Environmental Data Analysis with MatLab

5. Quantifying preconceptions

5.1 When least square fails83

5.2 Prior information84

5.3 Bayesian inference86

5.4 The product of Normal probability density distributions88

5.5 Generalized least squares90

5.6 The role of the covariance of the data92

5.7 Smoothness as prior information93

5.8 Sparse matrices95

5.9 Reorganizing grids of model parameters98

Problems101

References102

Chapter 5, Quantifying Preconceptions, argues that we usually know things about the systems we are studying that can be used to supplement actual observations. Temperatures often lie in specific ranges governed by freezing and boiling points. Chemical gradients often vary smoothly in space, owing to the process of diffusion. Energy and momentum obey conservation laws. The methodology ...