Bayesian analysis of multiple thresholds autoregressive model

Bayesian analysis of threshold autoregressive (TAR) model with various possible thresholds is considered. A method of Bayesian stochastic search selection is introduced to identify a threshold-dependent sequence with highest probability. All model parameters are computed by a hybrid Markov chain Monte Carlo (MCMC) method, which combines Metropolis-Hastings (M-H) algorithm and Gibbs sampler. The main innovation of the method introduced here is to estimate the TAR model without assuming the fixed number of threshold values, thus is more flexible and useful. Simulation experiments and a real data example lend further support to the proposed approach

Structural Prior Guided Generative Adversarial Transformers for Low-Light Image Enhancement

We propose an effective Structural Prior guided Generative Adversarial Transformer (SPGAT) to solve low-light image enhancement. Our SPGAT mainly contains a generator with two discriminators and a structural prior estimator (SPE). The generator is based on a U-shaped Transformer which is used to explore non-local information for better clear image restoration. The SPE is used to explore useful structures from images to guide the generator for better structural detail estimation. To generate more realistic images, we develop a new structural prior guided adversarial learning method by building the skip connections between the generator and discriminators so that the discriminators can better discriminate between real and fake features. Finally, we propose a parallel windows-based Swin Transformer block to aggregate different level hierarchical features for high-quality image restoration. Experimental results demonstrate that the proposed SPGAT performs favorably against recent state-of-the-art methods on both synthetic and real-world datasets

Testing a linear ARMA Model against threshold-ARMA models : a Bayesian approach

We introduce a Bayesian approach to test linear autoregressive moving-average (ARMA) models against threshold autoregressive moving-average (TARMA) models. Firstly, the marginal posterior densities of all parameters, including the threshold and delay, of a TARMA model are obtained by using Gibbs sampler with Metropolis-Hastings algorithm. Secondly, reversible-jump Markov chain Monte Carlo (RJMCMC) method is adopted to calculate the posterior probabilities for ARMA and TARMA models: Posterior evidence in favor of TARMA models indicates threshold nonlinearity. Finally, based on RJMCMC scheme and Akaike information criterion (AIC) or Bayesian information criterion (BIC), the procedure for modeling TARMA models is exploited. Simulation experiments and a real data example show that our method works well for distinguishing a ARMA from a TARMA model and for building TARMA models