Bayesian isotonic changepoint analysis

Álvarez, Enrique E.; Dey, Dipak K.

doi:10.1007/s10463-007-0148-y

Cited by 4 publications

(2 citation statements)

References 12 publications

(11 reference statements)

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“…Anomalies are departures from the temperatures average between 1961 and 1990. This data set has been used by several authors: Alvarez & Dey () use a Bayesian monotonic change point method to show the existence of an increasing trend in the global annual temperature between 1958 and 2000 and similar conclusions are obtained by Alvarez & Yohai (), Wu et al , (), and Zhao & Woodroofe () using isotonic estimation methods. In all these papers, observations are supposed to be independent and identically distributed; for simplicity, we make the same assumption in the present paper.…”

Section: Numerical Applicationsmentioning

confidence: 72%

Bayesian regression with B‐splines under combinations of shape constraints and smoothness properties

Abraham

Khadraoui

2014

Statistica Neerlandica

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In this paper, we approach the problem of shape constrained regression from a Bayesian perspective. A B-splines basis is used to model the regression function. The smoothness of the regression function is controlled by the order of the B-splines, and the shape is controlled by the shape of an associated control polygon. Controlling the shape of the control polygon reduces to some inequality constraints on the spline coefficients. Our approach enables us to take into account combinations of shape constraints and to localize each shape constraint on a given interval. The performance of our method is investigated through a simulation study. Applications to a real data sets in food industry and Global Warming are provided.

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Section: Numerical Applicationsmentioning

confidence: 72%

Bayesian regression with B‐splines under combinations of shape constraints and smoothness properties

Abraham

Khadraoui

2014

Statistica Neerlandica

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“…Example 2 We reconsider the Global Warming dataset first analyzed in the context of isotonic regression by Wu, Woodroofe and Mentz (2001) from a classical perspective and subsequently analyzed from a Bayesian perspective in Alvarez and Dey (2009). The original data is provided by Jones et al (see http//cdiac.esd.ornl.gov/trends/temp/jonescru/jones.html) containing annual temperature anomalies from 1858 to 2009, expressed in degrees Celsius and are relative to the 1961-1990 mean.…”

Section: Examplesmentioning

confidence: 99%

M-estimators for isotonic regression

Álvarez

Yohai

2012

Journal of Statistical Planning and Inference

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In this paper we propose a family of robust estimates for isotonic regression: isotonic M-estimators. We show that their asymptotic distribution is, up to an scalar factor, the same as that of Brunk 's classical isotonic estimator. We also derive the influence function and the breakdown point of these estimates. Finally we perform a Monte Carlo study that shows that the proposed family includes estimators that are simultaneously highly efficient under gaussian errors and highly robust when the error distribution has heavy tails.

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Nonparametric adaptive Bayesian regression using priors with tractable normalizing constants and under qualitative assumptions

Khadraoui

2017

International Journal of Approximate Reasoning

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Bayesian isotonic changepoint analysis

Abstract: Bayesian inference, Change point problem, Isotonic regression, Order restricted inference,

Cited by 4 publications

References 12 publications

Bayesian regression with B‐splines under combinations of shape constraints and smoothness properties

Bayesian regression with B‐splines under combinations of shape constraints and smoothness properties

M-estimators for isotonic regression

Nonparametric adaptive Bayesian regression using priors with tractable normalizing constants and under qualitative assumptions

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