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Title: Bayesian dynamic fused lasso Authors:  Kaoru Irie - University of Tokyo (Japan) [presenting]
Abstract: The new class of Markov processes is proposed to model the flexible shrinkage effects in the prior of time-varying parameters for time series analysis. The transition density of the new process consists of two penalty functions, similar to Bayesian fused LASSO in its functional form, that shrink the current state variable to its previous value and zero. The normalizing constant of this density, which is not ignorable in the posterior computation, is shown to be essentially the log-geometric mixture of double-exponential densities and treated as a part of the likelihood. By using this new process as a prior on dynamic coefficients, the dynamic regression model is conditionally Gaussian and linear in state variables, for which the posterior can be computed efficiently by the forward filtering and backward sampling in Gibbs sampler. The log-geometric distributed latent variable is understood as the amount of shrinkage to zero realized in the posterior and can be used to detect periods in which the corresponding dynamic coefficient becomes inactive. The new prior is compared with the standard double-exponential prior in the estimation of, and prediction by, the dynamic linear models with the simulated datasets for illustration. It is also applied to the time-varying vector autoregressive models for the US macroeconomic data, which exemplifies the use of the new prior as an alternative of the dynamic model of variable selection type, such as the latent threshold models.