Michael Baron. Recent projects in the area of

Applications of Statistics in Energy Finance, Semiconductor Manufacturing, Epidemiology, Developmental Psychology

M. Baron, C. K. Lakshminarayan, Z. Chen. Markov random fields in pattern recognition for semiconductor manufacturing. Technometrics, 43 (1), 66-72, 2001.

Abstract.
Under the most general conditions of a Markov random field, we model the two-dimensional spatial distribution of microchips on a silicon wafer. Its canonical parameters represent the density of failures, main effects and interactions of neighboring chips. Explicit forms of conditional distributions are derived, and maximum pseudo-likelihood estimates of canonical parameters are obtained. This ten-dimensional numerical characteristic summarizes general patterns of clusters of failing chips on a wafer, capturing their size, shape, direction density and thickness. It is used to classify incoming wafers to known root cause categories of failures by matching them to the closest pattern.

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M. Baron, M. Rosenberg, N. Sidorenko. Electricity pricing: modelling and prediction with automatic spike detection. Energy, Power, and Risk Management, 36-39, October 2001.

Abstract.
Power prices are modelled by a Markov chain switching between "regular" and "spike" phases according to the time of the year and other factors. Here we present simple methods of model calibration and optimal prediction.

M. Baron, M. Rosenberg, N. Sidorenko. Divide and conquer: forecasting power via automatic price regime separation. Energy, Power, and Risk Management, 70-73, March 2002.

Abstract.

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M. Rosenberg, J. D. Bryngelson, N. Sidorenko; M. Baron. Price spikes and real options: transmission valuation. In E. I. Ronn, ed., Real Options and Energy Management, pages 323--370, Risk Books, London, 2002.

In the same volume -

M. Rosenberg, J. D. Bryngelson; M. Baron. Probability and stochastic calculus: review of probability concepts. In E. I. Ronn, ed., Real Options and Energy Management, pages 659--697, Risk Books, London, 2002.

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M. Baron. Bayes and asymptotically pointwise optimal stopping rules for the detection of influenza epidemics. C. Gatsonis, R. E. Kass, A. Carriquiry, A. Gelman, D. Higdon, D. K. Pauler and I. Verdinelli, Eds., Case Studies in Bayesian Statistics, vol. 6, pages 153--163, 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. K. Lakshminarayan, M. Baron, Z. Chen. Pattern recognition in IC diagnostics using the linear discriminant classifier and artificial neural networks. Under review.

Abstract.
It is important in IC manufacturing to identify probable root causes, given a signature. The signature is a vector of electrical test parameters measured on process control bars on a wafer. Linear discriminant analysis and artificial neural networks are used to classify a signature of test electrical measurements of a failed chip to one of several pre-assigned root cause categories. An optimal decision rule that assigns a new incoming signature of a failed chip to a particular root cause category is employed such that the probability of misclassification is minimized. The problem of classifying patterns with missing data, outliers, collinearity, and non-normality are also addressed. The selected similarity metric in linear discriminant analysis, and the network topology, used in neural networks, result in a small number of misclassifications. An alternative classification scheme based on the locations of failed chips on a wafer and their spatial dependence is proposed.

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M. Baron and N. Granott. Small sample change-point analysis with applications to problem solving. Submitted.

Abstract.
The proposed scheme detects and post-estimates change points that can occur during early stages of an observed multistage process. The algorithm is designed to analyze change points that are likely to occur after very few observations and to be followed by other change points or more complicated patterns. Such models are justified in problem solving, quality control, and other processes. Special methods are derived in order to: (1) detect a change point even after a very brief period of observation, (2) estimate it with the theoretically highest degree of accuracy, (3) report a no-change case when a significant change has not occurred during the observed period, and (4) use minimum data after the change point to prevent mixing the post-change phase with subsequent phases and patterns. Unlike existing methods, the proposed algorithm produces a distribution consistent estimator of a change point. Details are elaborated for the case of Gamma distributions and demonstrated for a process of problem solving.