On robustness of the Shiryaev–Roberts change-point detection procedure under parameter misspecification in the post-change distribution

The gist of the quickest change-point detection problem is to detect the presence of a change in the statistical behavior of a series of sequentially made observations, and do so in an optimal detection-speed-versus-“false-positive”-risk manner. When optimality is understood either in the generalized Bayesian sense or as defined in Shiryaev's multi-cyclic setup, the so-called Shiryaev–Roberts (SR) detection procedure is known to be the “best one can do”, provided, however, that the observations’ pre- and post-change distributions are both fully specified. We consider a more realistic setup, viz. one where the post-change distribution is assumed known only up to a parameter, so that the latter may be misspecified. The question of interest is the sensitivity (or robustness) of the otherwise “best” SR procedure with respect to a possible misspecification of the post-change distribution parameter. To answer this question, we provide a case study where, in a specific Gaussian scenario, we allow the SR procedure to be “out of tune” in the way of the post-change distribution parameter, and numerically assess the effect of the “mistuning” on Shiryaev's (multi-cyclic) Stationary Average Detection Delay delivered by the SR procedure. The comprehensive quantitative robustness characterization of the SR procedure obtained in the study can be used to develop the respective theory as well as to provide a rational for practical design of the SR procedure. The overall qualitative conclusion of the study is an expected one: the SR procedure is less (more) robust for less (more) contrast changes and for lower (higher) levels of the false alarm risk.     

Perestroika,Second Edition

The author assesses the prospects of a "second perestroika" based on his interpretation of modern Russian history in terms of the concepts of revolution and counterrevolution.     

Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks

We consider the problems of minimum-cost design and augmentation of directed network clusters that have diameter 2 and maintain the same diameter after the deletion of up to R elements (nodes or arcs) anywhere in the cluster. The property of a network to maintain not only the overall connectivity, but also the same diameter after the deletion of multiple nodes/arcs is referred to as strong attack tolerance. This paper presents the proof of NP-completeness of the decision version of the problem, derives tight theoretical bounds, as well as develops a heuristic algorithm for the considered problems, which are extremely challenging to solve to optimality even for small networks. Computational experiments suggest that the proposed heuristic algorithm does identify high-quality near-optimal solutions; moreover, in the special case of undirected networks with identical arc construction costs, the algorithm provably produces an exact optimal solution to strongly attack-tolerant two-hop network design problem, regardless of the network size.     

Penalized maximum likelihood estimation for Gaussian hidden Markov models

ABSTRACT

The likelihood function of a Gaussian hidden Markov model is unbounded, which is why the maximum likelihood estimator (MLE) is not consistent. A penalized MLE is introduced along with a rigorous consistency proof.     

A stochastic process approach to multilayer neutron detectors

The sparsity of the isotope Helium‐3, ongoing since 2009, has initiated a new generation of neutron detectors. One particularly promising development line for detectors is the multilayer gaseous detector. In this paper, a stochastic process approach is used to determine the neutron energy from the additional data afforded by the multilayer nature of these novel detectors. The data from a multilayer detector consist of counts of the number of absorbed neutrons along the sequence of the detector's layers, in which the neutron absorption probability is unknown. We study the maximum likelihood estimator for the intensity and absorption probability and show its consistency and asymptotic normality, as the number of incoming neutrons goes to infinity. We combine these results with known results on the relation between the absorption probability and the wavelength to derive an estimator of the wavelength and to show its consistency and asymptotic normality.     

A vendor–purchaser economic lot size problem with remanufacturing

In this paper, we study a closed-loop supply chain in which a single purchaser orders a particular product from a single vendor and sells it on the market. A certain fraction of used items return from the market back to the purchaser, who is responsible for collecting and returning them to the vendor. In addition to manufacturing new items, the vendor is able to remanufacture the returns into as-good-as-new items which are subsequently used to serve market demand. Our framework features the conventional joint economic lot size (JELS) model extended to include the return flow of the used items. In line with the assumptions of the JELS model, we assume a deterministic constant demand for the product. The fraction of used items returning from the market is assumed to depend on the purchaser’s collection effort. To stimulate the returns, the vendor may offer the purchaser a transfer payment per item returned. The questions addressed by this study pertain to the optimal centralised control of this closed-loop supply chain, to the individually optimal policies of its members, and to the coordination within this supply chain under a decentralised control. In particular, we show that the transfer payment alone cannot coordinate the supply chain under consideration and may even fail to do so when combined with a two-part tariff—which is otherwise known to coordinate the corresponding forward supply chain. Our numerical study, though, has revealed that the combined contract is capable of substantially reducing the coordination deficit. We also introduce a novel three-part tariff which is shown to enable supply chain coordination in combination with the transfer payment.