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36
Commoninput models for multiple neural spiketrain data
 Data, Network: Comput. Neural Syst
, 2006
"... Recent developments in multielectrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenges in computational neuroscience today. In this work, we develop a multivariate pointprocess model in which th ..."
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Cited by 50 (20 self)
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Recent developments in multielectrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenges in computational neuroscience today. In this work, we develop a multivariate pointprocess model in which the observed activity of a network of neurons depends on three terms: 1) the experimentallycontrolled stimulus; 2) the spiking history of the observed neurons; and 3) a latent noise source that corresponds, for example, to “common input ” from an unobserved population of neurons that is presynaptic to two or more cells in the observed population. We develop an expectationmaximization algorithm for fitting the model parameters; here the expectation step is based on a continuoustime implementation of the extended Kalman smoother, and the maximization step involves two concave maximization problems which may be solved in parallel. The techniques developed allow us to solve a variety of inference problems in a straightforward, computationally efficient fashion; for example, we may use the model to predict network activity given an arbitrary stimulus, infer a neuron’s firing rate given the stimulus and the activity of the other observed neurons, and perform optimal stimulus decoding and prediction. We present several detailed simulation studies which explore the strengths and limitations of our approach. 1
Stochastic Risk Premiums, Stochastic Skewness
 in Currency Options, and Stochastic Discount Factors in International Economies,”
, 2008
"... ..."
Boredom: A Review
 Human Factors
, 1981
"... Edward Jenner, who discovered that it is possible to vaccinate against Small Pox using material from Cow Pox, is rightly the man who started the science of immunology. However, over the passage of time many of the details surrounding his astounding discovery have been lost or forgotten. Also, the en ..."
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Cited by 23 (0 self)
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Edward Jenner, who discovered that it is possible to vaccinate against Small Pox using material from Cow Pox, is rightly the man who started the science of immunology. However, over the passage of time many of the details surrounding his astounding discovery have been lost or forgotten. Also, the environment within which Jenner worked as a physician in the countryside, and the state of the art of medicine and society are difficult to appreciate today. It is important to recall that people were still being bled at the time, to relieve the presence of evil humors. Accordingly, this review details Jenner’s discovery and attempts to place it in historical context. Also, the vaccine that Jenner used, which decreased the prevalence of Small Pox worldwide in his own time, and later was used to eradicate Small Pox altogether, is discussed in light of recent data.
Sigmapoint Kalman filtering for integrated GPS and inertial navigation,”
 in AIAA Guidance, Navigation and Contol Conference,
, 2005
"... A sigmapoint Kalman filter is derived for integrating GPS measurements with inertial measurements from gyros and accelerometers to determine both the position and the attitude of a moving vehicle. Sigmapoint filters use a carefully selected set of sample points to more accurately map the probabil ..."
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Cited by 21 (1 self)
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A sigmapoint Kalman filter is derived for integrating GPS measurements with inertial measurements from gyros and accelerometers to determine both the position and the attitude of a moving vehicle. Sigmapoint filters use a carefully selected set of sample points to more accurately map the probability distribution than the linearization of the standard extended Kalman filter, leading to faster convergence from inaccurate initial conditions in position/attitude estimation problems. The filter formulation is based on standard inertial navigation equations. The global attitude parameterization is given by a quaternion, while a generalized threedimensional attitude representation is used to define the local attitude error. A multiplicative quaternionerror approach is used to guarantee that quaternion normalization is maintained in the filter. Simulation and experimental results are shown to compare the performance of the sigmapoint filter with a standard extended Kalman filter approach.
Modeling financial security returns using lévy processes
 In: Birge, J., Linetsky, V. (Eds.), Handbook of Financial Engineering. Elsevier
, 2007
"... Lévy processes can capture the behaviors of return innovations on a full range of financial securities. Applying stochastic time changes to the Lévy processes randomizes the clock on which the processes run, thus generating stochastic volatilities and stochastic higher return moments. Therefore, w ..."
