A Bayesian approach for the estimation of probability distributions under finite sample space

Demirhan, Haydar; Demirhan, Kamil

doi:10.1007/s00362-015-0669-z

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…Of course, 'histogram smoothing' in the context of pmf estimation is an old subject with several Bayesian approaches. For instance, see Leonard [22], where multivariate logistic-normal priors are considered; Dickey and Jiang [9], where 'filtered' Dirichlet distributions are proposed; Wong [27], where generalized Dirichlet distributions are used; and more recently Demirhan and Demirhan [8]; see also the survey Agresti and Hitchcock [2], and books Agresti [1], Ghosal and Van der Vaart [16], and Congdon [6,7] and references therein. We remark there is also a large body of work for 'histogram smoothing' with respect to Bayesian density estimation for continuous data, not unrelated to that for pmf inference.…”

Section: On Use Of the Msb(g) Measure As A Priormentioning

confidence: 99%

On the use of Markovian stick-breaking priors

Lippitt¹,

Sethuraman²

2021

Preprint

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In [10], a 'Markovian stick-breaking' process which generalizes the Dirichlet process (µ, θ) with respect to a discrete base space X was introduced. In particular, a sample from from the 'Markovian stick-breaking' processs may be represented in stick-breaking form i≥1 P i δ T i where {T i } is a stationary, irreducible Markov chain on X with stationary distribution µ, instead of i.i.d. {T i } each distributed as µ as in the Dirichlet case, and {P i } is a GEM(θ) residual allocation sequence. Although the motivation in [10] was to relate these Markovian stick-breaking processes to empirical distributional limits of types of simulated annealing chains, these processes may also be thought of as a class of priors in statistical problems. The aim of this work in this context is to identify the posterior distribution and to explore the role of the Markovian structure of {T i } in some inference test cases.Dedicated to Professor M.M. Rao on his 90th birthday.

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Section: On Use Of the Msb(g) Measure As A Priormentioning

confidence: 99%

On the use of Markovian stick-breaking priors

Lippitt¹,

Sethuraman²

2021

Preprint

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“…Since an unknown portion of the dose range will be too toxic for patients, a dose-escalation study is conducted, rather than randomly allocating patients over discrete dose levels and then estimating the MTD (Demirhan and Demirhan 2015). Furthermore, sample sizes in phase I oncology trials are often very small, which means that multiple testing procedures that incorporate dose-toxicity orders are not particularly useful (Pigeot 2000).…”

Section: Introductionmentioning

confidence: 99%

Incoherent dose-escalation in phase I trials using the escalation with overdose control approach

Wheeler

2016

Stat Papers

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A desirable property of any dose-escalation strategy for phase I oncology trials is coherence: if the previous patient experienced a toxicity, a higher dose is not recommended for the next patient; similarly, if the previous patient did not experience a toxicity, a lower dose is not recommended for the next patient. The escalation with overdose control (EWOC) approach is a model-based design that has been applied in practice, under which the dose assigned to the next patient is the one that, given all available data, has a posterior probability of exceeding the maximum tolerated dose equal to a pre-specified value known as the feasibility bound. Several methodological and applied publications have considered the EWOC approach with both feasibility bounds fixed and increasing throughout the trial. Whilst the EWOC approach with fixed feasibility bound has been proven to be coherent, some proposed methods of increasing the feasibility bound regardless of toxicity outcomes of patients can lead to incoherent dose-escalation. This paper formalises a proof that incoherent dose-escalation can occur if the feasibility bound is increased without consideration of preceding toxicity outcomes, and shows via simulation studies that only small increases in the feasibility bound are required for incoherent dose-escalations to occur.

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Research on Consensus Mechanism of Diagnosis and Treatment Conclusion of Consultation

et al. 2020

Proceedings of the Fourteenth International Conference on Management Science and Engineering Management

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A Bayesian approach for the estimation of probability distributions under finite sample space

Cited by 4 publications

References 16 publications

On the use of Markovian stick-breaking priors

On the use of Markovian stick-breaking priors

Incoherent dose-escalation in phase I trials using the escalation with overdose control approach

Research on Consensus Mechanism of Diagnosis and Treatment Conclusion of Consultation

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