Nearly-Optimal Sequential Tests for Finitely Many Parameter Values

Sequential joint detection and estimation

“…We can easily verify that we have equality when the decision function is according to (10). In the last sum in the previous expression it can be shown that the corresponding expectation is equal to c 1 +c e {μ…”

“…Actually, joint detection/estimation resembles to sequential multi-hypothesis testing, where there is a discrete set of possible probability measures that describe the observations and we need to select one of the existing possibilities. Characteristic articles treating this problem are: [1], [10], [17], [3]. The joint case studied in this work differs from the previous approaches in the sense that we have a parametric family of measures (parametrized by x) and we need to select the correct parameter value, after establishing that this value is not 0.…”

A Bayesian Sequential Experimental Study of Learning in Games

“…Those procedures (Kiefer and Sacks (1963), Lorden (1977)) stop when the odds ratio hits one of two boundaries that depend on the cost of sampling and some information numbers. The odds ratio is the ratio of the likelihoods of the two models, where each of the likelihoods is computed under each (E, q, a) vector and then integrated with respect to our prior on those nuisance parameters.…”

“…Our stopping criteria are not necessarily optimal for a number of reasons: First, we use an approximation as c -> 0, and, second, we ignore the problem of overshooting the boundaries (Lorden (1977)). Berger did not prove that the formulae he recommended (Berger (1985, 7.83 and 7.84, p.499)) are optimal, but we use them since they seem to be sensible means for computing the stopping boundaries.…”

Multisource Bayesian sequential binary hypothesis testing problem

“…The non-Bayes formulation of the sequential hypothesis testing problem has been studied by many authors, both in discrete-and continuous-time, and can be found in the recent reviews and contributions made by Lai (2000Lai ( , 2001, Dragalin et al (1999Dragalin et al ( , 2000, Lorden (1977). In the Bayesian framework, sequential hypothesis testing problems were studied in discrete-time for the identification of the distribution of i.i.d.…”