A Bayesian Approach to Inference about a Change-Point in a Sequence of Random Variables

Smith, A. F. M.

doi:10.2307/2335381

Cited by 20 publications

(21 citation statements)

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“…Bayesian methods applied to the problem of detecting shifts in the mean level of time series have been used, among others, by Smith (1975Smith ( , 1980, Lee and Heghinian (1977), Booth and Smith (1982), Broemeling (1985) and by Bernier (1994). These approaches are based on a single shifting model and all consider non-informative prior distributions on the unknown change-point.…”

Section: Introductionmentioning

confidence: 99%

Detection of changes in precipitation and runoff over eastern Canada and U.S. using a Bayesian approach

Perreault¹,

Haché

Slivitzky

et al. 1999

Stochastic Environmental Research and Risk Assessment (SERRA)

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Inference about the existence and characteristics of changes in mean level of hydrometeorological sequences that may be generated by climatic variability is an important step before developing management rules in water resources systems. This paper presents a Bayesian approach, based on a single shifting model, which can be used to study a change in the mean level of a set of independent normal random variables. Two different problems are considered: the ®rst is the detection of a change, while the second is the estimation of the change-point and its amplitude under the assumption that a change has occurred. This method is applied to precipitation and runoff data series over eastern Canada and U.S. during the twentieth century. The main results show an increase in the late sixties in the Eastern North American precipitation. This supports conclusions drawn from a number of studies which identi®ed the late sixties to early seventies as a period of possible change.

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Section: Introductionmentioning

confidence: 99%

Detection of changes in precipitation and runoff over eastern Canada and U.S. using a Bayesian approach

Perreault¹,

Haché

Slivitzky

et al. 1999

Stochastic Environmental Research and Risk Assessment (SERRA)

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“…The Bayesian literature on the change point problem focuses on the retrospective analysis for situations where f 0 (x) and f 1 (x) belong to a parametric family of densities; see, for instance, Ferreira (1975), Smith (1975), Choy and Broemeling (1980), Smith and Cook (1980), Menzefrike (1981), Raftery and Akman (1986), Carlin et al(1992), among others. When f 0 (x) and f 1 (x) are densities belonging to a parametric family to be denoted as f(x|h 1 ) and f(x|h 2 ) respectively, where h 1 and h 2 are unknown points of a parameter space Q, the sampling density of the first n observations is…”

Section: The Parametric Change Point Problemmentioning

confidence: 99%

“…A nonparametric analysis of the above data has been done by Petitt (1979) who obtained the estimation of the change pointr ¼ 17: Smith (1975) also found for the posterior mode the value 17 and 17.72 for the posterior mean; he used conjugate priors with subjective values for the hyperparameters.…”

Section: Examplementioning

confidence: 99%

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An objective Bayesian analysis of the change point problem

Moreno

Casella

Garcı́a-Ferrer

2005

Stoch Environ Res Ris Assess

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The Bayesian literature on the change point problem deals with the inference of a change in the distribution of a set of time-ordered data based on a sample of fixed size. This is the so-called ''retrospective or off-line'' analysis of the change point problem. A related but different problem is that of the ''sequential'' change point detection, mainly analyzed from a frequentist viewpoint. While the former typically focuses on the estimation of the position in which the change point occurs, the latter is a testing problem which has a natural formulation as a Bayesian model selection problem. In this paper we provide such a Bayesian formulation, which generalizes previous formulations such as the well-known CUSUM stopping rule. We show that the conventional improper priors (also called non-informative, objective or default), cannot be used either for sequential detection of the change or for retrospective estimation. Then, we propose objective intrinsic prior distributions for the unknown model parameters. The normal and Poisson cases are studied in detail and examples with simulated and real data are provided.

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“…Bayesian framework for inferences on changepoint dates back to work by Chernoff and Zacks (1964) and Shiryayev (1963). Smith (1975), Carlin et al (1992) and Dey and Purkayastha (1997) developed different Bayesian approaches including hierarchichal Bayesian methods for inferences related to changepoints. However, none of those papers consider isotonic structure.…”

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confidence: 99%