Numerical simulations illustrate the ability of this algorithm to detect and track multiple targets in a highly cluttered environment. Keywords : Bayesian filtering Markov chain Monte Carlo methods multitarget tracking nonlinear nonGaussian state-space model particle methods sequential Monte Carlo methods signal processing. Document type : Conference papers.
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Quadratic hill-climbing. Cited By Counts. Online Attention. So, MKP. Statistics and computing , v. When the state variable is non-Gaussian, particle filtering or smoothing may be used to numerically approximate the posterior distribution; when the parameter variable is non-Gaussian, Gaussian approximation, Gibbs sampling or Markov chain Monte Carlo MCMC approaches may be employed.
The common goal of these inference methods is to estimate the joint posterior of the state and the parameters using Bayes's rule. The denominator of equation 16 is a normalizing constant known as the partition function.
In general, Monte Carlo-based Bayesian inference or learning is powerful yet computationally expensive Doucet, de Frietas, and Gordon, ; Gilks, Richardson and Spiegelhalter, A trade-off between tractable computational complexity and good performance is to exploit various approximate Bayesian inference methods, such as expectation propagation Minka, , mean-field approximation Opper and Saad, and variational approximation Jordan et al.
Numerous applications of SSM to dynamic analyses of neuroscience data can be found in the literature Paninski et al.
Several important and representative applications are highlighted here. Truccolo et al. An important topic in state-space modeling is model selection, or specifically to select the discrete or continuous-valued state dimensionality. Moreover, inference of a large-scale SSM for neuroscience data remains another important research topic. Exploiting the structure of the system, such as the sparsity, smoothness and convexity, may allow for employing efficient state-of-the-art optimization routines and imposing domain-dependent priors for regularization Paninski et al.
Finally, developing consistent goodness-of-fit assessment for neuroscience data would help to validate and compare different statistical models Brown et al. Machine Learning , 50 1 : Neural Computation , Beal M, Ghahramani Z. Bayesian Analysis , 1 4 : Bertsekas D.
Boston, MA: Athena Scientific. Journal of Neuroscience , Proceedings of the National Academy of Sciences , In: Feng J. Computational Neuroscience : A Comprehensive Approach pp. Journal of Neurophysiology , Calabrese A, Paninski L.
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Journal of Neuroscience Methods , 1 : Neural Computation , 21 7 : In Oweiss K Ed. Academic Press. Journal of Computational Neuroscience , Journal of Neurophysiology , 99, Journal of the Royal Statistical Society , B NeuroImage , 23 2 : Ghahramani Z.
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NeuroImage , 53 1 : Journal of Neuroscience Methods , 1 Machine Learning , Kalman RE. Kobayashi R, Shinomoto S.
Physical Review E 75, Kulkarni J, Paninski L.