On Dynamic Generalized Linear Models with Applications

Methodology and Computing in Applied Probability - Tập 15 - Trang 407-421 - 2011
Sourish Das1, Dipak K. Dey2
1SAS Research and Development, Pune, India
2Department of Statistics, University of Connecticut, Storrs, USA

Tóm tắt

In this paper we combine the idea of ‘power steady model’, ‘discount factor’ and ‘power prior’, for a general class of filter model, more specifically within a class of dynamic generalized linear models (DGLM). We show an optimality property for our proposed method and present the particle filter algorithm for DGLM as an alternative to Markov chain Monte Carlo method. We also present two applications; one on dynamic Poisson models for hurricane count data in Atlantic ocean and the another on the dynamic Poisson regression model for longitudinal count data.

Tài liệu tham khảo

Chen MH, Ibrahim JG (2003) Conjugate priors for generalized linear models. Stat Sin 13:461–476 Chen MH, Ibrahim JG, Shao QM (2000) Power prior distribution for generalized linear models. J Stat Plan Inference 84:121–137 Das S (2008) Generalized linear models and beyond: an innovative approach from Bayesian Perspective. Ph.D. thesis, University of Connecticut Das S, Dey DK (2008) Analysis of 5 loxin® treatment for patients with osteoarthritis in clinical trial using power filter. Tech. Rep., Statistical and Applied Mathematical Science Institute (SAMSI). http://www.samsi.info/TR/tr2008-09.pdf Diggle PJ, Heagerty P, Liang K-Y, Zeger SL (2002) Analysis of longitudinal data, 2nd edn. Oxford University Press Fahrmeir L (1992) Posterior mode estimation by extended kalman filtering for multivariate dynamic generalized linear models. J Am Stat Assoc 87:501–509 Gamerman D (1998) Markov chain monte carlo for dynamic generalised linear models. Biometrika 85(1):215–227 Gilks WR, Berzuini C (2001) Following a moving target - monte carlo inference for dynamic bayesian models. J R Stat Soc Ser B 63:127–146 Greenberg E, Baron J, Stukel T, Stevens M, Mandel J, Spencer S, Elias P, Lowe N, Nierenberg D, Bayrd G, Vance J, Freeman D, Clendenning W, Kwan T (1990) A clinical trial of beta carotene to prevent basal-cell and squamous-cell cancers of the skin. N Engl J Med 323:789–795. The Skin Cancer Prevention Study Group Harrison PJ, Stevens C (1976) Bayesian forecasting (with discusssion). J R Stat Soc Ser B 38:205–247 Ho YC, Lee RCK (1964) Bayesian approach to problems in stochastic estimation and control. IEEE Trans Automat Contr 9:333–339 Hu X-L, Schön TB, Lennart L (2008) A basic convergence result for particle filtering. IEEE Trans Signal Process 56:1337–1348 Ibrahim JG, Chen MH, Sinha D (2003) On optimality properties of the power prior. J Am Stat Assoc 98:203–213 Kalman RE (1960) A new approach to linear filtering and prediction problem. Trans ASME Ser D J Basic Eng 82:34–45 Kalman RE, Bucy RS (1961) New results in linear filtering and prediction theory. Trans ASME Ser D J Basic Eng 83:95–107 Kolmogorov AN (1941) Stationary sequences in Hilbert spaces. Bull Math Univ. Moscow 2:40 (in Russian) Meinhold RJ, Singpurwalla ND (1983) Understanding the kalman filter. Am Stat 37:123–127 Rothkopf MH (2007) Decision analysis: the right tool for auctions. Decision Analysis 4:167–172 Rubin DB (1987) A noniterative sampling/importance resampling alternative to the data augmentation algorithm for creating a few imputations when the fraction of missing information is modest: the sir algorithm (discussion of tanner and wong). J Am Stat Assoc 82:543–546 Rubin DB (1988) Using the sir algorithm to simulate posterior distribution. In: Bernardo JM, DeGroot M, Lindley D, Smith A (eds) Bayesian statistics, vol 3. Oxford, Clarendon, UK, pp 395–402 Smith JQ (1979) A generalization of bayesian steady model. J R Stat Soc Ser B 41:375–387 Smith JQ (1981) The multiparameter steady model. J R Stat Soc Ser B 43:256–260 Spiegelhalter DJ, Best NG, Carlin BP, Linde AVD (2002) Bayesian measures of model complexity and fit. J R Statist Soc B 64:538–639 Trenberth K (2005) Uncertainty in hurricanes and global warming. Science 308:1753–1754 Webster PJ, Holland GJ, Curry JA, Chang H-R (2005) Changes in tropical cyclone number, duration, and intensity in a warming environment. Science 309:1844–1846 West M (1986) Bayesian model monitoring. J R Stat Soc Ser B 48:70–80 West M, Harrison J (1997) Bayesian forecasting and dynamic models. Springer West M, Harrison PJ, Migon HS (1985) Dynamic generalized linear models and bayesian forecasting (with discussion). J Am Stat Assoc 80:73–96 Wiener N (1949) Extrapolation, interpolation and smoothing of time series with engineering applications. Wiley, New York. Originally appears in 1942 as a classified National Defense Research Council Report. Also published under the title Time Series Analysis by MIT Press Zellner A (2002) Information processing and bayesian analysis. J Econom 107:41–50