12.S990 | Fall 2012 | Undergraduate, Graduate
Quantifying Uncertainty

Study Materials

Arulampalam, M. Sanjeev, Simon Maskell, et al. “A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking.” IEEE Transactions on Speech and Audio Processing 50, no. 2 (2002).

Besag, Julian. “Markov Chain Monte Carlo for Statistical Inference.” (PDF) Center for Statistics and the Social Sciences. Working paper, no. 9 (2001).

Brooks, S. “Markov Chain Monte Carlo Method and its Application.” (PDF) The Statistician 47, no. Part 1 (1998): 69–100.

Do, Chuong B, and Serafim Batzoglou. “What is the Expectation Maximization Algorithm?Nature Biotechnology 26 (2008): 897–9.

Elsner, James B., Xufeng Niu, et al. “Detecting Shifts in Hurricane Rates Using a Markov Chain Monte Carlo Approach.” Journal of Climate 17, no. 13 (2004): 2652–66.

Emanuel, K., S. Ravela, et al. “A Statistical Deterministic Approach to Hurricane Risk Assessment.” Bulletin of the American Meteorological Society 87, no. 3 (2006): 299–314.

Evensen, G. “The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation.” (PDF) Ocean Dynamics 53 (2003): 343–67.

———. “Sampling Strategies and Square Root Analysis Schemes for the EnKF.” (PDF) Ocean Dynamics 54 (2004): 539–60.

Evensen, G., and P. J. van Leeuwen. “An Ensemble Kalman Smoother for Nonlinear Dynamics.” Monthly Weather Review 128, no. 6 (2000): 1852–67.

Ferdosi, B. J., H. Buddelmeijer, et al. “Comparison of Density Estimation Methods for Astronomical Datasets.” Astronomy & Astrophysics 531, no. A114 (2011).

Figueiredo, Mario A. T., and Anil K. Jain. “Unsupervised Learning of Finite Mixture Models.” (PDF - 1.1MB) IEEE Transactions on Pattern Analysis and Machine Intelligence 24, no. 3 (2002).

Fletcher, Benjamin J., Stuart J. Brentnall, et al. “Atmospheric Carbon Dioxide Linked with Mesozoic and Early Cenozoic Climate Change.” Nature Geoscience 1 (2008): 43–8.

Geman, S., and D. Geman. “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images”. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, no. 6 (1984): 721–41.

Geman, S., Bienenstock, et al. “Neural Networks and the Bias/Variance Dilemma.” Neural Computation 4, no. 1 (1992): 1–58.

Gregory, Philip C. “Bayesian Exoplanet Tests of a New Method for MCMC Sampling in Highly Correlated Model Parameter Spaces.” Monthly Notices of the Royal Astronomical Society 410, no. 1 (2011): 94–110.

———. “Extra-solar Planets via Bayesian Fusion MCMC.” In Astrostatistical Challenges for the New Astronomy. Edited by J. M. Hilbe. Springer, 2012. ISBN: 9781461435075.

Hannachi, A. “Tropospheric Planetary Wave Dynamics and Mixture Modeling: Two Preferred Regimes and a Regime Shift.” Journal of the Atmospheric Sciences 64, no. 10 (2007): 3521–41.

Hansen, Mark H., and Bin Yu. “Model Selection and the Principle of Minimum Description Length.” (PDF) Journal of the American Statistical Association 96, no. 454 (2001): 746–74.

Hwang, Jenq-Neng, Shyh-Rong Lay, et al. “Nonparametric Multivariate Density Estimation: A Comparative Study.” IEEE Transactions on Signal Processing 42, no. 10 (1994): 2795–810.

Isukapalli, Sastry S. “Uncertainty Analysis of Transport-Transformation Models.”

Katz, Rick. “Sir Gilbert Walker and a Connection between El Nino and Statistics.” Statistical Science 17, no. 1 (2002): 97–112.

Katz, R., and X. Zheng. “Mixture Model for Overdispersion of Precipitation.” Journal of Climate 12, no. 8 (1999): 2528–37.

Lorenz, Edward N. “Deterministic Nonperiodic Flow.” Journal of Atmospheric Sciences 20, no. 2 (1963): 130–41.

Lorenz, Edward N., and Kerry A. Emanuel. “Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model.” (PDF) Journal of the Atmospheric Sciences 55 (1998): 399–414.

Martinez, Wendy L, and Angel R. Martinez. Computational Statistics Handbook with MATLAB, Second Edition (Chapman & Hall/CRC Computer Science & Data Analysis). Chapman and Hall/CRC, 2007. ISBN: 9781584885665.

