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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 …
Extending The Latent Multinomial Model With Complex Error Processes And Dynamic Markov Bases, Simon J. Bonner, Matthew R. Schofield, Patrik Noren, Steven J. Price
Extending The Latent Multinomial Model With Complex Error Processes And Dynamic Markov Bases, Simon J. Bonner, Matthew R. Schofield, Patrik Noren, Steven J. Price
Forestry and Natural Resources Faculty Publications
The latent multinomial model (LMM) of Link et al. [Biometrics 66 (2010) 178–185] provides a framework for modelling mark-recapture data with potential identification errors. Key is a Markov chain Monte Carlo (MCMC) scheme for sampling configurations of the latent counts of the true capture histories that could have generated the observed data. Assuming a linear map between the observed and latent counts, the MCMC algorithm uses vectors from a basis of the kernel to move between configurations of the latent data. Schofield and Bonner [Biometrics 71 (2015) 1070–1080] shows that this is sufficient for some models within the …