Nakai, T. A partially observable decision problem under a shifted likelihood ratio ordering. (English) Zbl 0840.90128 Math. Comput. Modelling 22, No. 10-12, 237-246 (1995). Summary: We discuss a partially observable sequential decision problem under a shifted likelihood ratio ordering. Since we employ the Bayes’ theorem for the learning procedure, we treat this problem under several assumptions. Under these assumptions, we obtain some fundamental results about the relation between prior and posterior information. We also consider an optimal stopping problem for this partially observable Markov decision process. Cited in 7 Documents MSC: 90C40 Markov and semi-Markov decision processes Keywords:partially observable sequential decision problem; shifted likelihood ratio ordering; prior and posterior information; optimal stopping PDFBibTeX XMLCite \textit{T. Nakai}, Math. Comput. Modelling 22, No. 10--12, 237--246 (1995; Zbl 0840.90128) Full Text: DOI References: [1] Shanthikumar, J. G.; Yao, D. D., The preservation of likelihood ratio ordering under convolution, Stochastic Processes and Their Applications, 23, 259-267 (1986) · Zbl 0611.60047 [2] Nakai, T., Optimal stopping problem in a finite state partially observable Markov chain, Journal of Information & Optimization Sciences, 2, 159-176 (1983) · Zbl 0511.60042 [3] Nakai, T., The problem of optimal stopping in a partially observable Markov chain, Journal of Optimization Theory and Applications, 45, 425-442 (1985) · Zbl 0543.60054 [4] Nakai, T., A sequential stochastic assignment problem in a partially observable Markov chain, Mathematics of Operations Research, 11, 230-240 (1986) · Zbl 0601.90137 [5] Nakai, T., A stochastic ordering and related sequential decision problems, Journal of Information & Optimization Sciences, 11, 49-65 (1990) · Zbl 0707.90096 [6] Nakai, T., A partially observable decision problem under a shifted likelihood ratio ordering, (Osaki, S.; Murthy, D. N.Pra, Proceedings of the Australia-Japan Workshop on Stochastic Models in Engineering, Technology and Management (1993), World Scientific), 413-422 · Zbl 0840.90128 [7] Keilson, J.; Sumita, U., Uniform stochastic ordering and related inequalities, The Canadian Journal of Statistics, 10, 181-198 (1982) · Zbl 0516.60063 [8] Ross, S. M., Stochastic Processes (1983), John Wiley and Sons: John Wiley and Sons New York · Zbl 0555.60002 [9] Nakai, T., Two orders related to the likelihood ratio and some properties on partially observable decision problems, Keizaigaku=Kenkyu, Journal of Political Economy, 57, 251-280 (1991), (in Japanese) [10] Ross, S. M., Applied Probability Models with Optimization Applications (1970), Holden-Day: Holden-Day San Francisco · Zbl 0213.19101 [11] De Vylder, F., Duality theorem for bounds in integrals with applications to stop loss premiums, Scandinavian Actuarial Journal, 129-147 (1983) · Zbl 0522.62087 [12] DeGroot, M. H., Optimal Statistical Decisions (1970), McGraw-Hill: McGraw-Hill New York · Zbl 0225.62006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.