Simo Särkkä
Academy Research Fellow, Dr.Tech.
(at BECS / Aalto University)
Docent, Adjunct Professor (both at
TUT and LUT)
Member of Bayesian Statistical Methods group
(led by Aki Vehtari).
Postal Address:
P.O.Box 12200
FIN00076 AALTO
FINLAND
Street Address:
Room F305, FTalo, 3rd Floor
Rakentajanaukio 2
Espoo, Finland
Contact:
Mobile: +358 50 512 4393
Email: simo.sarkka@aalto.fi
Skype: simosarkka
Web: becs.aalto.fi/~ssarkka
Twitter: @simosarkka
Current doctoral (PhD) students
Arno Solin (Aalto University)
Juha Sarmavuori (Nokia Ltd.)
Juho Kokkala (Aalto University)
Former doctoral students (Drs. now)
Isambi S. Mbalawata (University of Dar Es Salaam, Tanzania)Jouni Hartikainen (Rocsole Ltd.)
Biography
Current/previous positions:
 2013 Academy Research Fellow, Aalto University
 2013 Technical consultant/advisor of IndoorAtlas Ltd.
 2012 Docent (Adj.Prof.), Lappeenranta University of Technology
 2011 Docent (Adj.Prof.), Tampere University of Technology
 2007 Independent consultant
 2014 (May) Visiting Scholar, Chalmers University of Technology
 2013 (OctDec) Visiting Professor, University of Oxford
 2011 (AprDec) Visiting Scholar, University of Cambridge
 20102013 Senior Researcher, Aalto University
 20072009 Staff Scientist, Nalco / NalcoMobotec
 20022007 R&D Manager, Indagon Ltd.
 20002002 Research Engineer, Nokia Ltd.
Simo Särkkä received his Master of Science (Tech.) degree (with distinction) in engineering physics and mathematics, and Doctor of Science (Tech.) degree (with distinction) in electrical and communications engineering from Helsinki University of Technology, Espoo, Finland, in 2000 and 2006, respectively. From 2000 to 2010 he worked with Nokia Ltd., Indagon Ltd., and Nalco Company in various industrial research projects related to telecommunications, positioning systems, and industrial process control. From 2010 to 2013 he worked as a Senior Researcher with the Department of Biomedical Engineering and Computational Science (BECS) at Aalto University, Finland.
Currently, Dr. Särkkä is an Academy Research Fellow with Aalto University, Technical Advisor and Consultant of IndoorAtlas Ltd., and an Adjunct Professor with Tampere University of Technology and Lappeenranta University of Technology. In 2013 he was a Visiting Professor with the Department of Statistics of Oxford University and in 2011 he was a Visiting Scholar with the Department of Engineering at the University of Cambridge, UK. His research interests are in multisensor data processing systems with applications in location sensing, machine learning, inverse problems, and brain imaging. He has authored or coauthored 50 peerreviewed scientific articles and has 3 granted patents. His first book "Bayesian Filtering and Smoothing" was recently published via the Cambridge University Press. He is a Senior Member of IEEE.
Research Activities
Applications
 Signal processing and state estimation in brain imaging (fMRI/MEG/EEG/DOT)
 Spatiotemporal modeling in machine learning, inverse problems, and Kriging.
 Location sensing, target tracking, audio signal processing.
 Applications in medicine, biology, RF/RFID systems, telematics, optical/video tracking, inertial navigation, robotics, audio systems, etc.
Bayesian Inference Methods for Stochastic Dynamic Systems
 NonLinear Kalman/Bayesian filtering and smoothing
 Continuoustime stochastic models and stochastic differential equations (SDEs)
 Particle filtering and sequential Monte Carlo methods
Bayesian Inference Methods for Spatial and SpatioTemporal Systems
 Statespace, sparse, and reduced rank methods in Gaussian process regression.
 Stochastic partial/pseudo differential equations (SPDE).
 Infinitedimensional/distributedparameter Kalman filtering and smoothing.
Theoretical Analysis and Other Methodology
 Convergence and stability analysis of approximate Bayesian filters and smoothers
 Theoretical analysis of Gaussian process regressors
 Advanced Markov chain Monte Carlo methods
Publications
My Google Scholar profile: http://scholar.google.com/citations?user=QVhmc9cAAAAJ
See also Department's publication list.
