Michael Baron. Recent projects in the area of

Bayesian inference

M. Baron. On statistical inference under asymmetric loss functions. Statistics & Decisions, 18 (4), 367-388, 2000.

Abstract.
We introduce a wide class of asymmetric loss functions and show how to obtain decision rules optimal under these losses from the commonly used standard Bayesian procedures. Important properties of minimum risk and minimax estimators are established. In particular, we discuss their sensitivity to the asymmetry of the loss function.

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M. Baron. Bayes stopping rules in a change-point model with a random hazard rate. Sequential Analysis, 20 (3), 147-163, 2001.

Abstract.
In the Bayes sequential change-point problem, an assumption of a fully known prior distribution of a change-point is usually impracticable. At every moment, one often knows only the discrete hazard function, that is, the probability of a change occurring before the next observation is collected, given that it has not occurred so far. In the randomized model, the observed or predicted values of the hazard function are assumed to form a Markov chain. Under these assumptions, the optimal change-point detection stopping rules are derived for two popular loss functions introduced in Shiryaev (1978) and Ritov (1990). Derivations are based on the theory of optimal stopping of Markov sequences.

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M. Baron. Bayes and asymptotically pointwise optimal stopping rules for the detection of influenza epidemics. In A. Carriquiry, C. Gatsonis, A. Gelman, D. Higdon, R. Kass, D. Pauler and I. Verdinell, Eds., Case Studies in Bayesian Statistics, vol. 6, Springer-Verlag, New York, 2002.

Abstract.
Whereas it is customary to announce epidemics when influenza mortality exceeds the epidemic threshold, one can often detect the beginning of epidemics earlier, by solving a suitable change-point problem. We propose a hierarchical Bayesian change-point model for influenza epidemics. Prior probabilities of a change point depend on (random) factors that affect the spread of influenza. Theory of optimal stopping is used to obtain Bayes stopping rules for the detection of epidemic trends under the loss functions penalizing for delays and false alarms. The Bayes solution involves rather complicated computation of the corresponding payoff function. Alternatively, asymptotically pointwise optimal stopping rules can be computed easily and under weaker assumptions. Both methods are applied to the 1996--2001 influenza mortality data published by CDC.

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C. Schmegner and M. Baron. Principles of optimal sequential planning, Sequential Analysis, 23(1), 11--32, 2004.

Abstract.
It is often impractical or expensive to collect data according to a classical sequential scheme, that is, one observation at a time. Sequential planning extends and generalizes the ``pure'' sequential procedures by allowing to sample observations in groups. At any moment, all the collected data are used to determine the size of the next group and to decide whether or not sampling should be terminated.

This article discusses optimality of sequential plans in terms of a suitable risk function that balances an observation cost and a group cost. It is shown that only non-randomized sequential plans based on a sufficient statistic have to be considered in order to achieve optimality. Performance of several such plans is evaluated.

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