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Abstract
Predictive inference is one of the oldest methods of statistical analysis and it is based on observable data. Prior information plays an important role in the Bayesian methodology. Researchers in this field are often subjective to exercise noninformative prior. This study tests the effects of a range of prior distributions on the Bayesian predictive inference for different modelling situations such as linear regression models under normal and Student-t errors. Findings reveal that different choice of priors not only provide different prediction distributions of the future response(s) but also change the location and/or scale or shape parameters of the prediction distributions.
Highlights
The posterior distribution for parameters of a set of observations is typically the major objective of the Bayesian statistical analysis
This study tests the effects of a range of prior distributions on the Bayesian predictive inference for different modelling situations such as linear regression models under normal and Student-t errors
This study examines the effects of a range of prior distributions on predictive inference for different modelling situations under the normal and Student-t errors
Summary
The posterior distribution for parameters of a set of observations is typically the major objective of the Bayesian statistical analysis. Unlike others Rahman (2009, 2011) obtained prediction distribution using the Bayesian method for a range of statistical models under the t errors assumption. Some conflicts may cause by the data (for instance, outliers) or by the prior knowledge In such situations, if the models are with a light-tailed distribution, the conflict may strongly influence the posterior distribution and potentially lead to inappropriate statistical inferences (Andrade & O’Hagan, 2006). This study examines the effects of a range of prior distributions on predictive inference for different modelling situations under the normal and Student-t errors.
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