Bayesian Stochastic Inversion
There are two central motivations for considering Bayesian Stochastic Inversion (BSI) in our research. First, the method is central to doing a class of problems known as "inverse modeling". Through inverse modeling one may determine the necessary forcings or model configurations that allow a given model to reproduce observations. In this way BSI is a tool for finding connections between models and observations and evaluating uncertainties. The method is probably best used for non-linear problems where more traditional inverse methods fail. The second motivation for our interest in BSI is the expanded availability of high performance computing through Linux-based PC clusters. One such cluster was recently installed at the Texas Advanced Computing Center (figure 1). The Institute for Geophysics contributed to the purchase of this cluster through funds from the G. Unger Vetlesen Foundation and research grants.
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| Figure 1. Pictured is 'Lonestar', a cluster of 428 dual-processor personal computers. Dedicated on October 3rd, 2003, this cluster is currently ranked the 26th largest computer in the world. |
The Bayesian Stochastic Inversion approach to quantifying uncertainties is based on the mathematics of conditional probabilities. That is, estimated parameter probabilities indicate the degree to which one set of model configurations perform better relative to other choices that have been considered. BSI controls which model configurations are tested. This is commonly done in a stochastic manner either through Monte-Carlo (random) sampling or through other so-called ‘importance sampling’ techniques such as multiple Very Fast Simulated Annealing (VFSA) that we favor (figure 2).
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| Figure 1. Schematic diagram of the Metropolis and VFSA algorithms. Parameter moves/temperature gives the number of times a new model parameter set is selected and tested before lowering the temperature, T. Parameter ntarget specifies the convergence criterion and is given by the maximum number of failed attempts at finding an acceptable parameter set before stopping. |
UT Institute for Geophysics Publications related to BSI
concept papers
Jackson, C., M. Sen, and P. Stoffa (2004) An Efficient Stochastic Bayesian Approach to Optimal Parameter and Uncertainty Estimation for Climate Model Predictions, Journal of Climate, 17(14), 2828-2841. [pdf]
Sen, M.K., and P.L. Stoffa (1996) Bayesian inference, Gibbs' sampler and uncertainty estimation in geophysical inversion, Geophysical Prospecting, 44, 313-350.
applications
Jackson, C., Y. Xia, M. Sen, and P. Stoffa (2003) Optimal parameter and uncertainty estimation of a land surface model: A case example using data from Cabauw, Netherlands, Journal of Geophysical Research, 108 (D18), 4583 10.1029/2002JD002991. [pdf]
Xia, Y., M. K. Sen, C. Jackson, and P. L. Stoffa. Multi-dataset study of optimal parameter and uncertainty estimation of a land surface model with Bayesian Stochastic Inversion and multicriteria method (submitted to Journal of Applied Meteorology, 2003).
Xia, Y., Z. L. Yang, C. Jackson, P. L. Stoffa, and M. K. Sen, Impacts of data length on optimal parameter and uncertainty estimation of a land surface model (accepted for publication in Journal of Geophysical Research, 2003).
Xia, Y., P. L. Stoffa, C. Jackson, and M. Sen. Effect of forcing data errors on calibration and uncertainty estimates of CHASM model: a multi-dataset study. (accepted by "Observations, Theory, and Modeling of Atmospheric and Oceanic Variability", World Scientific Series on Meterology of East Asia, Vol. 4, World Scientific Publishing Corporation, Singapore, 2003).
