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. 2018;22(3):415-446.
Epub 2018 Jun 19.

THE PROHOROV METRIC FRAMEWORK AND AGGREGATE DATA INVERSE PROBLEMS FOR RANDOM PDEs

H T Banks  1 , K B Flores  1 , I G Rosen  2 , E M Rutter  1 , Melike Sirlanci  2 , W Clayton Thompson  1   3
Affiliations

THE PROHOROV METRIC FRAMEWORK AND AGGREGATE DATA INVERSE PROBLEMS FOR RANDOM PDEs

H T Banks et al. Commun Appl Anal. 2018.

Abstract

We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.

Keywords: 34A55; 46S50; 62G07; 93E24; aggregate data; existence and approximation of estimators; individual data; inverse problems.

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Figures

Figure 1:
Figure 1:
Alcohol Biosensor Devices: The WrisTAS (left) and the SCRAM (right).
Figure 2:
Figure 2:
BrAC and TAC measurements for multiple drinking episodes by a single subject.
Figure 3:
Figure 3:
Scatter plot of deterministically obtained parameter estimates for BrAC and TAC measurements from a single drinking episode from each of 18 subjects.
See this image and copyright information in PMC

References

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    1. Banks HT, Bortz D, Pinter G, and Potter L, Modeling and imaging techniques with potential for application in bioterrorism, Bioterrorism: Mathematical Modeling Applications in Homeland Security, SIAM, 2003, pp. 129–154.

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