A Predictive Approach to Bayesian Nonparametric Survival Analysis

Fong, Edwin; Lehmann, Brieuc

doi:10.48550/arxiv.2202.10361

Cited by 1 publication

(2 citation statements)

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“…sequences have been introduced in [5] and [43] and then investigated or applied in various papers; see e.g. [1], [2], [6], [7], [8], [9], [14], [26], [27], [30] and references therein.…”

Section: Conditionally Identically Distributed Datamentioning

confidence: 99%

“…If X is c.i.d., at each time n, the future observations (X k : k > n) are identically distributed given the past, and this is reasonable in several prediction problems. Examples arise in clinical trials, generalized Polya urns, species sampling models, survival analysis and disease surveillance; see [1], [2], [5], [14], [26], [27], [31]. A further reason for assuming X c.i.d.…”

Section: Conditionally Identically Distributed Datamentioning

confidence: 99%

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A predictive approach to Bayesian forecasting

Berti¹,

Dreassi²,

Leisen³

et al. 2022

Preprint

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Given a sequence X = (X 1 , X 2 , . . .) of random observations, a Bayesian forecaster aims to predict X n+1 based on (X 1 , . . . , Xn) for each n ≥ 0. To this end, she only needs to select a collection σ = (σ 0 , σ 1 , . . .), called "strategy" in what follows, where σ 0Because of the Ionescu-Tulcea theorem, σ can be assigned directly, without passing through the usual prior/posterior scheme. One main advantage is that no prior probability is to be selected. In a nutshell, this is the non-standard approach to Bayesian predictive inference. A concise review of the latter is provided in this paper. We try to put such an approach in the right framework, to make clear a few misunderstandings, and to provide a unifying view. Some recent results are discussed as well. In addition, some new strategies are introduced and the corresponding distribution of the data sequence X is determined. The strategies concern generalized Polya urns, random change points, covariates and stationary sequences.

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“…sequences have been introduced in [5] and [43] and then investigated or applied in various papers; see e.g. [1], [2], [6], [7], [8], [9], [14], [26], [27], [30] and references therein.…”

Section: Conditionally Identically Distributed Datamentioning

confidence: 99%