Showing papers by "Herman Chernoff published in 1986"
TL;DR: In this article, the solution of these free boundary problems can then be approximated by calculating the simpler optimal stopping problems by backward induction, which is not well adapted for very precise results but is surprisingly effective for rough pproximations.
Abstract: Certain sequential decision problems involving normal random variables reduce to optimal stopping problems which can be related to the solution of corresponding free boundary problems for the heat equation. The numerical solution of these free boundary problems can then be approximated by calculating the solution of simpler optimal stopping problems by backward induction. This approach is not well adapted for very precise results but is surprisingly effective for rough pproximations. An estimate of the difference between the solutions of the related problems permits one to make continuity corrections which provide considerably improved accuracy. Further reductions in the necessary computational effort are possible by considering truncated procedures for one-sided boundaries and by exploiting monotone and symmetric boundaries.
37 citations
TL;DR: This paper reviews chemical applications of information theory which have been reported in the literature including applications to qualitative analysis, quantitative analysis, structural analysis, and analytical techniques.
Abstract: One of the most important problems in chemical analysis is the interpretation of analytical data. The difficulty of this task has been further compounded by the data explosion. Chemical information relevant to the particular analysis problem is hidden within excessive amounts of data, This problem could be alleviated through knowledge and control of the information content of the data. Information theory provides a means for the definition, evaluation, and manipulation of quantitative information content measurements. This paper provides a general review of some of the basic concepts in information theory, including history, terminology, entropy, and other information content measures. The application of information theory to chemical problems requires some modifications. The analyst is usually only interested in a subset of the information (data) which has been collected. Also, this relevant chemical information is dependent upon not only the informational goals of the problem, but the completely specified procedure as well. This paper reviews chemical applications of information theory which have been reported in the literature including applications to qualitative analysis, quantitative analysis, structural analysis, and analytical techniques. Measures of information and information content and figures of merit for performance evaluations are discussed. The paper concludes with a detailed discussion of the application of information theory to electrochemical experiments and the empirical determination of the information content of electroanalytical data.
1 citations