## Generation and analysis of data in non-linear situations |

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analysis Bayes Box and Lucas calculated carbon dioxide Chapter chemical common variance r2 condition 1.18 confidence region consider contour diagram correlation current least squares degrees of freedom depend derivatives design matrix design vectors desirable dispersion matrix distribution after N+l elements equivalent to maximizing estimation situation example experimental conditions experimental design experimental points experimental variables factor space factorial design further given inadequate iterative kinetics least squares estimates likelihood function linear least squares locally uniform Lucas 19 maximize the determinant maximum likelihood estimates mechanism methane method minimize model is adequate model-building mole fraction N+l N+l N+l observations non-linear least squares non-linear situations obtain the t-distribution overall criterion parameter space parameters 9 planning experiments portmanteau criterion possible posterior distribution prior distribution problem quantities reactant reaction sequential design stage sum of squares Suppose three parameters true values u-th run u=l u=l unbiassed estimates variance-covariance matrix