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Bayesian Analysis of Nonlinear Autoregression Models Based on Neural Networks

amenchero{at}escet.urjc.es, GECD, Rey Juan Carlos University, Madrid 28925, Spain

R. Montes Diez

rmontes{at}escet.urjc.es, GECD, Rey Juan Carlos University, Madrid 28925, Spain

D. Ríos Insua

drios{at}escet.urjc.es, GECD, Rey Juan Carlos University, Madrid 28925, Spain

P. Müller

pm{at}odin.mdacc.tmc.edu, M. D. Anderson Cancer Center. University of Texas, Houston, TX 77030, U.S.A.

We show how Bayesian neural networks can be used for time-series analysis. We consider a block-based model building strategy to model linear and nonlinear features within the time series: a linear combination of a linear autoregression term and a feedforward neural network (FFNN) with an unknown number of hidden nodes. To allow for simpler models, we also consider these terms separately as competing models to select from. Model identifiability problems arise when FFNN sigmoidal activation functions exhibit almost linear behavior or when there are almost duplicate or irrelevant neural network nodes. New reversible-jump moves are proposed to facilitate model selection, mitigating model identifiability problems. We illustrate this methodology analyzing several time-series data examples.

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