The PDF preprints below are draft versions of the articles and they are here to give people an opportunity to check the relevance of the articles before purchasing the final articles from the publisher. Please send me an email if you want the latest preprints of the submitted articles.
Books

Simo Särkkä (2013). Bayesian Filtering and Smoothing. Cambridge University Press. Available from Cambridge University Press at http://www.cambridge.org/sarkka, from this CUPlink, or from, e.g., Amazon UK or Amazon USA.
Although the more convenient (and quite affordable) printed version of the book can be purchased from the above sources, with permission from the publisher, I am providing a PDF version of the book here:
 Full book in PDF format (4.3M)
This PDF version is made available for personal use. The copyright in all material rests with the author (Simo Särkkä). Commercial reproduction is prohibited, except as authorised by the author and publisher.
Journals
 Sean Anderson, Timothy D. Barfoot, Chi Hay Tong, and Simo Särkkä. Batch Nonlinear ContinuousTime Trajectory Estimation as Exactly Sparse Gaussian Process Regression. Conditionally accepted for publication in Autonomous Robots. (axXiv)
 Juho Kokkala and Simo Särkkä. Combining Particle MCMC with RaoBlackwellized Monte Carlo Data Association for Parameter Estimation in Multiple Target Tracking. Accepted for publication in Digital Signal Processing. (arXiv)
 J. AlaLuhtala, S. Särkkä, and R. Piché (2015). Gaussian filtering and variational approximations for Bayesian smoothing in continuousdiscrete stochastic dynamic systems. Signal Processing, Volume 111, Pages 124136. (DOI, arXiv)
 S. Särkkä, J. Hartikainen, I. S. Mbalawata, H. Haario (2015). Posterior Inference on Parameters of Stochastic Differential Equations via NonLinear Gaussian Filtering and Adaptive MCMC. Statistics and Computing, Volume 25, Issue 2, Pages 427437. (DOI, Preprint)
 I. S. Mbalawata, S. Särkkä, M. Vihola, H. Haario (2015). Adaptive Metropolis Algorithm Using Variational Bayesian Adaptive Kalman Filter. In Computational Statistics and Data Analysis, Volume 83, Pages 101115. (arXiv, DOI)
 S.M.J. Lyons, S. Särkkä, and A.J. Storkey (2014). Series Expansion Approximations of Brownian Motion for NonLinear Kalman Filtering of Diffusion Processes. IEEE Transactions on Signal Processing, Volume 62, Issue 6, Pages 15141524. (DOI, arXiv)
 A. Solin and S. Särkkä (2013). InfiniteDimensional Bayesian Filtering for Detection of QuasiPeriodic Phenomena in SpatioTemporal Data. Physical Review E, Volume 88, Issue 5, 052909. (arXiv, DOI)
 S. Särkkä, A. Solin, and J. Hartikainen (2013). SpatioTemporal Learning via InfiniteDimensional Bayesian Filtering and Smoothing. IEEE Signal Processing Magazine, Volume 30, Issue 4, Pages 5161. (Preprint, DOI)
 S. Särkkä and J. Sarmavuori (2013). Gaussian Filtering and Smoothing for ContinuousDiscrete Dynamic Systems. Signal Processing, Volume 93. Issue 2, Pages 500510. (Preprint, DOI, Matlab toolbox)
 I. S. Mbalawata, S. Särkkä, and H. Haario (2013). Parameter Estimation in Stochastic Differential Equations with Markov Chain Monte Carlo and NonLinear Kalman Filtering. Computational Statistics, Volume 28, Issue 3, Pages 11951223 (DOI)
 S. Särkkä, A. Solin, A. Nummenmaa, A. Vehtari, T. Auranen, S. Vanni, F.H. Lin (2012). Dynamic Retrospective Filtering of Physiological Noise in BOLD fMRI: DRIFTER. NeuroImage, Volume 60, Issue 2, Pages 15171527. (DOI, Preprint, Matlab toolbox)
 J. Sarmavuori and S. Särkkä (2012). FourierHermite Kalman Filter. IEEE Transactions on Automatic Control, Volume 57, Issue 6, Pages 15111515. (DOI, Preprint)
 S. Särkkä, V. Viikari, M. Huusko, and K. Jaakkola (2012). PhaseBased UHF RFID Tracking with NonLinear Kalman Filtering and Smoothing. IEEE Sensors Journal, Volume 12, Issue 5, Pages 904910. (DOI, Preprint)
 S. Särkkä and A. Huovilainen (2011). Accurate Discretization of Analog Audio Filters with Application to Parametric Equalizer Design. IEEE Transactions on Audio, Speech, and Language Processing, Volume 19, Issue 8, Pages 24862493. (DOI , Preprint, Matlab code, C++ code, VST Effect for OS X)
 P. Hiltunen, S. Särkkä, I. Nissilä, A. Lajunen and J. Lampinen (2011). State space regularization in the nonstationary inverse problem for diffuse optical tomography. Inverse Problems, Volume 27, Number 2. (DOI)
 S. Särkkä and J. Hartikainen (2010). On Gaussian Optimal Smoothing of NonLinear State Space Models. IEEE Transactions on Automatic Control, Volume 55, Issue 8, Pages 19381941. (DOI, Preprint, Matlab toolbox). See also errata DOI or Preprint.
