Page 8 - Numerical Methods for Chemical Engineering

viii Contents

MATLAB summary 364
Problems 365

8 Bayesian statistics and parameter estimation 372
General problem formulation 372
Example. Fitting kinetic parameters of a chemical reaction 373
Single-response linear regression 377
Linear least-squares regression 378
The Bayesian view of statistical inference 381
The least-squares method reconsidered 388
Selecting a prior for single-response data 389
Confidence intervals from the approximate posterior density 395
MCMC techniques in Bayesian analysis 403
MCMC computation of posterior predictions 404
Applying eigenvalue analysis to experimental design 412
Bayesian multi response regression 414
Analysis of composite data sets 421
Bayesian testing and model criticism 426
Further reading 431
MATLAB summary 431
Problems 432

9 Fourier analysis 436
Fourier series and transforms in one dimension 436
1-D Fourier transforms in MATLAB 445
Convolution and correlation 447
Fourier transforms in multiple dimensions 450
Scattering theory 452
MATLAB summary 459
Problems 459

References 461

Index 464