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75
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 846 (19 self)
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple changepoint analysis in one and two dimensions, and toaBayesian comparison of binomial experiments.
Forecasting Time Series Subject to Multiple Structural Breaks
, 2004
"... This paper provides a novel approach to forecasting time series subject to discrete structural breaks. We propose a Bayesian estimation and prediction procedure that allows for the possibility of new breaks over the forecast horizon, taking account of the size and duration of past breaks (if any) by ..."
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Cited by 53 (8 self)
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This paper provides a novel approach to forecasting time series subject to discrete structural breaks. We propose a Bayesian estimation and prediction procedure that allows for the possibility of new breaks over the forecast horizon, taking account of the size and duration of past breaks (if any) by means of a hierarchical hidden Markov chain model. Predictions are formed by integrating over the hyper parameters from the meta distributions that characterize the stochastic break point process. In an application to US Treasury bill rates, we find that the method leads to better outofsample forecasts than alternative methods that ignore breaks, particularly at long horizons.
The Equity Premium and Structural Breaks
, 2000
"... A long return history is useftil in estimating the current equity premium even if the historical distribution has experienced structural breaks. The long series helps not only if the timing of breaks is uncertain but also if one believes that large shifts in the premium are unlikely or that the prem ..."
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Cited by 39 (1 self)
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A long return history is useftil in estimating the current equity premium even if the historical distribution has experienced structural breaks. The long series helps not only if the timing of breaks is uncertain but also if one believes that large shifts in the premium are unlikely or that the premium is associated, in part, with volatility. Our framework incorporates these features along with a belief that prices are likely to move opposite to contemporaneous shifts in the premium. The estimated premium since 1834 fluctuates between four and six percent and exhibits its sharpest drop in the last decade.
Markov chain Monte Carlo for dynamic generalised linear models
, 1998
"... This paper presents a new methodological approach for carrying out Bayesian inference about dynamic models for exponential family observations. The approach is simulationbased and involves the use of Markov chain Monte Carlo techniques. A MetropolisHastings algorithm is combined with the Gibbs samp ..."
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Cited by 26 (1 self)
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This paper presents a new methodological approach for carrying out Bayesian inference about dynamic models for exponential family observations. The approach is simulationbased and involves the use of Markov chain Monte Carlo techniques. A MetropolisHastings algorithm is combined with the Gibbs sampler in repeated use of an adjusted version of normal dynamic linear models. Different alternative schemes based on sampling from the system disturbances and state parameters separately and in a block are derived and compared. The approach is fully Bayesian in obtaining posterior samples with state parameters and unknown hyperparameters. Illustrations with real datasets with sparse counts and missing values are presented. Extensions to accommodate more general evolution forms and distributions for observations and disturbances are outlined.
Nonlinearity, Structural Breaks Or Outliers In Economic Time Series?
 Nonlinear Econometric Modeling in Time Series Analysis
, 2000
"... This paper has its motivation from discussions at the EC ..."
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Cited by 16 (4 self)
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This paper has its motivation from discussions at the EC
Forecasting and Estimating Multiple Changepoint Models with an Unknown Number of Changepoints
, 2006
"... This paper develops a new approach to changepoint modeling that allows the number of changepoints in the observed sample to be unknown. The model we develop assumes regime durations have a Poisson distribution. It approximately nests the two most common approaches: the time varying parameter model ..."
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Cited by 12 (1 self)
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This paper develops a new approach to changepoint modeling that allows the number of changepoints in the observed sample to be unknown. The model we develop assumes regime durations have a Poisson distribution. It approximately nests the two most common approaches: the time varying parameter model with a changepoint every period and the changepoint model with a small number of regimes. We focus considerable attention on the construction of reasonable hierarchical priors both for regime durations and for the parameters which characterize each regime. A Markov Chain Monte Carlo posterior sampler is constructed to estimate a version of our model which allows for change in conditional means and variances. We show how real time forecasting can be done in an efficient manner using sequential importance sampling. Our techniques are found to work well in an empirical exercise involving US GDP growth and in‡ation. Empirical results suggest that the number of changepoints is larger than previously estimated in these series and the implied model is similar to a time varying parameter (with stochastic volatility) model.
