Inverse problems as statistics

Inverse Problems

Volumn 18, Issue 4, 2002, Pages

  Evans, Steven N ^a   Stark, Philip B ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; PROBABILITY DISTRIBUTIONS; REGRESSION ANALYSIS;

STATISTICAL ESTIMATION;

INVERSE PROBLEMS;

EID: 0036683968     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/18/4/201     Document Type: Review

References (65)

1. Theory of reproducing kernels
2. Inference from inadequate and inaccurate data I
3. Inference from inadequate and inaccurate data II
4. Inference from inadequate and inaccurate data III
5. The resolving power of gross earth data
6. Isotropic probability measures in infinite-dimensional spaces
7. Bayesian inference in geomagnetism
8. Comparing hard and soft prior bounds in geophysical inverse problems
9. Confidence set inference with a prior quadratic bound
10. Trimming and procrastination as inversion techniques
11. Linear inverse and ill-posed problems
12. Linear inverse problems with discrete data: I. General formulation and singular system analysis
13. Linear inverse problems with discrete data: II. Stability and regularization
14. Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data
15. Consistency of Bayes estimates for nonparametric regression: Normal theory
16. One-sided inference about functionals of a density
17. Exact asymptotic minimax risk for sup norm loss via optimal recovery
18. Statistical estimation and optimal recovery
19. Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
20. Maximum entropy and the nearly black object
21. Ideal spatial adaptation by wavelet shrinkage
22. Minimax estimation via wavelet shrinkage
23. Asymptotic minimaxity of wavelet estimators with sampled data
24. Wavelet shrinkage: Asymptopia? (with discussion)
25. Minimax quadratic estimation of a quadratic functional
26. Weak and strong consistency of the least squares estimators in regression models
27. Shrinkage estimators, Skorokhod's problem, and stochastic integration by parts
28. Well-posed stochastic extensions of ill-posed linear problems
29. Invariants under mixing which generalize de Finetti's theorem: Continuous time parameter
30. p misfit norms in linear inverse problems
31. Finite-sample confidence envelopes for shape-restricted densities
32. Estimation with quadratic loss
33. Wavelet threshold estimators for data with correlated noise
34. A wavelet shrinkage approach to tomographic image reconstruction
35. Maximum likelihood: An introduction
36. Consistent directions for least-squares estimates
37. A statistical perspective on ill-posed inverse problems
38. On methods of sieves and penalization
39. Inference in infinite-dimensional inverse problems: Discretization and duality
40. Minimax confidence intervals in geomagnetism
41. Inverse problems as statistics
42. Inadmissibility of the usual estimator of the mean of a multivariate normal distribution
43. Inverse problem theory
44. Statistical regnlarization of inverse problems
45. Bigger uncertainties and the big bang
46. Consistency for the least squares estimator in nonparametric regression
47. On inverse estimation
48. Characterizing the consistent directors of least squares estimates