Markov Chain Monte Carlo-Based Estimation of Stress–Strength Reliability Parameter for Generalized Linear Failure Rate Distributions

This paper provides Bayesian and classical inference of Stress–Strength reliability parameter, [Formula: see text], where both [Formula: see text] and [Formula: see text] are independently distributed as 3-parameter generalized linear failure rate (GLFR) random variables with different parameters. Due to importance of stress–strength models in various fields of engineering, we here address the maximum likelihood estimator (MLE) of [Formula: see text] and the corresponding interval estimate using some efficient numerical methods. The Bayes estimates of [Formula: see text] are derived, considering squared error loss functions. Because the Bayes estimates could not be expressed in closed forms, we employ a Markov Chain Monte Carlo procedure to calculate approximate Bayes estimates. To evaluate the performances of different estimators, extensive simulations are implemented and also real datasets are analyzed.

On Reasoning about Access to Knowledge

Controlling access to knowledge plays a crucial role in many multi-agent systems. In- deed, it is related to different central aspects in interactions among agents such as privacy, security, and cooperation. In this paper, we propose a framework for dealing with access to knowledge that is based on the inference process in classical propositional logic: an agent has access to every piece of knowledge that can be derived from the available knowledge using the classical inference process. We first introduce a basic problem in which an agent has to hide pieces of knowledge, and we show that this problem can be solved through the computation of maximal consistent subsets. In the same way, we also propose a coun- terpart of the previous problem in which an agent has to share pieces of knowledge, and we show that this problem can be solved through the computation of minimal inconsis- tent subsets. Then, we propose a generalization of the previous problem where an agent has to share pieces of knowledge and hide at the same time others. In this context, we introduce several concepts that allow capturing interesting aspects. Finally, we propose a weight-based approach by associating integers with the pieces of knowledge that have to be shared or hidden.

Implementation of Bayesian Multiple Comparison Correction in the Second-Level Analysis of fMRI Data: With Pilot Analyses of Simulation and Real fMRI Datasets Based on Voxelwise Inference

We developed and tested Bayesian multiple comparison correction method for Bayesian voxelwise second-level fMRI analysis with R. The performance of the developed method was tested with simulation and real image datasets. First, we compared false alarm and hit rates, which were used as proxies for selectivity and sensitivity, respectively, between Bayesian and classical inference were conducted. For the comparison, we created simulated images, added noise to the created images, and analyzed the noise-added images while applying Bayesian and classical multiple comparison correction methods. Second, we analyzed five real image datasets to examine how our Bayesian method worked in realistic settings. When the performance assessment was conducted, Bayesian correction method demonstrated good sensitivity (hit rate ≥ 75%) and acceptable selectivity (false alarm rate < 10%) when N ≤ 8. Furthermore, Bayesian correction method showed better sensitivity compared with classical correction method while maintaining the aforementioned acceptable selectivity.

The Burr X Fréchet Model for Extreme Values: Mathematical Properties, Classical Inference and Bayesian Analysis

In this paper, we investigate a new model based on Burr X and Fréchet distribution forextreme values and derive some of its properties. Maximum likelihood estimation alongwith asymptotic confidence intervals is considered for estimating the parameters of thedistribution. We demonstrate empirically the flexibility of the distribution in modelingvarious types of real data. Furthermore, we also provide Bayes estimators and highestposterior density intervals of the parameters of the distribution using Markov ChainMonte Carlo (MCMC) methods.