Sequential Bayesian Prediction in the Presence of Changepoints
"... We introduce a new sequential algorithm for making robust predictions in the presence of changepoints. Unlike previous approaches, which focus on the problem of detecting and locating changepoints, our algorithm focuses on the problem of making predictions even when such changes might be present. We ..."
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Cited by 9 (4 self)
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We introduce a new sequential algorithm for making robust predictions in the presence of changepoints. Unlike previous approaches, which focus on the problem of detecting and locating changepoints, our algorithm focuses on the problem of making predictions even when such changes might be present. We introduce nonstationary covariance functions to be used in Gaussian process prediction that model such changes, then proceed to demonstrate how to effectively manage the hyperparameters associated with those covariance functions. By using Bayesian quadrature, we can integrate out the hyperparameters, allowing us to calculate the marginal predictive distribution. Furthermore, if desired, the posterior distribution over putative changepoint locations can be calculated as a natural byproduct of our prediction algorithm. 1.
Prior elicitation in multiple changepoint models
"... This paper discusses Bayesian inference in changepoint models. The main existing approaches either attempt to be noninformative by using a Uniform prior over changepoints or use an informative hierarchical prior. Both these approaches assume a known number of changepoints. We show how they have s ..."
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Cited by 8 (1 self)
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This paper discusses Bayesian inference in changepoint models. The main existing approaches either attempt to be noninformative by using a Uniform prior over changepoints or use an informative hierarchical prior. Both these approaches assume a known number of changepoints. We show how they have some potentially undesirable properties and discuss how these properties relate to the imposition of a …xed number of changepoints. We develop a new Uniform prior which allows some of the changepoints to occur outof sample. This prior has desirable properties, can reasonably be interpreted as “noninformative”and handles the case where the number of changepoints We would like to thank Edward Leamer for useful conversations and also seminar participants at the Federal Reserve Bank of St. Louis and University of Kansas. The views expressed in this paper are those of the authors and do not necessarily re‡ect the views of the Federal Reserve Bank of New York or the Federal Reserve System. 1 is unknown. We show how the general ideas of our approach can be extended to informative hierarchical priors. With arti…cial data and two empirical illustrations, we show how these di¤erent priors can have a substantial impact on estimation and prediction even with moderately large data sets. 1
Prediction and Change Detection
"... We measure the ability of human observers to predict the next datum in a sequence that is generated by a simple statistical process undergoing change at random points in time. Accurate performance in this task requires the identification of changepoints. We assess individual differences between obse ..."
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Cited by 7 (1 self)
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We measure the ability of human observers to predict the next datum in a sequence that is generated by a simple statistical process undergoing change at random points in time. Accurate performance in this task requires the identification of changepoints. We assess individual differences between observers both empirically, and using two kinds of models: a Bayesian approach for change detection and a family of cognitively plausible fast and frugal models. Some individuals detect too many changes and hence perform suboptimally due to excess variability. Other individuals do not detect enough changes, and perform suboptimally because they fail to notice shortterm temporal trends. 1
Bayesian Hierarchical Nonparametric Inference for ChangePoint Problems
, 1995
"... this paper. First, one could avoid the parametric restrictions on the d.f. of the observable random variables. Second, it is often desirable to incorporate information about the direction of the changepoint. A proposal might be to assume X i j F i ¸ F i and F 1 ; F 2 ; : : : ; Fn distributed as a m ..."
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Cited by 6 (2 self)
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this paper. First, one could avoid the parametric restrictions on the d.f. of the observable random variables. Second, it is often desirable to incorporate information about the direction of the changepoint. A proposal might be to assume X i j F i ¸ F i and F 1 ; F 2 ; : : : ; Fn distributed as a mixture of products of Dirichlet processes D(ff i (\Delta; ; ` i )), with mixing distribution H(` 1 ; : : : ; ` n ). The mixing distribution H could incorporate the initial information about the c.p.'s. We plan on investigating this problem in future work.