MCMC in Exoplanets:

The Thermal Emission of the Young and Massive Planet CoRoT-2b at 4.5 and 8 μm

Lack of Inflated Radii for Kepler Giant Planet Candidates Receiving Modest Stellar Irradiation

The High Albedo of the Hot Jupiter Kepler-7 b

Discovery and Atmospheric Characterization of Giant Planet Kepler-12b: An Inflated Radius Outlier

The Hot-Jupiter Kepler-17b: Discovery, Obliquity from Stroboscopic Starspots, and Atmospheric Characterization

The Spitzer Search for the Transits of HARPS Low-mass Planets. I. No Transit for the Super-Earth HD 40307b

“Model Order Selection.” (PDF - 1.0MB) IEEE Signal Processing Magazine.

Model Order Reduction

Moon, Tood K. “The Expectation Maximization Algorithm.” (PDF) IEEE Signal Processing Magazine, November 1996, 47–60.

Neal, Radford M. “Slice Sampling.” (PDF) Technical Report No. 2005_,_ Department of Statistics, University of Toronto (2000).

Oh, Songhwai, S. Russell, et al. “Markov Chain Monte Carlo Data Association for General Multiple Target Tracking Problems.” IEEE Conference on Decision and Control 1 (2004): 735–42.

Ravela, Sai, and Dennis McLaughlin. “Fast Ensemble Smoothing.” Ocean Dynamics 57, no. 2 (2007): 123–34.

Reynolds, Douglas. “Gaussian Mixture Models.” (PDF)

Robertson, I., D. Lucy, et al. “A Kernel-based Bayesian Approach to Climatic Reconstruction.” The Holocene 9, no. 4 (1999): 495–500.

Schartau, Markus, Michael R. Landry, et al. “Density Estimation of Plankton Size Spectra: A Reanalysis of IronEx II Data.” Journal of Plankton Research 32, no. 8 (2010): 1167–84.

Schneider, Tapio. “Analysis of Incomplete Climate Data: Estimation of Mean Values and Covariance Matrices and Imputation of Missing Values.” Journal of Climate 14, no. 5 (2001): 853–71.

Scott, David W., and Stephan R. Sain. “Multi-dimensional Density Estimation.”

Siy, Peter W. “Matrix Factorization Techniques for Analysis of Imaging Mass Spectrometry Data.” (2008): 1–6.

Smerdon, Jason E., Alexey Kaplan, et al. “Companion Paper: On the Origin of the Standardization Sensitivity in RegEM Climate Field Reconstructions.” Journal of Climate 21, no. 4 (2008): 6710–23.

Smyth, Padhraic, Kayo Ide, et al. “Multiple Regimes in Northern Hemisphere Height Fields via MixtureModel Clustering.” Journal of the Atmospheric Sciences 56, no. 21 (1999): 3704–23.

Stauffer, C., and W. E. L. Grimson. “Adaptive Background Mixture Models for Real-time Tracking.” IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2 (1999).

Tatang, Menner A., Wenwei Pan, et al. “An Efficient Method for Parametric Uncertainty Analysis of Numerical Geophysical Models.” Journal of Geophysical Research 102, no. D18 (1997): 21925–32.

Tomassini, Lorenzo, Peter Reichert, et al. “Robust Bayesian Uncertainty Analysis of Climate System Properties Using Markov Chain Monte Carlo Methods.” Journal of Climate 20, no. 7 (2007): 1239–54.

Wainer, Howard. Picturing the Uncertain World: How to Understand, Communicate, and Control Uncertainty through Graphical Display. Princeton University Press, 2009. ISBN: 9780691137599. [Preview with Google Books]

Ward, Darren B. “Particle Filtering Algorithms for Tracking an Acoustic Source in a Reverberant Environment.” IEEE Transactions on Speech and Audio Processing 11, no. 6 (2003): 826–36.

Weinberg, M. “Computational Statistics using the Bayes Inference Engine.” Monthly Notices of the Royal Astronomical Society (2012): 1–17.

Willcox, K., and J. Peraire. “Balanced Model Reduction via the Proper Orthogonal Decomposition.” (PDF) AIAA Journal 40, no. 11 (2002): 2323–30.

Xiu, Dongbin, and George Em Karniadakis. “The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations.” (PDF)

Yang, Allen Y., Arvind Ganesh, et al. “A Review of Fast l1-Minimization Algorithms for Robust Face Recognition.” (PDF) (2010).

Zucchini, Walter. “An Introduction to Model Selection.” (PDF) Journal of Mathematical Psychology 44 (2000): 41–61.