A Bayesian Nonparametric Spiked Process Prior for Dynamic Model Selection

Cassese, Alberto; Zhu, Weixuan; Guindani, Michele; Vannucci, Marina

doi:10.1214/18-ba1116

Cited by 17 publications

(17 citation statements)

References 23 publications

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“…Several articles have used similar DP constructions that combine a DP with a finite mixture of a mass point and a nontruncated normal distribution (Canale, Durante, & Dunson, 2018; Cassese, Zhu, Guindani, & Vannucci, 2019; Herring, 2010) or a gamma distribution (Liu, Wang, & Liu, 2015).…”

Section: Methodsmentioning

confidence: 99%

Bayesian nonparametric monotone regression

et al. 2020

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In many applications there is interest in estimating the relation between a predictor and an outcome when the relation is known to be monotone or otherwise constrained due to the physical processes involved. We consider one such application-inferring time-resolved aerosol concentration from a low-cost differential pressure sensor. The objective is to estimate a monotone function and make inference on the scaled first derivative of the function. We proposed Bayesian nonparametric monotone regression, which uses a Bernstein polynomial basis to construct the regression function and puts a Dirichlet process prior on the regression coefficients. The base measure of the Dirichlet process is a finite mixture of a mass point at zero and a truncated normal. This construction imposes monotonicity while clustering the basis functions. Clustering the basis functions reduces the parameter space and allows the estimated regression function to be linear. With the proposed approach we can make closed-formed inference on the derivative of the estimated function including full quantification of uncertainty. In a simulation study the proposed method performs similar to other monotone regression approaches when the true function is wavy but performs better when the true function is linear. We apply the method to estimate time-resolved aerosol concentration with a newly developed portable aerosol monitor. The R package bnmr is made available to implement the method.

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Section: Methodsmentioning

confidence: 99%

Bayesian nonparametric monotone regression

et al. 2020

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“…Furthermore, conditional identity in distribution is more reasonable than exchangeability in a few real problems. Examples occur in various fields, including clinical trials, generalized Polya urns, species sampling models and disease surveillance; see [1], [2], [4], [11].…”

Section: Motivationsmentioning

confidence: 99%

“…sequences have been introduced in [4] and [22] and then investigated in various papers; see e.g. [1], [2], [5], [6], [7], [8], [9], [11], [15], [18], [19].…”

Section: Conditional Identity In Distributionmentioning

confidence: 99%

Bayesian Predictive Inference Without a Prior

Berti¹,

Dreassi²,

Leisen³

et al. 2024

STAT SINICA

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Let (Xn : n ≥ 1) be a sequence of random observations. Let σn(•) = P Xn+1 ∈ • | X1, . . . , Xn be the n-th predictive distribution and σ0(•)=P (X1 ∈ •) the marginal distribution of X1. To make predictions on (Xn), a Bayesian forecaster only needs the collection σ = (σn : n ≥ 0). Because 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 has to be selected. This point of view is adopted in this paper. The choice of σ is only subjected to two requirements: (i) The resulting sequence (Xn) is conditionally identically distributed, in the sense of [4]; (ii) Each σn+1 is a simple recursive update of σn. Various new σ satisfying (i)-(ii) are introduced and investigated.For such σ, the asymptotics of σn, as n → ∞, is determined. In some cases, the probability distribution of (Xn) is also evaluated.

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“…sequences have been introduced in [4] and [22] and then investigated in various papers; see e.g. [1], [2], [5], [6], [7], [8], [9], [11], [14], [17], [18].…”

Section: Conditional Identity In Distributionmentioning

confidence: 99%

Bayesian predictive inference without a prior

Berti¹,

Dreassi²,

Leisen³

et al. 2021

Preprint

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Let (Xn : n ≥ 1) be a sequence of random observations. Let σn(•) = P X n+1 ∈ • | X 1 , . . . , Xn be the n-th predictive distribution and σ 0 (•) = P (X 1 ∈ •) the marginal distribution of X 1 . In a Bayesian framework, to make predictions on (Xn), one only needs the collection σ = (σn : n ≥ 0). Because 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 has to be selected. In this paper, σ is subjected to two requirements: (i) The resulting sequence (Xn) is conditionally identically distributed, in the sense of [4]; (ii) Each σ n+1 is a simple recursive update of σn. Various new σ satisfying (i)-(ii) are introduced and investigated. For such σ, the asymptotics of σn, as n → ∞, is determined. In some cases, the probability distribution of (Xn) is also evaluated.

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A Bayesian Nonparametric Spiked Process Prior for Dynamic Model Selection

Cited by 17 publications

References 23 publications

Bayesian nonparametric monotone regression

Bayesian nonparametric monotone regression

Bayesian Predictive Inference Without a Prior

Bayesian predictive inference without a prior

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