A well-known stopping rule in adaptive mastery testing is to terminate the assessment once the examinee’s ability confidence interval lies entirely above or below the cut-off score. This article proposes new procedures that seek to improve such a variable-length stopping rule by coupling it with curtailment and stochastic curtailment. Under the new procedures, test termination can occur earlier...

We consider a change detection problem in which the arrival rate of a Poisson process changes suddenly at some unknown and unobservable disorder time. It is assumed that the prior distribution of the disorder time is known. The objective is to detect the disorder time with an online detection rule (a stopping time) in a way that balances the frequency of false alarm and detection delay. So far ...

The aim of this paper is to explore the possibility of approximating the Ferguson-Dirichlet prior and the distributions of its random functionals through the simulation of random probability measures. The proposed procedure is based on the constructive deenition illustrated in Sethuraman (1994) in conjunction with the use of a random stopping rule. This allows to set in advance the closeness to...

In positron emission tomography (PET), data is collected via the detection of photons emitted by a radioactive tracer within the subject. The noise in PET data is Poisson, and hence, it is typical to reconstruct the tracer density distribution via the computation of an approximate minimizer of the negative-log Poisson likelihood function. In this paper, we present an iterative method for the so...

There is a natural norm associated with a starting point of the homogeneous selfdual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. Th...

In this article we study the expected rank problem under full information. Our approach uses the planar Poisson approach from Gnedin (2007) to derive the expected rank of a stopping rule that is one of the simplest non-trivial examples combining rank dependent rules with threshold rules. This rule attains an expected rank lower than the best upper bounds obtained in the literature so far, in pa...

We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the ‘Track-and-Stop’ strategy, which we prove to be asymptotically optimal. It consists in a new sampling rule (which tracks the optimal proportions of arm draws highlighted by the lower bound) and in a stopping...

Let (Sn)n≥0 be a correlated random walk on the integers, let M0 ≥ S0 be an arbitrary integer, and let Mn = max{M0, S1, . . . , Sn}. An optimal stopping rule is derived for the sequence Mn − nc, where c > 0 is a fixed cost. The optimal rule is shown to be of threshold type: stop the first time that Mn−Sn ≥ ∆, where ∆ is a certain nonnegative integer. An explicit expression for this optimal thres...

In previous lectures, we have discussed that people often use so-called heuristics, e.g. anchoring and the representativeness heuristic, instead of behaving completely rationally. The present lecture, which is based on a paper by Seale and Rapoport (1997), shows how an experiment and a computer-simulation-study can be used to find out what decision rule/heuristic people use in a certain optimal...

The small (40S) subunit of eukaryotic ribosomes is believed to bind initially at the capped 5'-end of messenger RNA and then migrate, stopping at the first AUG codon in a favorable context for initiating translation. The first-AUG rule is not absolute, but there are rules for breaking the rule. Some anomalous observations that seemed to contradict the scanning mechanism now appear to be artifac...