On mixtures of distributions of Markov chains

Fortini, Sandra; Ladelli, Lucia; Petris, Giovanni De; Regazzini, Eugenio

doi:10.1016/s0304-4149(02)00093-5

Cited by 18 publications

(32 citation statements)

References 10 publications

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“…We adopt the definition of partial exchangeability given in [8], close to de Finetti's original [2]. The relation with the definition of partial exchangeability given in [4] is clarified in [8].…”

Section: Preliminariesmentioning

confidence: 99%

“…The relation with the definition of partial exchangeability given in [4] is clarified in [8]. The definition requires the introduction of the successors array V of a given random sequence (Y n ) on S, and the extension of S to S * = S ∪ {∂}, where ∂ / ∈ S is a fictitious state.…”

Section: Preliminariesmentioning

confidence: 99%

“…The matrix V = (V j,n ) j,n≥1 is defined setting V j,n equal to the value of Y immediately following the n-th visit to E j . As in the discrete case, if Y visits E j only m < ∞ times, set V j,n = ∂ for all n > m. In the uncountable case, V depends on the partition E. Definition 2.2 [8] A sequence of random variables (Y n ) on S, S is partially exchangeable if its successors array V is distributionally invariant under finite, not necessarily identical, permutations within each of its rows.…”

Section: Preliminariesmentioning

confidence: 99%

“…The reader should be aware of the fact that slightly different notions of partial exchangeability coexist in the literature for sequences of discrete-valued random variables. We recall the original definition, introduced in [2] and elaborated in [8]. The latter paper clarifies the relationship with the alternative definition given in [4].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Countable Partially Exchangeable Mixtures

Prosdocimi

Finesso

2014

J Theor Probab

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Partially exchangeable sequences representable as mixtures of Markov chains are completely specified by de Finetti's mixing measure. The paper characterizes, in terms of a subclass of hidden Markov models, the partially exchangeable sequences with mixing measure concentrated on a countable set, both for discrete valued and for Polish valued sequences.Comment: 24 pages, no figures in Journal of Theoretical Probability 201

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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Countable Partially Exchangeable Mixtures

Prosdocimi

Finesso

2014

J Theor Probab

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“…de Finetti's theorem has been developed to mixtures of Markov chains and some kinds of conditions of partial exchangeability have been investigated (see Diaconis and Freedman (1980); Zabell (1995); Fortini et al (2002); Quintana and Newton (1998)). Here, as a simple parametric model for Markov exchangeable sequence we sequentially construct mixtures of Markov chains using {Y n } defined in Sect.…”

Section: Sequential Construction Of Markov Exchangeable Sequencesmentioning

confidence: 99%

Statistical modeling for discrete patterns in a sequence of exchangeable trials

Aki

2011

Ann Inst Stat Math

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This paper proposes a new method for constructing a sequence of infinitely exchangeable uniform random variables on the unit interval. For constructing the sequence, we utilize a Pólya urn partially. The resulting exchangeable sequence depends on the initial numbers of balls of the Pólya urn. We also derive the de Finetti measure for the exchangeable sequence. For an arbitrarily given one-dimensional distribution function, we generate sequences of exchangeable random variables with the one-dimensional marginal distribution by transforming the exchangeable uniform sequences with the inverse function of the distribution function. Among them we mainly investigate sequences of exchangeable discrete random variables. They differ from the well-known exchangeable sequence generated only by the Pólya urn scheme. Some examples are also given as applications of the results to exact distributions of some statistics based on sequences of exchangeable trials. Further, from the above exchangeable uniform sequence we construct partial or Markov exchangeable sequences. We also provide numerical examples of statistical inference based on the exchangeable and Markov exchangeable sequences.

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Robust identification of highly persistent interest rate regimes

Peluso

Mira

Muliere

2017

International Journal of Approximate Reasoning

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Parametric specifications in State Space Models (SSMs) are a source of bias in case of mismatch between modeling assumptions and reality. We propose a Bayesian semiparametric SSM that is robust to misspecified emission distributions. The Markovian nature of the latent stochastic process creates a temporal dependence and links the random probability distributions of the observations in a mixture of products of Dirichlet processes (MPDP). The model is shown to be adequate and it is applied to simulated data and to the motivating empirical problem of regime shifts in interest rates with latent state persistence

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On mixtures of distributions of Markov chains

Cited by 18 publications

References 10 publications

Countable Partially Exchangeable Mixtures

Countable Partially Exchangeable Mixtures

Statistical modeling for discrete patterns in a sequence of exchangeable trials

Robust identification of highly persistent interest rate regimes

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