Roberta Paroli

Bayesian inference in non-homogeneous Markov mixtures of periodic autoregressions with state-dependent exogenous variables

The Bayesian analysis of a non-homogeneous Markov mixture of periodic autoregressions with state-dependent exogenous variables is proposed to investigate a non-linear and non-Normal time series. It is performed within a Markov chain Monte Carlo framework, along four consecutive steps: the specification of the identifiability constraint; the selection of the exogenous variables which influence the observed process and the time-varying transition probabilities of the hidden Markov chain; the choice of the cardinality of the hidden Markov chain state-space and the autoregressive order; the estimation of the parameters. The selection of the exogenous variables is performed in the complex case of correlation between variables, by means of a new procedure. An application for relating the hourly mean concentrations of sulphur dioxide with six meteorological variables, recorded for three years by an air pollution testing station located in the lagoon of Venice (Italy), is presented. The reconstruction of the sequence of the hidden states, the restoration of the missing values occurring within the observed series, the description of the periodic component are also given.

Bayesian Variable Selection in Markov Mixture Models

Bayesian methods for variable selection and model choice have become increasingly popular in recent years, due to advances in Markov Chain Monte Carlo (MCMC) computational algorithms. Several methods have been proposed in literature in the case of linear and generalized linear models. In this article, we adapt some of the most popular algorithms to a class of nonlinear and non Gaussian time series models, i.e., the Markov Mixture Models (MMM). We also propose the “Metropolization” of the algorithm of Kuo and Mallick (1998), in order to tackle variable selection efficiently, both when the complexity of the model is high, as in MMM, and when the exogenous variables are strongly correlated. Numerical comparisons among the competing MCMC algorithms are also presented via simulation examples.

Bayesian Inference and Forecasting in Dynamic Neural Networks with Fully Markov Switching ARCH Noises

We deal with one-layer feed-forward neural network for the Bayesian analysis of nonlinear time series. Noises are modeled nonlinearly and nonnormally, by means of ARCH models whose parameters are all dependent on a hidden Markov chain. Parameter estimation is performed by sampling from the posterior distribution via Evolutionary Monte Carlo algorithm, in which two new crossover operators have been introduced. Unknown parameters of the model also include the missing values which can occur within the observed series, so, considering future values as missing, it is also possible to compute point and interval multi-step-ahead predictions.

Periodic Markov switching autoregressive models for Bayesian analysis and forecasting of air pollution

Markov switching autoregressive models (MSARMs) are efficient tools to analyse nonlinear and non-Gaussian time series. A special MSARM with two harmonic components is proposed to analyse periodic time series. We present a full Bayesian analysis based on a Gibbs sampling algorithm for model choice and the estimations of the unknown parameters, missing data and predictive distributions. The implementation and modelling steps are developed by tackling the problem of the hidden states labeling by means of random permutation sampling and constrained permutation sampling. We apply MSARMs to study a data set about air pollution that presents periodicities since the hourly mean concentration of carbon monoxide varies according to the dynamics of the 24 day-hours and of the year. Hence, we introduce in the model both a hidden state-dependent daily component and a state-independent yearly component, giving rise to periodic MSARMs.

Inference on the CUB model: an MCMC approach

We consider a special finite mixture model for ordinal data expressing the preferences of raters with regards to items or services, named CUB (Covariate Uniform Binomial), recently introduced in statistical literature. The mixture is made up of two components that belong to different families of distributions: a shifted Binomial and a discrete Uniform. Bayesian analysis of the CUB model naturally comes from the elicitation of some priors on its parameters. In this case the parameters estimation must be performed through the analysis of the posterior distribution. In the theory of finite mixture models complex posterior distributions are usually evaluated through computational methods of simulation such as the Markov Chain Monte Carlo (MCMC) algorithms. Since the mixture type of the CUB model is non-standard, a suitable MCMC algorithm has been developed and its performance has been evaluated via a simulation study and an application on real data.

Bayesian variable selection in a class of mixture models for ordinal data: a comparative study

In this paper, we consider a special finite mixture model named Combination of Uniform and shifted Binomial (CUB), recently introduced in the statistical literature to analyse ordinal data expressing the preferences of raters with regards to items or services. Our aim is to develop a variable selection procedure for this model using a Bayesian approach. Bayesian methods for variable selection and model choice have become increasingly popular in recent years, due to advances in Markov chain Monte Carlo computational algorithms. Several methods have been proposed in the case of linear and generalized linear models (GLM). In this paper, we adapt to the CUB model some of these algorithms: the Kuo–Mallick method together with its ‘metropolized’ version and the Stochastic Search Variable Selection method. Several simulated examples are used to illustrate the algorithms and to compare their performance. Finally, an application to real data is introduced.