Bayesian Dynamic Fused LASSO
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The new class of Markov processes is proposed to realize the flexible shrinkage effects for the dynamic models. 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 the 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. The dynamic regression models with this new process used as a prior is conditionally Gaussian and linear in state variables, for which the posterior can be computed efficiently by utilizing the forward filtering and backward sampling in Gibbs sampler. The latent integer-valued parameter of the log-geometric distribution is understood as the amount of shrinkage to zero realized in the posterior and can be used to detect in which period the corresponding predictor becomes inactive. With the hyperparameters and observational variance estimated in Gibbs sampler, the new prior is compared with the standard double-exponential prior in the estimation of and prediction by the dynamic linear models for illustration. It is also applied to the time-varying vector autoregressive models for the US macroeconomic data and performs as an alternative of the dynamic model of variable selection type, such as the latent threshold models.
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