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Model selection strategies have been routinely employed to determine a model for data analysis in statistic, and further study and inference then often proceed as though the selected model were the true model that were known a priori. This practice does not account for the uncertainty introduced by the selection process and the fact that the selected model can possibly be a wrong one. Model averaging approaches try to remedy this issue by combining estimators for a set of candidate models. Specifically, instead of deciding which model is the 'right' one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using certain data adaptive weights. In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It greatly broadens the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account. We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.

This paper proposes a dynamic system, with an associated fusion learning inference procedure, to perform real-time detection and localization of nuclear sources using a network of mobile sensors. This is motivated by the need for a reliable detection system in order to prevent nuclear attacks in major cities such as New York City. The approach advocated here installs a large number of relatively inexpensive (and perhaps relatively less accurate) nuclear source detection sensors and GPS devices in taxis and police vehicles moving in the city. Sensor readings and GPS information are sent to a control center at a high frequency, where the information is immediately processed and fused with the earlier signals. We develop a real-time detection and localization method aimed at detecting the presence of a nuclear source and estimating its location and power. We adopt a Bayesian framework to perform the fusion learning and use a sequential Monte Carlo algorithm to estimate the parameters of the model and to perform real-time localization. A simulation study is provided to assess the performance of the method for both stationary and moving sources. The results provide guidance and recommendations for an actual implementation of such a surveillance system.Appl. Stochastic Models Bus. Ind. 2018, 34 4-19 GRELAUD ET AL. t ), of all the sensors in the system and the binary signals the sensors send to the control center t = (d (1) t , · · · , d (n t ) t ). Here, n t is the number of active sensors. The locations, t , are assumed to be accurate, but the signals received by the control center could possibly be false.This model assumes the presence of one source. It is compared with the baseline model, where no source is present, for the purpose of detecting the presence of a source. Details of the comparison are presented in Section 3.2. The extension to multiple source detection is discussed in Section 6.State-space models have been widely used in many applications, including source tracking [29,30,[36][37][38][39][40][41][42][43]. However, our approach is different from standard source tracking problems, mainly because in our case, both negative and positive binary signals are observed and used. The use of state-space formation allows the data collected at time t to be used for the estimation of the location of the source x t with the information observed in the past, through an updating of the previous estimation of x t−1 , instead of performing an independent analysis at each time point. A source's motion possesses 6

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