Using Bayesian inference for parameter estimation when the system response and experimental conditions are measured with error and some variables are considered as nuisance variables

Measurement Science and Technology

Volumn 18, Issue 1, 2007, Pages 19-29

  Emery, A F ^a   Valenti, E ^a   Bardot, D ^a  

^a University of Washington   (United States)

Author keywords

Bayesian inference; Error in variables model; Inverse problems; Nuisance variables; Optimal design; Parameter estimation; Regularization

Indexed keywords

ERROR ANALYSIS; INVERSE PROBLEMS; MATHEMATICAL MODELS; SENSORS;

BAYESIAN INFERENCE; NUISANCE VARIABLES; REGULARIZATION;

PARAMETER ESTIMATION;

ERROR ANALYSIS; INVERSE PROBLEMS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; SENSORS;

EID: 33947658976     PISSN: 09570233     EISSN: 13616501     Source Type: Journal    
DOI: 10.1088/0957-0233/18/1/003     Document Type: Conference Paper

References (38)

1. Coleman H W and Steele W G Jr 1999 Experimentation and Uncertainty Analysis for Engineers (New York: Wiley)
2. Lehmann E L and Casella G 1998 Theory of Point Estimation (New York: Springer)
3. Turchin V F and Nozik V Z 1969 Statistical regularization of the solution of incorrectly posed problems Izv. Atmos. Ocean. Phys. 5 29-38
4. D'Ambrogi B, Mäenpää S and Markkanen M 1999 Discretization independent retrieval of atmospheric ozone profile Geophysica 35 87-99
5. Bolstad W M 2004 Introduction To Bayesian Statistics (New York: Wiley)
6. O'Hagan A and Forster J 2004 Bayesian Inference, Kendall's Advanced Theory of Statistics vol 2b (Oxford: Oxford University Press)
7. D'Agostini G 2003 Bayesian Reasoning in Data Analysis: A Critical Introduction (London: World Scientific)
8. Gamerman D 1997 Markov Chain Monte Carlo (New York: Chapman and Hall)
9. Efron B 2005 Bayesian, frequentists, and scientists J. Am. Stat. Assoc. 100 1-5
10. Evans M and Swartz T 1995 Methods for approximating integrals in statistics with special emphasis on Bayesian integration problems Stat. Sci. 10 254-72
11. Li J and Gray R M 2000 Image Segmentation and Compression Using Hidden Markov Models (Boston, MA: Kluwer)
12. Gelman A, Carlin J B, Stern H S and Rubin D B 2004 Bayesian Data Analysis (Boca Raton, FL: Chapman and Hall/CRC Press)
13. Wang J and Zabaras N 2005 Using Bayesian statistics in the estimation of heat source in radiation Int. J. Heat Mass Transfer 48 15-29
14. Hammersley J M and Handscomb D C 1965 Monte Carlo Methods (London: Methuen)
15. Cooke R M 1991 Experts in Uncertainty: Opinion and Subjective Probability in Science (Oxford: Oxford University Press)
16. Garthwaite P H, Kadane J B and O'Hagan A 2005 Statistical methods for eliciting probability distributions J. Am. Stat. Assoc. 100 680-701
17. Anderson B D O and Moore J B 1979 Optimal Filtering (Englewood Cliffs, NJ: Prentice-Hall)
18. Haylock R G and O'Hagan A 1996 On inference for outputs of computationally expensive algorithms with uncertainty on the inputs Bayesian Statistics 5 (Oxford: Oxford University Press) pp 629-37
19. Emery A F and Bardot D 2005 Modeling the response of a transient thermal system using Gaussian processes Proc. 2005 ASME IMECE Meeting (Orlando, FL) paper 82089
20. Seber G A F and Wild C J 1989 Nonlinear Regression (New York: Wiley)
21. Papoulis A and Pillai S V 2002 Probability, Random Variables and Stochastic Processes (New York: McGraw-Hill)
22. Shiavi R 1999 Introduction to Applied Statistical Signal Analysis (New York: Academic)
23. Emery A F, Blackwell B F and Dowding K J 2002 The relationship between information, sampling rates, and parameter estimation models ASME J. Heat Transfer 124 1192-9
24. Pawatin Y 2001 In All Likelihood: Statistical Modelling and Inference Using Likelihood (Oxford: Oxford University Press)
25. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Boston, MA: Kluwer)
26. Hofmann B 1986 Regularization for Applied Inverse and Ill-posed Problems: A Numerical Approach (Leipzig: Teubner)
27. Gruber M H J 1990 Regression Estimators : A Comparative Study (Boston, MA: Academic)
28. Wald A 1950 Statistical Decision Functions (New York: Wiley)
29. Pazman A 1986 Foundations of Optimal Design (Boston, MA: Reidel)
30. Atkinson A C 1992 Optimum Experimental Designs (Oxford: Oxford Scientific Press)
31. Emery A F and Nenarokomov A V 1998 Optimal experiment design Meas. Sci. Technol. 9 864-76
32. Sacks J, Schiller S B and Welch W J 1989 Designs for computer experiments Technometrics 31 41-7
33. Neal R M 1998 Regression and classification using Gaussian process priors Bayesian Statistics 6 (Oxford: Oxford University Press)
34. Incropera F P and DeWitt D P 2001 Introduction to Heat Transfer (New York: Wiley)
35. Burns G W and Scroger M G 1989 The Calibration of Thermocouples And Thermocouple Materials (Washington, DC: NIST) SP-250-35
36. Cheng C-L and Van Ness J W 1999 Statistical Regression with Measurement Error (Oxford: Oxford University Press)
37. Zellner A 1996 An Introduction to Bayesian Inference in Econometrics (New York: Wiley)
38. Press S J 2003 Subjective and Objective Bayesian Statistics: Principles, Models and Applications (New York: Wiley)