# Abstract/Details

## Applications of Bayesian statistics

2009 2009

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### Abstract (summary)

Facing challenges like designing complex models, summarizing large data sets and fitting probability models, applied statisticians frequently appeal to using commercial software packages. A majority of the packages use a classical or a frequentist statistical process. Bayesian Analysis, an alternative to the classical one, comes as a rather effective way to deal with statistical problems and it has many applications. Fitting a simple linear regression model is commonly solved by estimating the parameters by the Least Square Estimation method. One limitation of the Least Square Estimation method comes when looking at how to assess the effect of covariates on a specific quantile of the dependent variables. Quantile Regression is used in that respect and it is a convenient way to perform linear regression by estimating the conditional quantiles. When we think about the precision of our estimates, the Bayesian approach of Quantile Regression has one advantage in that it is possible to have the exact posterior distribution of the conditional coefficients of the regression model. E.Tsionas [1] gives an effective approach to obtain the posterior probabilities from the assumption of a scale mixture of the normal distribution on the error term of the linear model. The posterior distribution of the parameter of interest can be obtained using data augmentation around Gibbs Sampling with WinBUGS. In that case, Bayesian Median regression seems to be easily tractable - it remains a challenge to obtain the distribution of other specific quantiles. In this thesis, we will first start with Bayesian Median regression, and continue by segmenting the conditional response variable which would have in this case a conditional distribution. Using R which is a convenient environment to implement with the package BRugs and after a limited number of estimations, we will derive a regression model on those parameters estimates in order to infer about the estimated ones.

### Indexing (details)

Subject
Statistics
Classification
0463: Statistics
Identifier / keyword
Pure sciences; Bayesian analysis; Bayesian quantile regression; Gibbs sampling; Least square estimation; Winbugs
Title
Applications of Bayesian statistics
Author
Nono, Bertin
Number of pages
63
Publication year
2009
Degree date
2009
School code
0390
Source
MAI 47/05M, Masters Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109142006
Smith, David D.
Committee member
Allen, Michael; Machida, Motoya
University/institution
Tennessee Technological University
Department
Mathematics
University location
United States -- Tennessee
Degree
M.S.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
1464340
ProQuest document ID
305059336