 S. Särkkä (2010). ContinuousTime and ContinuousDiscreteTime Unscented RauchTungStriebel Smoothers. Signal Processing, Volume 90, Issue 1, Pages 225235. (DOI, Preprint)
 S. Särkkä and A. Nummenmaa (2009). Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations. IEEE Transactions on Automatic Control, Volume 54, Issue 3, Pages 596600. (DOI, Preprint, Matlab code)
 S. Särkkä and T. Sottinen (2008). Application of Girsanov Theorem to Particle Filtering of Discretely Observed ContinuousTime NonLinear Systems. Bayesian Analysis, Volume 3, Number 03, Pages 555584. (DOI)
 S. Särkkä (2008). Unscented RauchTungStriebel Smoother. IEEE Transactions on Automatic Control, Volume 53, Issue 3, Pages 845849. (DOI, Preprint, Matlab toolbox)
 S. Särkkä, A. Vehtari, and J. Lampinen (2007). RaoBlackwellized Particle Filter for Multiple Target Tracking. Information Fusion Journal, Volume 8, Issue 1, Pages 215. (DOI, Preprint, Matlab toolbox)
 S. Särkkä, A. Vehtari, and J. Lampinen (2007). CATS Benchmark Time Series Prediction by Kalman Smoother with CrossValidated Noise Density. Neurocomputing, Volume 70, Issues 1315, Pages 23312341. (DOI Preprint)
 S. Särkkä (2007). On Unscented Kalman Filtering for State Estimation of ContinuousTime Nonlinear Systems. IEEE Transactions on Automatic Control, Volume 52, Issue 9, Pages 16311641. (DOI, Preprint)
Conference Proceedings
 Arno Solin and Simo Särkkä (2015).
State Space Methods for Efficient Inference in Studentt Process Regression.
To appear in Proceedings of AISTATS.  Jayaprasad Bojja, Jussi Collin, Simo Särkkä, and Jarmo Takala (2015). Pedestrian Localization in Moving Platforms Using Dead Reckoning, Particle Filtering and Map Matching. To appear in Proceedings of ICASSP.
 A. Solin and S. Särkkä (2014). The 10th Annual MLSP Competition: First Place. In Proceedings of MLSP. (Preprint as PDF)
 A. Solin and S. Särkkä (2014). Gaussian quadratures for state space approximation of scale mixtures of squared exponential covariance functions. In Proceedings of MLSP. (Preprint as PDF)
 S. Särkkä and R. Piché (2014). On convergence and accuracy of statespace approximations of squared exponential covariance functions. In Proceedings of MLSP. (Preprint as PDF, Code in Bitbucket)
 I. S. Mbalawata and S. Särkkä (2014). Weight Moment Conditions for L4 Convergence of Particle Filters for Unbounded Test Functions. In Proceedings of EUSIPCO 2014. (Preprint as PDF)
 S. Särkkä, V. Viikari, K. Jaakkola (2014). RFIDBased Butterfly Location Sensing System. In Proceedings of EUSIPCO 2014. (Preprint as PDF)
 J. Kokkala, A. Solin, and S. Särkkä (2014). Expectation Maximization Based Parameter Estimation by SigmaPoint and Particle Smoothing. In Proceedings of FUSION 2014. (Preprint as PDF)
 S. Särkkä, J. Hartikainen, L. Svensson, and F. Sandblom (2014). Gaussian Process Quadratures in Nonlinear SigmaPoint Filtering and Smoothing. In Proceedings of FUSION 2014. (Preprint as PDF)
 T. D. Barfoot, C. H. Tong, and S. Särkkä (2014). Batch ContinuousTime Trajectory Estimation as Exactly Sparse Gaussian Process Regression. In Proceedings of Robotics: Science and Systems (RSS). (PDF)
 I. S. Mbalawata and S. Särkkä (2014). On The L^{4} Convergence of Particle Filters with General Importance Distributions. In Proceedings of ICASSP. (Preprint as PDF)
 A. Solin and S. Särkkä (2014). Explicit Link Between Periodic Covariance Functions and State Space Models. JMLR Workshop and Conference Proceedings Volume 33 (AISTATS 2014), Pages 904912. (Preprint as PDF, PDF)
 A. Solin, S. Särkkä, A. Nummenmaa, A. Vehtari, T. Auranen, F.H. Lin (2014). Catching Physiological Noise: Comparison of DRIFTER in Image and kSpace. In Proceedings of ISMRM 2014 (abstract and poster).
