The well-known cumulative sum (CUSUM) sequential rule for abrupt model change detection in stochastic dynamic systems relies on the knowledge of the probability density functions of the system output variables conditional on their past values and on the system functioning mode at each time step. This paper shows how to build an asymptotically optimal detection rule under the common average run length (ARL) constraint when these densities are not available but can be consistently estimated. This is the case for nonlinear state–space systems observed through output variables: for such systems, a new class of particle filters based on convolution kernels allows to get consistent estimates of the conditional densities, leading to an optimal CUSUM-like filter detection rule (FDR).

A Bayesian method for the comparison and selection of multioutput feedforward neural network topology, based on the predictive capability, is proposed. As a measure of the prediction fitness potential, an expected utility criterion is considered which is consistently estimated by a sample-reuse computation. As opposed to classic point-prediction-based cross-validation methods, this expected utility is defined from the logarithmic score of the neural model predictive probability density. It is shown how the advocated choice of a conjugate probability distribution as prior for the parameters of a competing network, allows a consistent approximation of the network posterior predictive density. A comparison of the performances of the proposed method with the performances of usual selection procedures based on classic cross-validation and information-theoretic criteria, is performed first on a simulated case study, and then on a well known food analysis dataset.

This paper presents a new method to deal with nonlinear filtering problems in discrete time. Our approach is based on radial basis neural networks and on the principle of particles filters. More precisely, the usual learning phase of the network is replaced by the generation of a lot of particles, i.e. simulated system trajectories. Particles so generated correspond to neural centers. Inspite of its complex structure such a network possesses good properties. First, we show that the network output converges to the optimal filter when the number of particles grows. Second, the implementation is very simple and the computational time is reasonable. And finally, on simulations good performances are observed with respect to that of the extended kalman filter and that of an optimal recurrent neural network.

A Bayesian method for the selection of multioutput feedforward neural networks based on their respective predictive capability is proposed. This paper extends, with full theoretical arguments, an approach initiated previously for the selection of single-output feedforward neural networks. As measure of the future prediction fitness, an expected utility criterion is considered which is consistently estimated by a sample-reuse computation. As opposed to classic point-prediction-based cross-validation methods, this expected utility is defined from the logarithmic score of the neural model predictive probability density. It is shown how the advocated choice of conjugates distributions as priors for the network predictive posterior densities, in the set of competing networks. A comparison of the performance of the proposed method with those of usual selection procedures such as classic cross-validation and information theoretic criteria, is performed first on the data of a well-known case study and then on the data of a simulated case study.

In order to select the best predictive neural-network architecture in a set of several candidate networks, we propose a general Bayesian nonlinear regression model comparison procedure, based on the maximization of an expected utility criterion. This criterion selects the model under which the training set achieves the highest level of internal consistency, through the predictive probability distribution of each model. The density of this distribution is computed as the model posterior predictive density and is asymptotically approximated from the assumed Gaussian likelihood of the data set and the related conjugate prior density of the parameters. The use of such a conjugate prior allows the analytic calculation of the parameter posterior and predictive posterior densities, in an empirical-Bayes-like approach. This Bayesian selection procedure allows us to compare general nonlinear regression models and in particular feedforward neural networks, in addition to embedded models as usual with asymptotic comparison tests.