The Non-Informative and Informative Prior Distributions in Estimating Variance Parameter of Normal Distribution | Chapter 7 | Research Updates in Mathematics and Computer Science Vol. 4

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.

Author(s) Details:

Autcha Araveeporn,
Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok-10520, Thailand.

Please see the link here: https://stm.bookpi.org/RUMCS-V4/article/view/14101

The Parametric and Nonparametric Estimations of Normal Distribution for Mean Parameter | Chapter 12 | Research and Applications Towards Mathematics and Computer Science Vol. 7

 This stage's objective describes the point and pause estimations on the mean that is a part of life after death parameter of sane distribution. The mean represents the allocation's central locale or average, while the standard deviation measures the spread or instability of the data.   Point estimation includes providing a specific advantage to estimate a population limit. The interval estimation supplies a range or interval of principles to estimate a population parameter, named a confidence pause. These estimations are estimated for one parametric method by using the maximum prospect, Bayesian, and Markov Chain Monte Carlo procedures. The nonparametric method consists of the start operating system and the Jackknife arrangements. Maximum likelihood is the familiar method to approximate parameters cause there are the characteristics of the unbiased estimator, consistency, and adeptness estimator. The Bayesian method is a mathematical approach based on feasibility, prior, and posterior distribution. The Markov Chain Gambling establishment technique influences Markov chains and random sampling to estimate complex anticipation distributions and involves the Bayesian method. The start operating system and Jackknife forms are the resampling techniques by repeatedly illustration samples from the available dossier.

Author(s) Details:

Autcha Araveeporn,
Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok-10520, Thailand.

Somsri Banditvilai,
Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok-10520, Thailand.

Please see the link here: https://stm.bookpi.org/RATMCS-V7/article/view/12883