The method of control variates is one of the most widely used variance reduction techniques associated with Monte Carlo simulation. This paper studies the method of control variates from several different viewpoints, and establishes new connections between the method of control variates and: conditional Monte Carlo, antithetics, rotation sampling, stratification, and nonparametric maximum likelihood. We also develop limit theory for the method of control variates under weak assumptions on the estimator of the optimal control coefficient.
In insurgency situations, the government-organized force is confronted by a small guerrilla group that is dispersed in the general population with no or a very small signature. Effective counterinsurgency operations require good intelligence. Absent intelligence, not only might the insurgents escape unharmed and continue their violent actions, but collateral damage caused to the general population from poor targeting may generate adverse response against the government and create popular support for the insurgents, which may result in higher recruitment to the insurgency. We model the dynamic relations among intelligence, collateral casualties in the population, attrition, recruitment to the insurgency, and reinforcement to the government force. Even under best-case assumptions, we show that the government cannot totally eradicate the insurgency by force. The best it can do is contain it at a certain fixed level.
A target is hidden in one of several possible locations, and the objective is to nd the target as fast as possible. One common measure of eectiveness for the search process is the expected time of the search. This type of search optimization problem has been addressed and solved in the literature for the case where the searcher has imperfect sensitivity (possible false negative results), but perfect specicity (no false positive detections). In this paper, which is motivated by recent military and homeland security search situations, we extend the results to the case where the search is subject to false positive detections. ueywordsX disrete serhD imperfet speiityD uniformly optimlF 1 Introduction hisrete serh prolems hve een out of vogue for over two dedesF roweverD reent defense prolemsD suh s serhing for hostge hidden in ity @eFgFD reltively reent events in the qz stripA or deteting improvised explosive devies @sihA in srqD hve undersored the need for eient nd eetive serh methods for deteting trgets of vrious typesF e onsider surveillne systemD the purpose of whih is to nd trget tht is hidden in one out of n possile lotionsF he trget lotion is unertin ut there is some prior informtion tht is quntied in prior proility distriutionF he surveillne system omprises sensor nd verition temF he sensorD whih serhes sequentilly the n lotionsD is imperfet nd therefore its ues re sujet to errorsF he verition temD whih mkes no errorsD investigtes positive detetions y the imperfet sensor nd veries if they re true or flseF uh serh proess tkes timeD nd the ojetive is to nd serh poliy tht minimizes the expeted serh time until the trget is found or optimizes some other mesures of eetiveness @wyisA suh s the proility of detetionF hisrete serh prolems of the type mentioned ove re not newF yptiml whereout is studied in I nd TF ghew Q onsiders n optiml serh with stopping rule where I
During counterinsurgency operations, government forces with superior firepower confront weaker low-signature insurgents. Under what conditions should government (Blue) forces attack insurgent (Red) strongholds? How should the government allocate its force across different strongholds when the insurgents' threat to the Blue civilian population must be taken into account? How should the government respond to "smart" insurgents who anticipate the government's optimal plan of attack and prepare accordingly? How do the results change when the government takes Red civilian casualties resulting from attacks on insurgent strongholds into account? This article addresses these questions. Using Lanchester models modified to account for imperfect intelligence, we formulate an optimal force allocation problem for the government and develop a knapsack approximation that has tight error bounds. We also model a sequential force allocation game between the insurgents and the government and solve for its equilibrium. When the government has perfect intelligence, in equilibrium the insurgents concentrate their force in a single stronghold that the government either attacks or not depending upon the resulting casualty count. Otherwise, under reasonable assumptions regarding the government's behavior and intelligence capabilities, it is optimal for the insurgents to "spread out" in a way that maximizes the number of soldiers required to win all battles. If the government worries about Red civilian casualties, the insurgents have a strong incentive to blend in with the Red civilian population, because this can prevent government attacks while allowing the insurgents to inflict casualties on Blue civilians. Such strategic behavior makes it harder for the government to protect its citizens from insurgent attacks.
A B S T R A C TBackground: The US invests considerable effort in searching and interdicting drug-trafficking vessels in the Caribbean and Eastern Pacific regions. While some vessels are indeed interdicted, resulting in confiscation of substantial quantities of drugs, many such vessels manage to avoid detection and arrive safely at their destinations in Central America and Mexico with their drug load intact. The agency in charge of interdicting this traffic, Joint Interagency Task Force South-JIATF-S, sends out both aerial and surface assets for search and interdiction missions. Methods: An important parameter for planning search and interdiction missions is an estimate of the expected steady-state number of the various types of drug trafficking vessels present in the search regions at any given time. In this paper we use various publicly available sources to estimate these numbers. Results: We estimate that the number of drug shipments initiated per month ranges between four and six dozen, and at any given time there are between two and four vessels, of all types, on the high seas. These estimates remain quite robust over a relatively large range of assumptions and estimates regarding the size and distribution of the drug flow, mix of vessel types, and physical characteristics of those vessels. Conclusion: Our analysis provides insight for how to allocate assets to search, detect, and interdict drug trafficking vessels. The results can also be useful to vet informants to check if their information is consistent with our flow estimates. To the best of our knowledge this is the first time such flow estimates appear in the open literature.Published by Elsevier B.V.
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