Bayesian bootstrap prediction

Fushiki, Tadayoshi

doi:10.1016/j.jspi.2009.06.007

Cited by 21 publications

(20 citation statements)

References 16 publications

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“…The predictive distribution in equation was named the “parametric bootstrap predictive distribution” by Harris [] and has been further developed by other authors [e.g., Basu and Harris , ; Vidoni , ; Fushiki et al ., ; Fushiki , ]. A similar approach termed “bagging predictors” [e.g., Breiman , ] is used in the field of machine learning.…”

Section: A Data‐based Comparison Frameworkmentioning

confidence: 99%

Data‐based comparison of frequency analysis methods: A general framework

Renard¹,

Kochanek

Lang³

et al. 2013

Water Resources Research

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[1] An abundance of methods have been developed over the years to perform the frequency analysis (FA) of extreme environmental variables. Although numerous comparisons between these methods have been implemented, no general comparison framework has been agreed upon so far. The objective of this paper is to build the foundation of a data-based comparison framework, which aims at complementing more standard comparison schemes based on Monte Carlo simulations or statistical testing. This framework is based on the following general principles: (i) emphasis is put on the predictive ability of competing FA implementations, rather than their sole descriptive ability measured by some goodness-of-fit criterion; (ii) predictive ability is quantified by means of reliability indices, describing the consistency between validation data (not used for calibration) and FA predictions; (iii) stability is also quantified, i.e., the ability of a FA implementation to yield similar estimates when calibration data change; and (iv) the necessity to subject uncertainty estimates to the same scrutiny as point estimates is recognized, and a practical approach based on the use of the predictive distribution is proposed for this purpose. This framework is then applied to a case study involving 364 gauging stations in France, where 10 FA implementations are compared. These implementations correspond to the local, regional, and local-regional estimation of Gumbel and generalized extreme value distributions. Results show that reliability and stability indices are able to reveal marked differences between FA implementations. Moreover, the case study also confirms that using the predictive distribution to indirectly scrutinize uncertainty estimates is a viable approach, with distinct FA implementations showing marked differences in the reliability of their uncertainty estimates. The proposed comparison framework therefore constitutes a valuable tool to compare the predictive reliability of competing FA implementations, along with the reliability of their uncertainty estimates.

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Section: A Data‐based Comparison Frameworkmentioning

confidence: 99%

Data‐based comparison of frequency analysis methods: A general framework

Renard¹,

Kochanek

Lang³

et al. 2013

Water Resources Research

View full text Add to dashboard Cite

show abstract

“…For ordinary LS, small samples makes mandatory resorting to nonlinear optimization techniques such as the "Levenberg-Marquardt" with multiple initializations, or better, global optimization methods such as genetic algorithms. Bayesian bootstrap predictions with bagging (see Fushiki, 2010, for details) of parameter histograms directly is the alternative of choice, mainly when errors in model structure are significant.…”

Section: Model Updatementioning

confidence: 99%

Dynamic optimization of bioreactors using probabilistic tendency models and Bayesian active learning

Martínez

Cristaldi

Grau

2013

Computers & Chemical Engineering

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“…In [13], a Bayesian nonparametric procedure based on the Rubin's bootstrap technique ( [14]) is proposed to obtain a new class of algorithms called by the authors Bayesian Forests, under the idea that ensemble tree models can be represented as a sample from a posterior distribution over trees. Rubin's bootstrap has been discussed as bagging procedure for different prediction models also in [15,16], proving that Bayesian bootstrap lead to more stable prediction results in particular with small sample sized datasets.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap

et al. 2021

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Bootstrap resampling techniques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional ϕ(F), where F is a random distribution function. Efron’s and Rubin’s bootstrap procedures can be extended, introducing an informative prior through the Proper Bayesian bootstrap. In this paper different bootstrap techniques are used and compared in predictive classification and regression models based on ensemble approaches, i.e., bagging models involving decision trees. Proper Bayesian bootstrap, proposed by Muliere and Secchi, is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable. The results obtained are compared with respect to other competitive procedures employing different bootstrap techniques. The empirical analysis reports the results obtained on simulated and real data.

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Bayesian bootstrap prediction

Cited by 21 publications

References 16 publications

Data‐based comparison of frequency analysis methods: A general framework

Data‐based comparison of frequency analysis methods: A general framework

Dynamic optimization of bioreactors using probabilistic tendency models and Bayesian active learning

A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap

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