Asymptotic behavior of posterior distributions for random processes under incorrect models

  • Keigo Yamada
Optimal Control Stochastic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 41)


In this paper, the asymptotic behavior of posterior distributions on parameters contained in random processes is examined when the specified model for the densities is not necessarily correct. Uniform convergence of likelihood functions in some way is shown to be a sufficient condition for the posterior distributions to be asymptotically confined to a set (Theorem 1). For ergodic stationary Markov processes uniform convergence of likelihood functions is established by the ergodic theorem for Banach-valued stationary processes (Proposition 1). A sufficient condition for the uniform convergence is also shown for general random processes (Proposition 2).

These results are used to analyze the asymptotic behavior of posterior distributions on parameters contained in linear systems under incorrect models (Example 1 and 2).


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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Keigo Yamada
    • 1
  1. 1.Japan UNIVAC Research InstituteTokyoJapan

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