Page 475 - Numerical Methods for Chemical Engineering

Index

A-conjugacy 222 Example. fitting the kinetic parameters of a
Aliasing 446 chemical reaction
Arc length continuation 203 fitting kinetic parameters to rate data by
Example. multiple steady states in a nonisothermal transformation to linear model 380
CSTR 204–206 fitting rate constant and generating CI from
Augmented Lagrangian method 231–240 dynamic reactor data 402
Automatic mesh generation 300–303 fitting rate constant to multiresponse kinetic data
Delaunay tessellation (see also Delaunay 418–419
tessellation) 303 MCMC analysis of elementary reaction
Voronoi polyhedra (see also Voronoi polyhedra) hypothesis 411
303 MCMC generation of CI for rate constant from
multiresponse data 420–421
Balances MCMC rate constant fitting and CI generation
constitutive equation 259 from composite data set 422–426
control volume 258 Gauss-Markov conditions 384
field 258 general problem formulation 372–373
macroscopic 259 hypothesis testing 426–427
microscopic 259 Bayes’ factor 427
Bayesian statistics 372–432 probability of hypothesis being true as posterior
Bayes’ factor 427 expectation 403
Bayes’ theorem 321, 382–383 likelihood function 386, 415
Bayesian Information Criterion (BIC) of Schwartz Markov Chain Monte Carlo (MCMC) simulation
430 Metropolis-Hastings sampling 404
Bayesian view of statistical inference 381–387 multiresponse data 419–421
composite data sets 421–426 single-response data 403–411
marginal posterior for model parameters model parameters 372
422 model selection 428
Credible (Confidence) Interval (CI) 397 multiresponse regression 414–421
approximate analytical CI for single-response definition 372
data 395–399; for model parameters 398; for fitting by simulated annealing 417–419
predicted responses 399 likelihood function 415
calculation of Highest Probability Density (HPD) marginal posterior for model parameters 415
CI’s 409–411 Markov Chain Monte Carlo (MCMC) simulation
MATLAB nlparci 401 419–421; calculation of highest probability
MATLAB nlpredci 401 density (HPD) CI’s 420; calculation of
MATLAB norminv 397 marginal posterior densities 420; calculation
outliers 399 of posterior expectations 419
design matrix noninformative prior 415
for linear regression 377 posterior density 415
linearized for nonlinear regression 389 sum of squared errors matrix 412
eigenvalue analysis; Principle Component Analysis posterior probability distribution 385
(PCA) 412–414 marginal posterior density 395; for
Example. comparing protein expression levels of multiresponse data 415; kernel method 407;
two bacterial strains nuisance parameter 395
as linear regression problem 380–381 multiresponse data 415
MCMC analysis of hypothesis 406–407 single-response data 394
MCMC calculation of marginal posterior density predicted responses 377
408–409 predictor variables 372

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