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This paper describes a continuous-time state-process, discretetime observation, Interacting Multiple Model (IMM) tracking algorithm, and its applications to financial market modeling and asset allocation. The system state is modeled as a continuous-time, affine-Gaussian stochastic dynamical process driven by a white process noise, as well as by structural changes modeled by a finitestate, continuous-time, Markov process. The system generally assumes multiple models with different state space dimensions and an affine-Gaussian state jump whenever a model transition occurs. The underlying problem is a standard filtering problem for estimating the system state based on a sequence of discrete-time, linear- Gaussian observations of partial system states. To demonstrate the new method, we apply the IMM algorithm to financial market modeling for dynamic asset allocation. The resulting performance shows the potential applicability of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of distributed fusion when the conditional independence assumptions on sensor measurements or local estimates are not met. A new data fusion algorithm called Copula fusion is presented. The proposed method is grounded on Copula statistical modeling and Bayesian analysis. The primary advantage of the Copula-based methodology is that it could reveal the unknown correlation that allows one to build joint probability distributions with potentially arbitrary underlying marginals and a desired intermodal dependence. The proposed fusion algorithm requires no a priori knowledge of communications patterns or network connectivity. The simulation results show that the Copula fusion brings a consistent estimate for a wide range of process noises. [ABSTRACT FROM AUTHOR]

The traditional message passing algorithm was originally developed by Pearl in the 1980s for computing exact inference solutions for discrete polytree Bayesian networks. When a loop is present in the network, propagating messages are not exact, but the loopy algorithm usually converges and provides good approximate solutions. However, in general hybrid Bayesian networks, the message representation and manipulation for arbitrary continuous variable and message propagation between different types of variables are still open problems. The novelty of the work presented here is to propose a framework to compute, propagate, and integrate messages for hybrid models. First, we combine unscented transformation and Pearl's message passing algorithm to deal with the arbitrary functional relationships between continuous variables in the network. For the general hybrid model, we partition the network into separate network segments by introducing the concept of interface node. We then apply different algorithms for each subnetwork. Finally we integrate the information through the channel of interface nodes and then estimate the posterior distributions for all hidden variables. The numerical experiments show that the algorithm works well for nonlinear hybrid BNs. [ABSTRACT FROM AUTHOR]

A Bayesian network (BN) is a compact representation for probabilistic models and inference. They have been used successfully for many military and civilian applications. It is well known that, in general, the inference algorithms to compute the exact a posterior probability of a target node given observed evidence are either computationally infeasible for dense networks or impossible for general hybrid networks. In those cases, one either computes the approximate results using stochastic simulation methods or approximates the model using discretization or a Gaussian mixture model before applying an exact inference algorithm. This paper combines the concept of simulation and model approximation to propose an efficient algorithm for those cases. The main contribution here is a unified treatment of arbitrary (nonlinear non-Gaussian) hybrid (discrete and continuous) BN inference having both computation and accuracy scalability. The key idea is to precompile the high-dimensional hybrid distribution using a hypercube representation and apply it for both static and dynamic BN inference. Since the inference process essentially becomes a combination of table look-up and some simple operations, the method is shown to be extremely efficient. It can also be scaled to achieve any desirable accuracy given sufficient preprocessing time and memory for the cases where exact inference is not possible. [ABSTRACT FROM AUTHOR]

This paper generalises the concept of grey relational analysis to develop a technique, called grey relational pattern analysis, for analysing the similarity between given patterns. Based on this technique, a clustering algorithm is proposed for finding cluster centres of a given data set. This approach can be categorised as an unsupervised clustering algorithm because it does not need predetermination of appropriate cluster centres in the initialisation. The problem of determining the optimal number of clusters and optimal locations of cluster centres is also considered. Finally, the approach is used to solve several data clustering problems as examples. In each example, the performance of the proposed algorithm is compared with other well-known algorithms such as the fuzzy c-means method and the hard c-means method. Simulation results demonstrate the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a quantitative performance evaluation method for the maximum a posteriori (MAP) state estimate fusion algorithm. Under ideal conditions where data association is assumed to be perfect, it has been shown that the MAP or best linear unbiased estimate (BLUE) fusion formula provides the best linear minimum mean squared estimate (LMMSE) given local estimates under the linear Gaussian assumption for a static system. However, for a dynamic system where fusion is recursively performed by the fusion center on local estimates generated from local measurements, it is not obvious how the MAP algorithm will perform. In the past, several performance evaluation methods have been proposed for various fusion algorithms, including simple convex combination, cross-covariance combination, information matrix, and MAP fusion. However, not much has been done to quantify the steady state behavior of these fusion methods for a dynamic system. The goal of this work is to present analytical fusion performance results for MAP state estimate fusion without extensive Monte Carlo simulations, using an approach developed for steady state performance evaluation for track fusion. Two different communication strategies are considered: fusion with and without feedback to the sensors. Analytic curves for the steady state performance of the fusion algorithm for various communication patterns are presented under different operating conditions. [ABSTRACT FROM AUTHOR]

Presents information on a study which described a linear predictive algorithm for bandwidth conservation. System concept; Analysis of a linear predictive algorithm based on linear regression; Numerical results; Conclusions.