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Cited by 8 (0 self)
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Lévy processes can capture the behaviors of return innovations on a full range of financial securities. Applying stochastic time changes to the Lévy processes randomizes the clock on which the processes run, thus generating stochastic volatilities and stochastic higher return moments. Therefore, with appropriate choices of Lévy processes and stochastic time changes, we can capture the return dynamics of virtually all financial securities. Furthermore, in contrast to the hidden factor approach, we can readily assign explicit economic meanings to each Lévy process component and its associated time change in the return dynamics. The explicit economic mapping not only facilitates the interpretation of existing models and their structural parameters, but also adds economic intuition and direction for designing new models capturing new economic behaviors. Finally, under this framework, the analytical tractability of a model for derivative pricing and model estimation originates from the tractability of the Lévy process specification and the tractability of the activity rate dynamics underlying the time change. Thus, we can design tractable models using any combination of tractable Lévy specifications and tractable activity rate dynamics. In this regard, we can incorporate and therefore encompass all tractable models in literature into our framework as building blocks. Examples include Brownian motions, compound
Optimal Filtering with Kalman Filters and Smoothers a Manual for the Matlab toolbox EKF/UKF Version 1.3
"... In this paper we present a documentation for an optimal filtering toolbox for the mathematical software package Matlab. The toolbox features many filtering methods for discretetime state space models, including the wellknown linear Kalman filter and several nonlinear extensions to it. These nonl ..."
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Cited by 7 (0 self)
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In this paper we present a documentation for an optimal filtering toolbox for the mathematical software package Matlab. The toolbox features many filtering methods for discretetime state space models, including the wellknown linear Kalman filter and several nonlinear extensions to it. These nonlinear methods are the extended Kalman filter, the unscented Kalman filter, the GaussHermite Kalman filter and the thirdorder symmetric cubature Kalman filter. Algorithms for multiple model systems are provided in the form of an Interacting Multiple Model (IMM) filter and it’s nonlinear extensions, which are based on banks of extended and unscented Kalman filters. Also included in the toolbox are the RauchTungStriebel and twofilter smoother counterparts for the filters, which can be used to smooth the previous state estimates, after obtaining new measurements. The usage
An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models
"... In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit crosssectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool ..."
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Cited by 5 (2 self)
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In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit crosssectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log–likelihood of nonlinear state–space models and (2) to fit timevarying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predatorprey model with time series and multiple–subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction. Dynamical systems are systems that change over time such that their current states are somehow dependent upon their previous states (Alligood, Sauer, & Yorke, 1996). Change concepts described in most dynamical systems models are by no means novel to psychologists. From the rather controversial difference scores (e.g., Bereiter, 1963; CronWe thank Jack McArdle, Ellen Bass, Howard Epstein, Fumiaki Hamagami and a few anonymous reviewers for their valuable comments on earlier versions of this article. This study was supported by a National
Cubature Integration Methods in NonLinear Kalman Filtering and Smoothing
, 2010
"... Optimal estimation problems arise in various different settings where indirect noisy observations are used to determine the underlying state of a timevarying system. For systems with nonlinear dynamics there exist various methods that extend linear filtering and smoothing methods to handle nonlin ..."
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Cited by 2 (2 self)
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Optimal estimation problems arise in various different settings where indirect noisy observations are used to determine the underlying state of a timevarying system. For systems with nonlinear dynamics there exist various methods that extend linear filtering and smoothing methods to handle nonlinearities. In this thesis the nonlinear optimal estimation framework is presented with the help of an assumed density approach. The Gaussian integrals that arise in this setting are solved using two different cubature integration methods. Cubature integration extends the weighted sum approach from univariate quadrature methods to multidimensional cubature methods. In this thesis the focus is put on two methods that use deterministically chosen sigma points to form the desired approximation. The Gauss–Hermite rule uses a simple product rule method to fill the multidimensional space with cubature points, whereas the spherical–radial rule uses invariant theory to diminish the number of points by utilizing symmetries. The