The Non-Informative and Informative Prior Distributions in Estimating Variance Parameter of Normal Distribution

This chapter aims to elucidate the concepts of non-informative and informative prior distributions concerning the variance, a crucial component of the unknown parameter within a normal distribution. The variance serves as a representation of the distribution's spread or variability. The estimation variance is exhibited in the point and interval estimations based on non-informative and informative prior distributions. Point estimation entails furnishing a specific value to estimate a population parameter. In contrast, interval estimation provides a range or interval of values to estimate a population parameter, commonly called a confidence interval. While non-informative priors express a need for prior knowledge, informative priors bring valuable insight into the modeling process. The non-informative priors encompass the maximum likelihood method, the Jackknife method, and the bootstrap method. Maximum likelihood is widely recognized for approximating parameters and boasting properties such as unbiased estimation, consistency, and efficiency. The informative prior distribution employs the Bayesian and Markov Chain Monte Carlo methods. These methods involve the prior distribution, given the probability distribution and approach to the posterior distribution.