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4395 results in Advances in Applied Probability

Page 204 of 220

  • Bounds on the probability of the union and intersection of m events

  • Seymour M. Kwerel
  • Journal:
    Advances in Applied Probability / Volume 7 / Issue 2 / June 1975
    Published online by Cambridge University Press:
    01 July 2016, pp. 431-448
    Print publication:
    June 1975

  • For dependent probability systems of m events partially specified only by the quantities S1, the sum of the probabilities of the m individual events; S2, the sum of the probabilities of each of the (m) pairs of events and S3 the sum of the probabilities of each of the (m 3) combinations of three events; this paper develops the most stringent upper and lower bounds on P1, the probability of the union of the m events; and on P[m], the probability of the simultaneous occurrence of the m events.

  • Bayesian dynamic programming

  • Ulrich Rieder
  • Journal:
    Advances in Applied Probability / Volume 7 / Issue 2 / June 1975
    Published online by Cambridge University Press:
    01 July 2016, pp. 330-348
    Print publication:
    June 1975

  • We consider a non-stationary Bayesian dynamic decision model with general state, action and parameter spaces. It is shown that this model can be reduced to a non-Markovian (resp. Markovian) decision model with completely known transition probabilities. Under rather weak convergence assumptions on the expected total rewards some general results are presented concerning the restriction on deterministic generalized Markov policies, the criteria of optimality and the existence of Bayes policies. These facts are based on the above transformations and on results of Hindererand Schäl.

Page 204 of 220