 X. Chen, S. Särkkä, and S. Godsill (2013). Probabilistic Initiation and Termination for MEG Multiple Dipole Localization Using Sequential Monte Carlo Methods. In Proceedings of FUSION 2013.
 S. Särkkä and A. Solin (2013). ContinuousSpace Gaussian Process Regression and Generalized Wiener Filtering with Application to Learning Curves. In Proceedings of SCIA 2013. (Preprint as PDF, DOI)
 S. Särkkä and J. Hartikainen (2013). NonLinear Noise Adaptive Kalman Filtering via Variational Bayes. In Proceedings of MLSP 2013. (Preprint as PDE)
 A. Solin, E. Glerean, and S. Särkkä (2013). TimeFrequency Dynamics of Brain Connectivity by Stochastic Oscillator Models and Kalman Filtering. In Proceedings of OHBM 2013 (abstract and poster).
 A. Solin, S. Särkkä, A. Nummenmaa, A. Vehtari, T. Auranen, S. Vanni, F.H. Lin (2013). Volumetric SpaceTime Structure of Physiological Noise in BOLD fMRI. In Proceedings of ISMRM 2013 (abstract and poster). (Abstract, Poster)
 S.M.J. Lyons, A.J. Storkey, and S. Särkkä (2012). The Coloured Noise Expansion and Parameter Estimation of Diffusion Processes. Proceedings of NIPS, pages 19611969. (PDF)
 R. Piché, S. Särkkä and J. Hartikainen (2012). Recursive OutlierRobust Filtering and Smoothing for Nonlinear Systems Using the Multivariate Studentt Distribution. In Proceedings of MLSP. (Preprint as PDF)
 J. Sarmavuori and S. Särkkä (2012). FourierHermite RauchTungStriebel Smoother. Proceedings of EUSIPCO, pages 21092113. (Preprint as PDF)
 S. Särkkä, P. Bunch and S. J. Godsill (2012). A BackwardSimulation Based RaoBlackwellized Particle Smoother for Conditionally Linear Gaussian Models. Proceedings of SYSID 2012, pages 506511. (invited paper). (Preprint as PDF)
 S. Särkkä and A. Solin (2012). On ContinuousDiscrete Cubature Kalman Filtering. Proceedings of SYSID 2012, pages 12101215. (Preprint)
 J. Hartikainen, M. Seppänen and S. Särkkä (2012). StateSpace Inference for NonLinear Latent Force Models with Application to Satellite Orbit Prediction. Proceedings of The 29th International Conference on Machine Learning (ICML 2012). (PDF)
 S. Särkkä and J. Hartikainen (2012). InfiniteDimensional Kalman Filtering Approach to SpatioTemporal Gaussian Process Regression. JMLR Workshop and Conference Proceedings Volume 22: AISTATS 2012, Pages 9931001. (Preprint)
 S. Särkkä, A. Solin, A. Nummenmaa, A. Vehtari, T. Auranen, S. Vanni and F.H. Lin (2012). Identification of SpatioTemporal Oscillatory Signal Structure in Cerebral Hemodynamics Using DRIFTER. Proceedings of ISMRM 2012. (EPoster, Abstract)
 J. Hartikainen and S. Särkkä (2011). Sequential Inference for Latent Force Models. Proceedings of The 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011) (Preprint)
 J. Hartikainen, J. Riihimäki and S. Särkkä (2011). Sparse SpatioTemporal Gaussian Processes with General Likelihoods. Proceedings of International Conference on Artificial Neural Networks (ICANN) (DOI, Preprint)
 S. Särkkä (2011). Linear Operators and Stochastic Partial Differential Equations in Gaussian Process Regression. Proceedings of International Conference on Artificial Neural Networks (ICANN) (DOI, Preprint)
