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  • 1.
    Hall, P
    et al.
    Australian Natl Univ, Ctr Math & Applicat, Canberra, ACT 0200, Australia Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Peng, L
    Australian Natl Univ, Ctr Math & Applicat, Canberra, ACT 0200, Australia Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Tajvidi, N
    Australian Natl Univ, Ctr Math & Applicat, Canberra, ACT 0200, Australia Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    On prediction intervals based on predictive likelihood or bootstrap methods1999In: Biometrika, ISSN 0006-3444, E-ISSN 1464-3510, Vol. 86, no 4, p. 871-880Article in journal (Refereed)
    Abstract [en]

    We argue that prediction intervals based on predictive likelihood do not correct for curvature with respect to the parameter value when they implicitly approximate an unknown probability density. Partly as a result of this difficulty, the order of coverage error associated with predictive intervals and predictive limits is equal to only the inverse of sample size. In this respect those methods do not improve on the simpler,'naive' or 'estimative' approach. Moreover, in cases of practical importance the latter can be preferable, in terms of both the size and sign of coverage error. We show that bootstrap calibration of both naive and predictive-likelihood approaches increases coverage accuracy of prediction intervals by an order of magnitude, and, in the case of naive intervals, preserves that method's numerical and analytical simplicity. Therefore, we argue, the bootstrap-calibrated naive approach is a particularly competitive alternative to more conventional, but more complex, techniques based on predictive likelihood.

  • 2.
    Singh, S. S.
    et al.
    Univ Cambridge, Dept Engn, Trumpington St, Cambridge CB2 1PZ, England.
    Lindsten, Fredrik
    Uppsala universitet, Reglerteknik, Sweden.
    Moulines, E.
    Ecole Polytech, Ctr Math Appl, Route Saclay, F-91128 Palaiseau, France.
    Blocking strategies and stability of particle Gibbs samplers2017In: Biometrika, ISSN 0006-3444, E-ISSN 1464-3510, Vol. 104, no 4, p. 953-969Article in journal (Refereed)
    Abstract [en]

    Sampling from the posterior probability distribution of the latent states of a hidden Markov model is nontrivial even in the context of Markov chain Monte Carlo. To address this, Andrieu et al. (2010) proposed a way of using a particle filter to construct a Markov kernel that leaves the posterior distribution invariant. Recent theoretical results have established the uniform ergodicity of this Markov kernel and shown that the mixing rate does not deteriorate provided the number of particles grows at least linearly with the number of latent states. However, this gives rise to a cost per application of the kernel that is quadratic in the number of latent states, which can be prohibitive for long observation sequences. Using blocking strategies, we devise samplers that have a stable mixing rate for a cost per iteration that is linear in the number of latent states and which are easily parallelizable.

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