Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. We found that when only a small number of physically motivated models were considered and one was clearly best, the method quickly converged to the best model, and the cost of model uncertainty was small; indeed DMA performed slightly better than the best physical model. When model uncertainty and the number of models considered were large, our method ensured that the penalty for model uncertainty was small. At the beginning of the process, when control is most difficult, we found that DMA over a large model space led to better predictions than the single best performing physically motivated model. AbstractWe consider the problem of online prediction when it is uncertain what the best prediction model to use is. We develop a method called Dynamic Model Averaging (DMA) in which a state space model for the parameters of each model is combined with a Markov chain model for the correct model. This allows the "correct" model to vary over time. The state space and Markov chain models are both specified in terms of forgetting, leading to a highly parsimonious representation. The method is applied to the problem of predicting the output strip thickness for a cold rolling mill, where the output is measured with a time delay. We found that when only a small number of physically motivated models were considered and one was clearly best, the method quickly converged to the best model, and the cost of model uncertainty was small; indeed DMA performed slightly better than the best physical model. When model uncertainty and the number of models considered were large, our method ensured that the penalty for model uncertainty was small. At the beginning of the process, when control is most difficult, we found that DMA over a large model space led to better predictions than the single best performing physically motivated model.

Any cooperation in multiple-participant decision making (DM) relies on an exchange of individual knowledge pieces and aims. A general methodology of their rational exploitation without calling for an objective mediator is still missing. Desired methodology is proposed for an important particular case, when a participant, performing Bayesian parameter estimation, is offered a model relating the observable data to their past history.The designed solution is based on the so-called fully probabilistic design (FPD) of DM strategies. The result reduces to an 'ordinary' Bayesian estimation if the offered model is the sample probability density function (pdf), i.e. if it provides additional observations.

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The complexity of the problems to be addressed in an e-democracy framework and the variety of involved stakeholders, with different backgrounds, views and access to information sources, lead to consider the case in which enegotiation should be performed among subjects who have partial, sometimes incompatible, information and can hardly be gathered to discuss issues altogether, under the supervision of a facilitator. We propose a statistical method which addresses the issue of partial and incompatible information, merging it and then using it to get a final decision, possibly in an automatic way, through the processes of e-negotiation and e-arbitration.

Non-symmetric Kullback-Leibler divergence (KLD) measures proximity of probability density functions (pdfs). Bernardo (Ann. Stat. 1979; 7(3):686-690) had shown its unique role in approximation of pdfs. The order of the KLD arguments is also implied by his methodological result. Functional approximation of estimation and stabilized forgetting, serving for tracking of slowly varying parameters, use the reversed order. This choice has the pragmatic motivation: recursive estimator often approximates the parametric model by a member of exponential family (EF) as it maps prior pdfs from the set of conjugate pdfs (CEF) back to the CEF. Approximations based on the KLD with the reversed order of arguments preserves this property. In the paper, the approximation performed within the CEF but with the proper order of arguments of the KLD is advocated. It is applied to the parameter tracking and performance improvements are demonstrated. This practical result is of importance for adaptive systems and opens a way for improving the functional approximation.