The decentralized wald problem

Two detectors making independent observations must decide which one of two hypotheses is true. The decisions are coupled through a common cost function. It is shown that the detectors' optimal decisions are characterized by thresholds which are coupled and whose computation requires the solution of two coupled sets of dynamic programming equations. An approximate computation of the thresholds is proposed and numerical results are presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26739/1/0000291.pd

Unstructured sequential testing in sensor networks

We consider the problem of quickly detecting a signal in a sensor network when the subset of sensors in which signal may be present is completely unknown. We formulate this problem as a sequential hypothesis testing problem with a simple null (signal is absent everywhere) and a composite alternative (signal is present somewhere). We introduce a novel class of scalable sequential tests which, for any subset of affected sensors, minimize the expected sample size for a decision asymptotically, that is as the error probabilities go to 0. Moreover, we propose sequential tests that require minimal transmission activity from the sensors to the fusion center, while preserving this asymptotic optimality property.Comment: 6 two-column pages, To appear in the Proceedings 2013 IEEE Conference on Decision and Control, Firenze, Italy, December 201

Asymptotic Optimality Theory For Decentralized Sequential Multihypothesis Testing Problems

The Bayesian formulation of sequentially testing $M \ge 3$ hypotheses is studied in the context of a decentralized sensor network system. In such a system, local sensors observe raw observations and send quantized sensor messages to a fusion center which makes a final decision when stopping taking observations. Asymptotically optimal decentralized sequential tests are developed from a class of "two-stage" tests that allows the sensor network system to make a preliminary decision in the first stage and then optimize each local sensor quantizer accordingly in the second stage. It is shown that the optimal local quantizer at each local sensor in the second stage can be defined as a maximin quantizer which turns out to be a randomization of at most $M-1$ unambiguous likelihood quantizers (ULQ). We first present in detail our results for the system with a single sensor and binary sensor messages, and then extend to more general cases involving any finite alphabet sensor messages, multiple sensors, or composite hypotheses.Comment: 14 pages, 1 figure, submitted to IEEE Trans. Inf. Theor

On optimal quantization rules for some problems in sequential decentralized detection

We consider the design of systems for sequential decentralized detection, a problem that entails several interdependent choices: the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two competing hypotheses), and a set of quantization rules (the local decisions on the basis of which the global decision is made). This paper addresses an open problem of whether in the Bayesian formulation of sequential decentralized detection, optimal local decision functions can be found within the class of stationary rules. We develop an asymptotic approximation to the optimal cost of stationary quantization rules and exploit this approximation to show that stationary quantizers are not optimal in a broad class of settings. We also consider the class of blockwise stationary quantizers, and show that asymptotically optimal quantizers are likelihood-based threshold rules.Comment: Published as IEEE Transactions on Information Theory, Vol. 54(7), 3285-3295, 200

Preventing competition because of “solidarity”: Rhetoric and reality of airport investments in Spain

Spain is the only large European country in which airport management is strictly centralized and publicly owned. This peculiar institutional setting prevents competition among Spanish airports, and policy makers and bureaucrats in charge of the system regularly justify it on grounds of interterritorial solidarity. This paper tests whether allocation of investments in airports is effectively based on redistributive purposes, as claimed and looks at other factors to explain such allocation. Our empirical analysis suggests that neither a progressive redistribution target nor the scale economies criterion explain allocation decisions. Instead, we find that political factors have significant influence on the allocation decisions made by the government.Public Enterprise, Legal monopolies, Air Transportation, Models with Panel Data