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Bayesian Inference

Bayesian methods form the basis of a wide variety of predictive modeling systems throughout the laboratory. Bayesian statistics is essentially a mathematical framework for rationally and coherently propagating uncertainty: this includes uncertainty about the value of a parameter in a model; uncertainty about which of several models more accurately captures dynamics of a stochastic system; and uncertainty about the predicted output of a system given its inputs. The ability to formally propagate uncertainties about the properties of an observed system into the decision tasks faced in operational settings is a key feature of Bayesian methods.

A unifying theme of all Bayesian methods is the prior-to-posterior inference process. This approach to inference makes it possible to combine information representing the practitioner's current, or "prior" understanding of the system, with information obtained through observation of the system, in order to produce a "posterior" understanding of the system. This prior-to-posterior updating strategy makes Bayesian methods especially well suited for dynamic systems, for which the goal is to perform continuous learning about the ever-changing system. In such settings, one moment's "posterior" becomes the next moment's "prior", thereby forming a continuous inferential loop.

Current/recent laboratory applications of Bayesian methods include uncertainty quantification in climate modeling, adaptive design of computer experiments for complex simulations, dynamic classification and anomaly detection for cyber security, video image tracking, structural reliability modeling, biophysical model assessment, and seismic event localization.

Gardar Johannesson
(925) 422-3901

Prenger, R., Chen, B., Lemmond, T., Hanley, W., and Merl, D., 2011, Fast MAP search for compact additive tree ensembles, Lawrence Livermore National Laboratory Technical Report.

Arora, N., Russell, S., Kidwell, P., and Suddereth, E., 2010, "Global Seismic Monitoring as Probablistic Inference," Advances in Neural Information Processing Systems, 24.

Eubank, R. and Kupresanin, A., 2011, Statistical Computing in C++ and R, Chapman & Hall/CRC.

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