Chapter 8 Efficient Computation of Confidence Intervals for Bayesian Model Predictions Based on Multidimensional Parameter Space

Author(s):  
Amber D. Smith ◽  
Alan Genz ◽  
David M. Freiberger ◽  
Gregory Belenky ◽  
Hans P.A. Van Dongen
Author(s):  
I. A. Kuznetsov ◽  
A. V. Kuznetsov

In this paper, we first develop a model of axonal transport of tubulin-associated unit (tau) protein. We determine the minimum number of parameters necessary to reproduce published experimental results, reducing the number of parameters from 18 in the full model to eight in the simplified model. We then address the following questions: Is it possible to estimate parameter values for this model using the very limited amount of published experimental data? Furthermore, is it possible to estimate confidence intervals for the determined parameters? The idea that is explored in this paper is based on using bootstrapping. Model parameters were estimated by minimizing the objective function that simulates the discrepancy between the model predictions and experimental data. Residuals were then identified by calculating the differences between the experimental data and model predictions. New, surrogate ‘experimental’ data were generated by randomly resampling residuals. By finding sets of best-fit parameters for a large number of surrogate data the histograms for the model parameters were produced. These histograms were then used to estimate confidence intervals for the model parameters, by using the percentile bootstrap. Once the model was calibrated, we applied it to analysing some features of tau transport that are not accessible to current experimental techniques.


2020 ◽  
Author(s):  
Steven J. Phipps ◽  
Jason L. Roberts ◽  
Matt A. King

Abstract. Physical processes within geoscientific models are sometimes described by simplified schemes known as parameterisations. The values of the parameters within these schemes can be poorly constrained by theory or observation. Uncertainty in the parameter values translates into uncertainty in the outputs of the models. Proper quantification of the uncertainty in model predictions therefore requires a systematic approach for sampling parameter space. In this study, we develop a simple and efficient approach to identify regions of multi-dimensional parameter space that are consistent with observations. Using the Parallel Ice Sheet Model to simulate the present-day state of the Antarctic Ice Sheet, we find that co-dependencies between parameters preclude the identification of a single optimal set of parameter values. Approaches such as large ensemble modelling are therefore required in order to generate model predictions that incorporate proper quantification of the uncertainty arising from the parameterisation of physical processes.


2017 ◽  
Vol 49 (3) ◽  
pp. 954-970 ◽  
Author(s):  
Shanhu Jiang ◽  
Liliang Ren ◽  
Chong-Yu Xu ◽  
Shuya Liu ◽  
Fei Yuan ◽  
...  

Abstract This study focuses on a quantitative multi-source uncertainty analysis of multi-model predictions. Three widely used hydrological models, i.e., Xinanjiang (XAJ), hybrid rainfall–runoff (HYB), and HYMOD (HYM), were calibrated by two parameter optimization algorithms, namely, shuffled complex evolution (SCE-UA) method and shuffled complex evolution metropolis (SCEM-UA) method on the Mishui basin, south China. The input uncertainty was quantified by utilizing a normally distributed error multiplier. The ensemble simulation sets calculated from the three models were combined using the Bayesian model averaging (BMA) method. Results indicate the following. (1) Both SCE-UA and SCEM-UA resulted in good and comparable streamflow simulations. Specifically, the SCEM-UA implied parameter uncertainty and provided the posterior distribution of the parameters. (2) In terms of the precipitation input uncertainty, precision of streamflow simulations did not improve remarkably. (3) The BMA combination not only improved the precision of streamflow prediction, but also quantified the uncertainty bounds of the simulation. (4) The prediction interval calculated using the SCEM-UA-based BMA combination approach appears superior to that calculated using the SCE-UA-based BMA combination for both high flows and low flows. Results suggest that the comprehensive uncertainty analysis by using the SCEM-UA algorithm and BMA method is superior for streamflow predictions and flood forecasting.


2012 ◽  
Vol 15 (2) ◽  
pp. 161-169 ◽  
Author(s):  
Raoul Naumann d'Alnoncourt ◽  
Yury V. Kolen'ko ◽  
Robert Schlogl ◽  
Annette Trunschke

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