Construction of Bayesian Prediction Intervals for Smart Systems

2013 ◽  
Author(s):  
Mami T. Wentworth ◽  
Ralph C. Smith
Keyword(s):  
Measurement Errors ◽  
Smart Material ◽  
Bayesian Prediction ◽  
Prediction Intervals ◽  
Smart Systems ◽  
Mcmc Algorithms ◽  
Quantity Of Interest ◽  
Input Parameters ◽  
Quantities Of Interest

In this paper, we employ adaptive Metropolis algorithms to construct densities for parameters and quantities of interest for models arising in the analysis of smart material structures. In the first step of the construction, MCMC algorithms are used to quantify the uncertainty in parameters due to measurement errors. We then combine uncertainties from the input parameters and measurement errors, and construct prediction intervals for the quantity of interest by propagating uncertainties through the models.

scholarly journals Exploring the Sensitivity of Photosynthesis and Stomatal Resistance Parameters in a Land Surface Model

2017 ◽  
Vol 18 (3) ◽  
pp. 897-915 ◽  
Author(s):  
Jennifer L. Jefferson ◽  
Reed M. Maxwell ◽  
Paul G. Constantine
Keyword(s):  
Land Surface ◽  
Stomatal Resistance ◽  
Hydrologic Model ◽  
Surface Model ◽  
Land Surface Models ◽  
Common Land Model ◽  
Surface Models ◽  
Input Parameters ◽  
Rate Of Photosynthesis ◽  
Quantities Of Interest

Abstract Land surface models, like the Common Land Model component of the ParFlow integrated hydrologic model (PF-CLM), are used to estimate transpiration from vegetated surfaces. Transpiration rates quantify how much water moves from the subsurface through the plant and into the atmosphere. This rate is controlled by the stomatal resistance term in land surface models. The Ball–Berry stomatal resistance parameterization relies, in part, on the rate of photosynthesis, and together these equations require the specification of 20 input parameters. Here, the active subspace method is applied to 2100 year-long PF-CLM simulations, forced by atmospheric data from California, Colorado, and Oklahoma, to identify which input parameters are important and how they relate to three quantities of interest: transpiration, stomatal resistance from the sunlit portion of the canopy, and stomatal resistance from the shaded portion. The slope (mp) and intercept (bp) parameters associated with the Ball–Berry parameterization are consistently important for all locations, along with five parameters associated with ribulose bisphosphate carboxylase/oxygenase (RuBisCO)- and light-limited rates of photosynthesis [CO2 Michaelis–Menten constant at 25°C (kc25), maximum ratio of oxygenation to carboxylation (ocr), quantum efficiency at 25°C (qe25), maximum rate of carboxylation at 25°C (vcmx25), and multiplier in the denominator of the equation used to compute the light-limited rate of photosynthesis (wj1)]. The importance of these input parameters, quantified by the active variable weight, and the relationship between the input parameters and quantities of interest vary seasonally and diurnally. Input parameter values influence transpiration rates most during midday, summertime hours when fluxes are large. This research informs model users about which photosynthesis and stomatal resistance parameters should be more carefully selected. Quantifying sensitivities associated with the stomatal resistance term is necessary to better understand transpiration estimates from land surface models.

Bayesian Prediction Bounds for the Exponential-Type Distribution Based on Ordered Ranked Set Sampling

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Mohammed S. Kotb
Keyword(s):  
Exponential Type ◽  
Bayesian Prediction ◽  
Prediction Intervals ◽  
Prior Density ◽  
Type Distribution ◽  
Ranked Set Sample ◽  
Cumulative Function ◽  
Sample Method ◽  
Special Case ◽  
Sample Case

AbstractWe suggest a ranked set sample method to improve Bayesian prediction intervals. The paper deals with the Bayesian prediction intervals in the context of an ordered ranked set sample from a certain class of exponential-type distributions. A proper general prior density function is used and the predictive cumulative function is obtained in the two-sample case. The special case of linear exponential distributed observations is considered and completed with numerical results.

Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 1005-1016 ◽  
Author(s):  
Alberto Malinverno ◽  
Victoria A. Briggs
Keyword(s):  
Standard Deviation ◽  
Inverse Problems ◽  
Prior Distribution ◽  
Measurement Errors ◽  
Empirical Bayes ◽  
A Priori ◽  
Compressional Wave ◽  
Hierarchical Bayes ◽  
Earth Model ◽  
Quantities Of Interest

A common way to account for uncertainty in inverse problems is to apply Bayes' rule and obtain a posterior distribution of the quantities of interest given a set of measurements. A conventional Bayesian treatment, however, requires assuming specific values for parameters of the prior distribution and of the distribution of the measurement errors (e.g., the standard deviation of the errors). In practice, these parameters are often poorly known a priori, and choosing a particular value is often problematic. Moreover, the posterior uncertainty is computed assuming that these parameters are fixed; if they are not well known a priori, the posterior uncertainties have dubious value. This paper describes extensions to the conventional Bayesian treatment that assign uncertainty to the parameters defining the prior distribution and the distribution of the measurement errors. These extensions are known in the statistical literature as “empirical Bayes” and “hierarchical Bayes.” We demonstrate the practical application of these approaches to a simple linear inverse problem: using seismic traveltimes measured by a receiver in a well to infer compressional wave slowness in a 1D earth model. These procedures do not require choosing fixed values for poorly known parameters and, at most, need a realistic range (e.g., a minimum and maximum value for the standard deviation of the measurement errors). Inversion is thus made easier for general users, who are not required to set parameters they know little about.

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