Abstract
Bayesian multiple change-point models are built with data from normal, exponential, binomial and Poisson distributions with a truncated Poisson prior for the number of change-points and conjugate prior for the distributional parameters. We applied Annealing Stochastic Approximation Monte Carlo (ASAMC) for posterior probability calculations for the possible set of change-points. The proposed methods are studied in simulation and applied to temperature and the number of respiratory deaths in Seoul, South Korea.
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References
Barry D, Hartigan JA (1993) A Bayesian analysis for change-point problems. J Am Stat Assoc 88: 309–319
Belisle P, Joseph L, MacGibbon B, Wolfson DB, Berger R (1998) Change-point analysis of neuron spike train data. Biometrics 54: 113–123
Braga ALF, Zanobetti A, Schwartz I J (2002) The Effect of weather on respiratory and cardiovascular deaths in 12 U.S. Cities. Environ Health Perspect 110(9): 859–863
Carlin BP, Gelfand AE, Smith AFM (1992) Hierarchical Bayesian analysis of change point problems. Appl Stat 41: 389–405
Celeux G, Forbes F, Robert CP, Titterington DM (2006) Rejoinder. Bayesian Stat 1: 701–796
Chernoff H, Zacks S (1964) Estimating the current mean of a normal distribution which is subject to changes in time. Ann Math Stat 35: 999–1018
Chib S (1998) Estimation and comparison of multiple change-point models. J Econom 86: 221–241
Fearnhead P (2006) Exact and efficient Bayesian inference for multiple changepoint problems. Stat Comp 16: 203–213
Filleul L, Vandentorren S, Baldi I, Tessier JF (2001) Daily respiratory mortality and PM10 pollution in Mexico City. Euro Respir J 17: 1055–1056
Gauvin S, Zmirou D, Pin I, Quentin J, Balducci F, Boudet C, Poizeau D, Brambilla C (1999) Short-term effect of exposure to suspended particulate matter (PM10) on the respiratory function of urban asthmatic and control adults. J Environ Med 1: 71–79
Gelfand A, Smith A (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85: 398–409
Gelman A, Roberts GO, Gilks WR (1996) Efficient Metropolis jumping rules. Bayesian Stat 5: 599–607
Gelman A, Carlin J, Stern H, Rubin D (2003) Bayesian data analysis. Chapman and Hall, New York
Green PJ (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82: 711–732
Hawkins DM (2001) Finding multiple change-point models to data. Comp Stat Data Anal 37: 323–341
Hinkley DV (1970) Inference about the change-point in a sequence of random variables. Biometrika 57: 1–17
Kander Z, Zacks S (1966) Test procedure for possible changes in parameter of statistical distributions occurring at unknown time points. Ann Math Stat 37: 1196–1210
Kass RE, Raftery A (1995) Bayes factors. J Am Stat Assoc 90: 773–795
Koop GM, Potter SM (2004) Forecasting and estimating multiple change-point models with an unknown number of change-points, Federal Reserve Bank of New York Staff Reports, no. 196
Liang F (2007) Annealing stochastic approximation Monte Carlo for neural network training. Mach Learn 68(3): 201–233
Liang F, Wong WH (2000) Evolutionary Monte Carlo applications to C p model sampling and change-point problems. Stat Sinica 10: 317–342
Liang F, Liu C, Carroll R (2007) Stochastic approximation in Monte Carlo computation. J Am Stat Assoc 102: 305–320
Lupo AR, Kelsey EP, McCoy EA, Halcomb C, Aldrich E, Allen SN, Akyuz A, Skellenger S, Beiger DG, Wise E, Schmidt D, Edwards M (2003) The presentation of temperature information in television broadcasts: what is normal?. Natl Weather Dig 27(4): 53–58
Maguire BA, Pearson ES, Wynn AHA (1952) The time intervals between industrial accidents. Biometrika 38: 168–180
Nevel’son MB, Has’minskii RZ (1973) Stochastic approximation and recursive estimation. American Mathematical Society, Providence RI
Raftery AE, Akman VE (1986) Bayesian analysis of a Poisson process with a change-point. Biometrika 73: 85–89
Robbins H, Monro S (1951) A stochastic approximation method. Ann Math Stat 22: 400–407
Schwartz J (1994) Nonparametric smoothing in the analysis of air pollution and respiratory illness. Can J Stat 22(4): 471–487
Smith AFM (1975) A Bayesian approach to inference about a change-point in a sequence of random variables. Biometrika 62: 407–416
Stephens DA (1994) Bayesian retrospective multiple-change-point identification. Appl Stat 43: 159–178
Tierney L (1994) Markov chains for exploring posterior distributions (with discussion). Ann Stat 22: 1701–1762
Venter JH, Steel SJ (1996) Finding multiple abrupt change-points. Comp Stat Data Anal 22: 481–504
Wang F, Landau DP (2001) Efficient, multiple-range random walk algorithm to calculate the density of states. Phys Rev Lett 86: 2050–2053
Yao YC (1984) Estimation of a noisy discrete-time step function: Bayes and empirical Bayes approaches. Ann Stat 12: 1434–1447
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This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (No. R01-2008-000-10133-0).
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Kim, J., Cheon, S. Bayesian multiple change-point estimation with annealing stochastic approximation Monte Carlo. Comput Stat 25, 215–239 (2010). https://doi.org/10.1007/s00180-009-0172-x
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DOI: https://doi.org/10.1007/s00180-009-0172-x