Bayesian Estimation Via Sequential Monte Carlo Sampling-Constrained Dynamic Systems

Nonlinear and non-Gaussian processes with constraints are commonly encountered in dynamic estimation problems. Methods for solving such problems either ignore the constraints or rely on crude approximations of the model or probability distributions. Such approximations may reduce the accuracy of the estimates since they often fail to capture the variety of probability distributions encountered in constrained linear and nonlinear dynamic systems. This article describes a practical approach that overcomes these shortcomings via a novel extension of sequential Monte Carlo (SMC) sampling or particle filtering. Inequality constraints are imposed by accept/reject steps in the algorithm. The proposed approach provides samples representing the posterior distribution at each time point, and is shown to satisfy the same theoretical properties as unconstrained SMC. Illustrative examples show that results of the proposed approach are at least as accurate as moving horizon estimation, but computationally more efficient and in addition, the approach indicates the uncertainty associated with these estimates

Independent Component Analysis of the Effect of L-dopa on fMRI of Language Processing

L-dopa, which is a precursor for dopamine, acts to amplify strong signals, and dampen weak signals as suggested by previous studies. The effect of L-dopa has been demonstrated in language studies, suggesting restriction of the semantic network. In this study, we aimed to examine the effect of L-dopa on language processing with fMRI using Independent Component Analysis (ICA). Two types of language tasks (phonological and semantic categorization tasks) were tested under two drug conditions (placebo and L-dopa) in 16 healthy subjects. Probabilistic ICA (PICA), part of FSL, was implemented to generate Independent Components (IC) for each subject for the four conditions and the ICs were classified into task-relevant source groups by a correlation threshold criterion. Our key findings include: (i) The highly task-relevant brain regions including the Left Inferior Frontal Gyrus (LIFG), Left Fusiform Gyrus (LFUS), Left Parietal lobe (LPAR) and Superior Temporal Gyrus (STG) were activated with both L-dopa and placebo for both tasks, and (ii) as compared to placebo, L-dopa was associated with increased activity in posterior regions, including the superior temporal area (BA 22), and decreased activity in the thalamus (pulvinar) and inferior frontal gyrus (BA 11/47) for both tasks. These results raise the possibility that L-dopa may exert an indirect effect on posterior regions mediated by the thalamus (pulvinar)

Anomalies in the Foundations of Ridge Regression: Some Clarifications

Several anomalies in the foundations of ridge regression from the perspective of constrained least-square (LS) problems were pointed out in Jensen & Ramirez. Some of these so-called anomalies, attributed to the non-monotonic behaviour of the norm of unconstrained ridge estimators and the consequent lack of sufficiency of Lagrange's principle, are shown to be incorrect. It is noted in this paper that, for a fixed  Y, norms of unconstrained ridge estimators corresponding to the given basis are indeed strictly monotone. Furthermore, the conditions for sufficiency of Lagrange's principle are valid for a suitable range of the constraint parameter. The discrepancy arose in the context of one data set due to confusion between estimates of the parameter vector,  β , corresponding to different parametrization (choice of bases) and/or constraint norms. In order to avoid such confusion, it is suggested that the parameter  β  correspondi ng to each basis be labelled appropriately. Copyright (c) 2010 The Authors. Journal compilation (c) 2010 International Statistical Institute.

Bayesian Estimation by Sequential Monte Carlo Sampling: Application to High-Dimensional Nonlinear Dynamic Systems

Modern industrial enterprises have invested significant resources for collecting and distributing data, with the expectation that it will enhance profitability via better decision making. Due to the complexity of these problems, existing approaches tend to make convenient, but invalid assumptions so that tractable solution may be found. For example, for estimation in nonlinear dynamic systems, extended Kalman filtering (EKF) relies on Gaussian approximation and local linearization to find a closed-form solution. Moving horizon based least-squares estimation (MHE) also relies on Gaussian approximation, but the use of nonlinear models and constraints eliminates most of the computational benefits of this approximation, but can provide more accurate estimates than EKF. Unfortunately, in most practical nonlinear dynamic systems, the posterior distributions are often far from Gaussian, and continually change their shape

Identifying Homogeneous Periods in Bus Route Origin-Destination Passenger Flow Patterns from Automatic Passenger Counter Data

Bus passenger origin-destination (O-D) flow matrices portray information on travel patterns that can be used for route planning, design, and operations functions. Because travel patterns are known to vary throughout the day, O-D flow matrices can be expected to vary throughout the day as well. A method identifies time-of-day periods of homogeneous normalized bus route O-D passenger flow matrices in which a normalized matrix depicts the probabilities that a random passenger in the homogeneous period will travel from various origin stops to various destination stops on the route. The method uses bus trip automatic passenger counter data to estimate trip-level O-D matrices, aggregates the trip-level O-D matrices into elemental matrices for relatively short time periods, and then considers these elemental matrices as inputs to a traditional clustering procedure that is modified to ensure that a cluster indicating a period of homogeneous normalized O-D flow spans a continuous time period during the day. The homogeneous O-D flow period method is applied to empirical automatic passenger counter data collected on a bus route for which temporal travel patterns are understood. The time periods identified correspond well to the a priori understanding of travel patterns. A parallel method that uses passenger volume, rather than estimated normalized O-D flow matrices, is applied to the same data. The periods identified by this volume-based approach are not responsive to the changes in the normalized O-D flow patterns determined by the homogeneous O-D flow period identification method