Bayesian analysis of a Poisson process with a change-point

Raftery, Adrian E.; Akman, Varol

doi:10.1093/biomet/73.1.85

Cited by 202 publications

(144 citation statements)

References 14 publications

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“…The value of the statistic (3) is 1.110 at i = 186, so that i last = 125. We conclude that the proposed procedure supports that there exists only one changepoint between the 124th and 125th accidents, as in Raftery and Akman (1986) and Yang and Kuo (2001). A confidence interval for the changepoint can be found based on the limiting distribution given in Theorem 3.…”

Section: A Real Data Examplesupporting

confidence: 72%

“…The data was initially gathered by Maguire et al (1952), corrected by Jarrett (1979) and finally extended by Raftery and Akman (1986) to the period between January 1, 1851, and December 31, 1962. Figure 2 shows the dates of the 192 disasters together with the cumulative counting process.…”

Section: A Real Data Examplementioning

confidence: 99%

“…Figure 2 shows the dates of the 192 disasters together with the cumulative counting process. With the final set, Raftery and Akman (1986) assumed a single changepoint and estimated the posterior mode of the location of the change between the 124th and 125th accidents. Carlin et al (1992), assuming a single changepoint, estimated the mode of the change around the 127th accident.…”

Section: A Real Data Examplementioning

confidence: 99%

“…Lately, most of the works dealing with changepoints in Poisson processes are from a Bayesian perspective. Raftery and Akman (1986), Carlin et al (1992) and Raftery (1994) study the single changepoint case. Multiple changepoints are analyzed by Green (1995), who proposed a reversible jump Markov chain Monte Carlo method for locating the multiple changepoints and estimating 1 the corresponding rate parameters.…”

Section: Introductionmentioning

confidence: 99%

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The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process

Galeano

2007

Computational Statistics & Data Analysis

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This paper studies the problem of multiple changepoints in rate parameter of a Poisson process. We propose a binary segmentation algorithm in conjunction with a cumulative sums statistic for detection of changepoints such that in each step we need only to test the presence of a simple changepoint. We derive the asymptotic distribution of the proposed statistic, prove its consistency and obtain the limiting distribution of the estimate of the changepoint. A Monte Carlo analysis shows the good performance of the proposed procedure, which is illustrated with a real data example. Keywords AbstractThis paper studies the problem of multiple changepoints in rate parameter of a Poisson process. We propose a binary segmentation algorithm in conjunction with a cumulative sums statistic for detection of changepoints such that in each step we need only to test the presence of a simple changepoint. We derive the asymptotic distribution of the proposed statistic, prove its consistency and obtain the limiting distribution of the estimate of the changepoint. A Monte Carlo analysis shows the good performance of the proposed procedure, which is illustrated with a real data example.

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Section: A Real Data Examplesupporting

confidence: 72%

Section: A Real Data Examplementioning

confidence: 99%

Section: A Real Data Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process

Galeano

2007

Computational Statistics & Data Analysis

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“…Some examples include Poisson processes with a piece-wise constant rate parameter (Raftery and Akman, 1986;Yang and Kuo, 2001;Ritov et al, 2002), changing linear regression models (Carlin et al, 1992;Lund and Reeves, 2002), Gaussian observations with varying mean (Worsley, 1979) or variance (Chen and Gupta, 1997;Johnson et al, 2003), and Markov models with time-varying transition matrices (Braun and Muller, 1998). Such models have been used for modelling stock prices, muscle activation, climatic time-series, DNA sequences and neuronal activity in the brain, amongst many other applications…”

Section: Introductionmentioning

confidence: 99%

Exact and efficient Bayesian inference for multiple changepoint problems

2006

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Summary We demonstrate how to perform direct simulation from the posterior distribution of a class of multiple changepoint models where the number of changepoints is unknown. The class of models assumes independence between the posterior distribution of the parameters associated with segments of data between successive changepoints. This approach is based on the use of recursions, and is related to work on product partition models. The computational complexity of the approach is quadratic in the number of observations, but an approximate version, which introduces negligible error, and whose computational cost is roughly linear in the number of observations, is also possible. Our approach can be useful, for example within an MCMC algorithm, even when the independence assumptions do not hold. We demonstrate our approach on well-log data. Our method can cope with a range of models for this data, and exact simulation from the posterior distribution is possible in a matter of minutes.

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Change‐Point Problem

Pettitt¹

2004

Encyclopedia of Statistical Sciences

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Bayesian analysis of a Poisson process with a change-point

Cited by 202 publications

References 14 publications

The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process

The use of cumulative sums for detection of changepoints in the rate parameter of a Poisson Process

Exact and efficient Bayesian inference for multiple changepoint problems

Change‐Point Problem

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