 S. Särkkä (2011). Learning Curves for Gaussian Processes via Numerical Cubature Integration. Proceedings of International Conference on Artificial Neural Networks (ICANN) (DOI, Preprint)
 S. Särkkä, A. Nummenmaa, A. Solin, A. Vehtari, T. Witzel, T. Auranen, S. Vanni, M.S. Hämäläinen, and FH. Lin. Dynamical statistical modeling of physiological noise for fast BOLD fMRI. Proceedings of ISMRM 2011. (EPoster)
 J. Hartikainen and S. Särkkä (2010). Kalman Filtering and Smoothing Solutions to Temporal Gaussian Process Regression Models. Proceedings of IEEE International Workshop on Machine Learning for Signal Processing (MLSP) (Preprint)
 S. Särkkä and J. Hartikainen (2010). Sigma Point Methods in Optimal Smoothing of NonLinear Stochastic State Space Models. Proceedings of IEEE International Workshop on Machine Learning for Signal Processing (MLSP) (Preprint)
 S. Särkkä, A. Vehtari, and J. Lampinen (2007). Prediction of ESTSP Competition Time Series by Unscented Kalman Filter and RTS Smoother. Proceedings of ESTSP 2007 (Preprint)
 S. Särkkä (2006). On Sequential Monte Carlo Sampling of Discretely Observed Stochastic Differential Equations. Proceedings of NSSPW, (Preprint)
 S. Särkkä, A. Vehtari, and J. Lampinen (2004). Time series prediction by Kalman smoother with cross validated noise density. Proceedings of IJCNN 2004. The Winner of Time Series Prediction Competition  The CATS Benchmark (Preprint)
 S. Särkkä, A. Vehtari, and J. Lampinen (2004). RaoBlackwellized Monte Carlo data association for multiple target tracking. Proceedings of FUSION 2004 (Preprint, Matlab toolbox)
 A. Vehtari, S. Särkkä, and J. Lampinen (2000). On MCMC sampling in Bayesian MLP neural networks. Proceedings of the IJCNN 2000 (Preprint as ps.gz)
Doctoral Dissertation
 S. Särkkä (2006). Recursive Bayesian Inference on Stochastic Differential Equations. Doctoral dissertation, Helsinki University of Technology (Thesis as PDF)
Technical Reports
 S. Särkkä and J. Hartikainen. Variational Bayesian Adaptation of Noise Covariances in NonLinear Kalman Filtering. (arXiv)
 S. Särkkä (2007). Notes on Quaternions. Technical report. (Report as PDF)
 S. Särkkä, Toni Tamminen, Aki Vehtari, and Jouko Lampinen (2004). Probabilistic methods in multiple target tracking  Review and bibliography. Technical report B36, ISBN 9512269384, Helsinki University of Technology. Laboratory of Computational Engineering (Report as PDF)
 S. Särkkä (2000). Bayesilaiset menetelmät audiovisuaalisen puheen havaitsemisen mallintamisessa. Diploma thesis, (in Finnish) (Thesis as ps.gz)
 S. Särkkä (1999). MCMCmenetelmät ja diagnostiikat. Technical report (in Finnish). (HTML, ps.gz)
Course material:
 Simo Särkkä and Arno Solin (2014). Applied Stochastic Differential Equations. Lecture notes of the course Becs114.4202 Special Course in Computational Engineering II held in Autumn 2014. (Booklet as PDF, Slides and exercises). (2012 material is here).
 S. Särkkä (2012). Bayesian Estimation of TimeVarying Systems: DiscreteTime Systems. Lectures notes of the course S114.4610 held in Spring 2012 (Booklet as PDF, Slides and Exercises). (2011 material is here).
