Mark Abramson | Searcharxiv

arXiv2021

A Markov-Modulated (s, S) Inventory System with Repeated Calls and Blocked Demands

In this article, we consider a continuous review (s, S) inventory system with failures of demand fulfillment (service) modeled as a Markov-modulated retrial queueing system. The inventory system features a single product that experiences Markovian inter-demand and service intervals with random service interruptions and instantaneous replenishments. A recently developed criterion for the ergodicity of a class of discrete-time level-dependent-quasi-birth-and-death (LDQBD) processes with convergent transition matrix rows is applied to the jump chain of the process in order to elicit a closed-form traffic-intensity formula. An analytic solution for the steady-state average minimum cost is provided.

math.PR↗

arXiv2019

Regression Analysis of Unmeasured Confounding

When studying the causal effect of $x$ on $y$, researchers may conduct regression and report a confidence interval for the slope coefficient $β_{x}$. This common confidence interval provides an assessment of uncertainty from sampling error, but it does not assess uncertainty from confounding. An intervention on $x$ may produce a response in $y$ that is unexpected, and our misinterpretation of the slope happens when there are confounding factors $w$. When $w$ are measured we may conduct multiple regression, but when $w$ are unmeasured it is common practice to include a precautionary statement when reporting the confidence interval, warning against unwarranted causal interpretation. If the goal is robust causal interpretation then we can do something more informative. Uncertainty in the specification of three confounding parameters can be propagated through an equation to produce a confounding interval. Here we develop supporting mathematical theory and describe an example application. Our proposed methodology applies well to studies of a continuous response or rare outcome. It is a general method for quantifying error from model uncertainty. Whereas confidence intervals are used to assess uncertainty from unmeasured individuals, confounding intervals can be used to assess uncertainty from unmeasured attributes.

stat.ME↗