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Full-Text Articles in Statistics and Probability
Monte Carlo Methods In Bayesian Inference: Theory, Methods And Applications, Huarui Zhang
Monte Carlo Methods In Bayesian Inference: Theory, Methods And Applications, Huarui Zhang
Graduate Theses and Dissertations
Monte Carlo methods are becoming more and more popular in statistics due to the fast development of efficient computing technologies. One of the major beneficiaries of this advent is the field of Bayesian inference. The aim of this thesis is two-fold: (i) to explain the theory justifying the validity of the simulation-based schemes in a Bayesian setting (why they should work) and (ii) to apply them in several different types of data analysis that a statistician has to routinely encounter. In Chapter 1, I introduce key concepts in Bayesian statistics. Then we discuss Monte Carlo Simulation methods in detail. Our …
Developing Bayesian-Based Confidence Bounds For Non-Identically Distributed Observations Using The Lyapunov Condition, Garry M. Jacyna, Scott L. Rosen
Developing Bayesian-Based Confidence Bounds For Non-Identically Distributed Observations Using The Lyapunov Condition, Garry M. Jacyna, Scott L. Rosen
Journal of Modern Applied Statistical Methods
The purpose of this paper is to establish a direct method for assessing the confidence in the detection and identification probabilities for segmented observations that are not identically distributed across assigned segments within a region. This paper arrives at easily computable confidence intervals by showing through mathematical analysis that:
I. The probability of successful detection within each test segment can be characterized by a Beta distribution;
II. The distribution of a weighted sum of independent but non-identically distributed sample means is asymptotically Normally distributed by the Lyapunov variant of the Central Limit Theorem, i.e., the approximation improves as the number …