating process These models attemptto identify which are sampling zeros and model them along with the positive counts Hurdle models on the other

عزيزي كوهانستاني، مينا

تحليل بيزي رگرسيون چندكي براي داده هاي شمارشي صفرآماسيده

توزيع لاپلاس نامتقارن , داده هاي شمارشي , رگرسيون چندكي بيزي , زنجيره ماركف مونت كارلو , صفرآماسيده , مدل دوبخشي , مدل هاردل