Patents
Working papers
 Ángel F. GarcíaFernández, Lennart Svensson, Mark R. Morelande, Simo Särkkä. Posterior linearisation filter: principles and implementation using sigma points. Submitted.
 Simo Särkkä, Jouni Hartikainen, Lennart Svensson, Fredrik Sandblom. On the relation between Gaussian process quadratures and sigmapoint methods. Submitted. (arXiv)
 Juho Kokkala, Arno Solin, Simo Särkkä. SigmaPoint Filtering Based Parameter Estimation in Nonlinear Dynamic Systems. Submitted. (arXiv)
 Xi Chen, Simo Särkkä, Simon Godsill. A Bayesian Particle Filtering Method For Brain Source Localisation. Submitted. (arXiv)
 Lassi Roininen, Sari Lasanen, Mikko Orispää, and Simo Särkkä. Sparse Approximations of Fractional Matern Fields. Submitted. (arXiv)
 Fredrik Lindsten, Pete Bunch, Simo Särkkä, Thomas Schön, Simon Godsill. RaoBlackwellized particle smoothers for conditionally linear Gaussian models. Submitted.
 I. S. Mbalawata and S. Särkkä. Moment Conditions for Convergence of Particle Filters with Unbounded Importance Weights. Submitted. (arXiv)
 A. Solin and S. Särkkä. Hilbert Space Methods for ReducedRank Gaussian Process Regression. Submitted. (arXiv)
Software
Software Packages
Some Matlab toolboxes where I have contributed to (see also the code examples linked in the publication list above):
 LFM Toolbox for Matlab
 DRIFTER Toolbox for Matlab
 RBMCDA Toolbox for Matlab
 EKF/UKF Toolbox for Matlab
 MCMC Methods for MLP and GP and Stuff (for Matlab)
 MCMC Diagnostics for Matlab
 FBM tools for Matlab
Teaching
Some courses etc. that I am giving / have given / will give soon:
 Spring 2015: Becs114.4610 Special Course in Bayesian Modelling: Bayesian estimation of timevarying systems (5 p) P
 Autumn 2014: Becs114.4202/Mat1.C Special Course in Computational Engineering II: Applied Stochastic Differential Equations (3 cr).
 Autumn 2014: Tutorial on Bayesian Filtering and Smoothing at EUSIPCO'2014 conference in Lisbon/Portugal.
 Spring 2014: ASE 5036 Optimal Estimation at TUT.
 Michaelmas 2013: Minicourse on Stochastic Differential Equations in Bayesian Dynamic Models and Machine Learning at University of Oxford, UK.
 Autumn 2013: Lecture in fMRI school 2013 of O.V. Lounasmaa Laboratory.
 Summer 2013: Lecture in Gaussian Process Models summer school, University of Sheffield, UK.
 Spring 2013: Guest lecture on course ASE5030/6 Optimal estimation at TUT.
 Spring 2013: Becs114.4610 Special Course in Bayesian Modelling: Bayesian estimation of timevarying systems (5 p) P
 Fall 2012: MAT55216 Topics in Applied Mathematics: Applied stochastic differential equations (3 cr) at TUT
 Spring 2012: Lecture in fMRI school 2012 of O.V. Lounasmaa Laboratory.
 Spring 2012: S114.4610 Special Course in Bayesian Modelling: Bayesian estimation of timevarying processes (5 p) P
 Spring 2011: MAT55216 Topics in Applied Mathematics: Bayesian estimation of timevarying processes: discretetime systems (5 cr) at TUT
 Spring 2011: S114.4220 Research Seminar on Computational Science: Numerical Methods for Stochastic Differential Equations (3 p) P
 Spring 2010: S114.4202 Special Course in Computational Engineering II: Bayesian Estimation of TimeVarying Processes (5 p)
 Spring 2009: S114.4202 Special Course in Computational Engineering II: Bayesian Estimation of TimeVarying Processes (5 p)
 Spring 2008: S114.4220 Research Seminar on Computational Science: Stochastic Models in Spatial and Image Analysis
 Fall 2007: S114.4220 Research Seminar on Computational Science: Stochastic and Adaptive Control of Uncertain Systems (5 p) L V
 Fall 2006: S114.4220 Research Seminar on Computational Science: Bayesian Estimation of TimeVarying Processes (5 p) L V