We provide a detailed, introductory exposition of the Metropolis-Hastings algorithm, a powerful Markov chain method to simulate multivariate distributions. A simple, intuitive derivation of this method is given along with guidance on implementation. Also discussed are two applications of the algorithm, one for implementing acceptance-rejection sampling when a blanketing function is not available and the other for implementing the algorithm with block-at-a-time scans. In the latter situation, many different algorithms, including the Gibbs sampler, are shown to be special cases of the Metropolis-Hastings algorithm. The methods are illustrated with examples.

/pdf/understanding-the-metropolis-hastings-algorithm-43977vycuo.pdf

Understanding the Metropolis-Hastings Algorithm

A survey of maintenance policies of deteriorating systems

An introduction to survival and event history analysis.- Stochastic processes in event history analysis.- Nonparametric analysis of survival and event history data.- Regression models.- Parametric counting process models.- Unobserved heterogeneity: The odd effects of frailty.- Multivariate frailty models.- Marginal and dynamic models for recurrent events and clustered survival data.- Causality.- First passage time models: Understanding the shape of the hazard rate.- Diffusion and L#x00E9 vy process models for dynamic frailty.

https://www.springer.com/productFlyer_978-0-387-20287-7.pdf?SGWID=0-0-1297-52088484-0

Survival and Event History Analysis: A Process Point of View

Invited reviewImperfect maintenance

New product warranty: A literature review

In developing any successful maintenance strategy it is important to be able to estimate the rate of occurrence of maintenance events. In a previous paper the authors have argued that there are advantages to using a non-parametric or semi-parametric approach to such analysis. In this paper the authors explore the use of the approach to data from the water industry using a case study. The approach provides insight into the context revealing the impact of maintenance on the process. The effect of the maintenance strategy can be evaluated. The paper explores the practical issues of missing values and implementation of an appropriate maintenance strategy.

Assessing the maintenance in a process using a semi-parametric approach

An algorithm is described for generating von Mises variates using Forsythe's method. The performance is analysed with respect to speed, and compactness. Conclusions are drawn as to when it is preferred to Best and Fisher's envelope rejection method.

Sampling from the von Mises distribution via a comparison of random numbers

The number of COVID-19 deaths reported from European countries has varied more than 100-fold. In terms of coronavirus transmission, the relatively low death rates in some countries could be due to low intrinsic (e.g. low population density) or imposed contact rates (e.g. non-pharmaceutical interventions) among individuals, or because fewer people were exposed or susceptible to infection (e.g. smaller populations). Here we develop a flexible empirical model (skew-logistic) to distinguish among these possibilities. We find that countries reporting fewer deaths did not generally have intrinsically lower rates of transmission and epidemic growth, and flatter epidemic curves. Rather, countries with fewer deaths locked down earlier, had shorter epidemics that peaked sooner, and smaller populations. Consequently, as lockdowns are eased we expect, and are starting to see, a resurgence of COVID-19 across Europe. One Sentence Summary A flexible empirical model shows that European countries reporting fewer COVID-19 deaths locked down earlier, had shorter epidemics that peaked sooner, and smaller populations.

https://medrxiv.org/content/10.1101/2020.06.26.20131144v1.full.pdf

The scale and dynamics of COVID-19 epidemics across Europe

Optimal repair-cost limit for a consumer following expiry of a warranty

In this paper we consider an age replacement strategy, where downtimes are non-zero. Although this model is well known, the literature gives no necessary and sufficient conditions for age replacement to be preferred to replacement on failure. In this paper we derive such conditions in terms of the minimum of the mean residual life function. When age replacement is indicated, we derive sufficient conditions for the existence of a global minimum to the asymptotic expected cost rate function. These results are illustrated for the Weibull and Gamma distributions.

John Dagpunar

Papers

Assessing the maintenance in a process using a semi-parametric approach

Sampling from the von Mises distribution via a comparison of random numbers

The scale and dynamics of COVID-19 epidemics across Europe

Optimal repair-cost limit for a consumer following expiry of a warranty

Some Necessary and Sufficient Conditions for Age Replacement with Non-zero Downtimes