67,814 research outputs found
Spatial Filtering Pipeline Evaluation of Cortically Coupled Computer Vision System for Rapid Serial Visual Presentation
Rapid Serial Visual Presentation (RSVP) is a paradigm that supports the
application of cortically coupled computer vision to rapid image search. In
RSVP, images are presented to participants in a rapid serial sequence which can
evoke Event-related Potentials (ERPs) detectable in their Electroencephalogram
(EEG). The contemporary approach to this problem involves supervised spatial
filtering techniques which are applied for the purposes of enhancing the
discriminative information in the EEG data. In this paper we make two primary
contributions to that field: 1) We propose a novel spatial filtering method
which we call the Multiple Time Window LDA Beamformer (MTWLB) method; 2) we
provide a comprehensive comparison of nine spatial filtering pipelines using
three spatial filtering schemes namely, MTWLB, xDAWN, Common Spatial Pattern
(CSP) and three linear classification methods Linear Discriminant Analysis
(LDA), Bayesian Linear Regression (BLR) and Logistic Regression (LR). Three
pipelines without spatial filtering are used as baseline comparison. The Area
Under Curve (AUC) is used as an evaluation metric in this paper. The results
reveal that MTWLB and xDAWN spatial filtering techniques enhance the
classification performance of the pipeline but CSP does not. The results also
support the conclusion that LR can be effective for RSVP based BCI if
discriminative features are available
Distributed Bayesian Filtering using Logarithmic Opinion Pool for Dynamic Sensor Networks
The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented
for the problem of tracking a target dynamic model using a time-varying network
of heterogeneous sensing agents. In the DBF algorithm, the sensing agents
combine their normalized likelihood functions in a distributed manner using the
logarithmic opinion pool and the dynamic average consensus algorithm. We show
that each agent's estimated likelihood function globally exponentially
converges to an error ball centered on the joint likelihood function of the
centralized multi-sensor Bayesian filtering algorithm. We rigorously
characterize the convergence, stability, and robustness properties of the DBF
algorithm. Moreover, we provide an explicit bound on the time step size of the
DBF algorithm that depends on the time-scale of the target dynamics, the
desired convergence error bound, and the modeling and communication error
bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into
a modified form of the Kalman information filter. The performance and robust
properties of the DBF algorithm are validated using numerical simulations
Utility indifference pricing with market incompleteness
Utility indifference pricing and hedging theory is presented, showing
how it leads to linear or to non-linear pricing rules for contingent
claims. Convex duality is first used to derive probabilistic
representations for exponential utility-based prices, in a general
setting with locally bounded semi-martingale price processes. The
indifference price for a finite number of claims gives a non-linear
pricing rule, which reduces to a linear pricing rule as the number of
claims tends to zero, resulting in the so-called marginal
utility-based price of the claim. Applications to basis risk models
with lognormal price processes, under full and partial information
scenarios are then worked out in detail. In the full information case,
a claim on a non-traded asset is priced and hedged using a correlated
traded asset. The resulting hedge requires knowledge of the drift
parameters of the asset price processes, which are very difficult to
estimate with any precision. This leads naturally to a further
application, a partial information problem, with the drift parameters
assumed to be random variables whose values are revealed to the hedger
in a Bayesian fashion via a filtering algorithm. The indifference
price is given by the solution to a non-linear PDE, reducing to a
linear PDE for the marginal price when the number of claims becomes
infinitesimally small
Inverse Modeling for MEG/EEG data
We provide an overview of the state-of-the-art for mathematical methods that
are used to reconstruct brain activity from neurophysiological data. After a
brief introduction on the mathematics of the forward problem, we discuss
standard and recently proposed regularization methods, as well as Monte Carlo
techniques for Bayesian inference. We classify the inverse methods based on the
underlying source model, and discuss advantages and disadvantages. Finally we
describe an application to the pre-surgical evaluation of epileptic patients.Comment: 15 pages, 1 figur
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