Bayes procedures for detecting a shift in the probability of success in a series of Bernoulli trials

Zacks, Shelemyahu; Barzily, Zeev

doi:10.1016/0378-3758(81)90021-5

Cited by 26 publications

(12 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Brown and Zacks (2006) investigated the detection of changes in a Poisson process. Zacks and Barzily (1981) extended the work of Shiryaev for the case of Bernoulli sequences. Optimal stopping rules based on Dynamic Programming procedures were discussed.…”

Section: Introductionmentioning

confidence: 92%

See 1 more Smart Citation

Detection of Changes in a Multinomial Process

Brown¹

2012

IJSP

View full text Add to dashboard Cite

We look at a multinomial distribution where the probabilities of landing in each category change at some unknown integer. We assume that the probability structure both before and after the change is known, and the problem is to find the probability that the probability structure has changed. For a loss function consisting of the cost of late detection and a penalty for early stopping, we develop, using dynamic programming, the one and two steps look ahead Bayesian stopping rules. We provide some numerical results to illustrate the effectiveness of the detection procedures. We show that the two step ahead procedure is a slight improvement over the one step ahead procedure. However the two procedures are very consistant in their stopping times.

show abstract

Section: Introductionmentioning

confidence: 92%

“…We utilize the Dynamic Programming procedure developed by Zacks and Barzily (1981). We assume we must stop after observing n * observations if we have not stopped earlier.…”

Section: Optimal Stopping Rulementioning

confidence: 99%

Detection of Changes in a Multinomial Process

Brown¹

2012

IJSP

View full text Add to dashboard Cite

show abstract

“…Even in parametric models these distributions may depend on unknown parameters, which have to be estimated from the data during the detection processes. Bayesian solutions to such cases have been developed by Zacks and Barzily (1981) using the backward induction principle of dynamic programming. They also considered the problem of detecting a change in the success probability in a sequence of binomial trials using a two-step look-ahead stopping rule.…”

Section: { /~11 -T-(1 -~)#1o : ]~1mentioning

confidence: 99%

“…EMPIRICAL BAYES DETECTION 231 Clearly, if B = p-l(c_p) with c > p, then r* is the optimal rule for the variational problem. The stopping rule r* is equivalent to the one-step look-ahead stopping rule for the present problem; see, e.g., Zacks (1991) or Zacks and Barzily (1981). Optimality of myopic rules, such as r*, have been examined by Chow and Robbins (1961) and Abdel-Hameed (1977), among others.…”

Section: Introductionmentioning

confidence: 99%

Empirical Bayes detection of a change in distribution

Karunamuni

Zhang

1996

Ann Inst Stat Math

View full text Add to dashboard Cite

show abstract

“…In his discussion of Mei's paper, Zacks (2008, p. 413), also said that "cases of unknown prechange or postchange parameters should be dealt within a Bayesian framework" and refers to Zacks (1991, Sec. 5), Zacks and Barzily (1981), Kenett and Zacks (1994), and Brown and Zacks (2006) for related developments. He also pointed out that "important characteristics of the posterior processes, such as recursive determination of posterior probabilities, do not exist when the densities before and after the change are not completely known."…”

Section: Introductionmentioning

confidence: 98%

A Bayesian Approach to Sequential Surveillance in Exponential Families

Lai

Liu

Xing

2009

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

We describe herein a Bayesian change-point model and the associated recursive formulas for the estimated time-varying parameters and the posterior probability that a change-point has occurred at a particular time. The proposed model is a variant of that of Chernoff and Zacks (1964) for the case of normal means with known common variance. It considers more generally the multiparameter exponential family and addresses the complex statistical issues due to multiple change-points and unknown pre-and post-change system parameters in sequential surveillance. A sequential detection rule based on the proposed model is also introduced and its false alarm rate and mean detection delay are studied in the multiple change-point setting.

show abstract

Bayes procedures for detecting a shift in the probability of success in a series of Bernoulli trials

Cited by 26 publications

References 5 publications

Detection of Changes in a Multinomial Process

Detection of Changes in a Multinomial Process

Empirical Bayes detection of a change in distribution

A Bayesian Approach to Sequential Surveillance in Exponential Families

Contact Info

Product

Resources

About