Mathematical Modeling of Serial Data Modeling Serial Data Differs from simple equation fitting in that the parameters of the equation must have meaning.

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Presentation transcript:

Mathematical Modeling of Serial Data

Modeling Serial Data Differs from simple equation fitting in that the parameters of the equation must have meaning – Can be used to smooth – Can explain phenomena – Can be used to predict

Mathematical Modeling of Serial Data Steps in Mathematical Modeling Identification of the mechanism Translation of that phenomenon into a mathematical equation Testing the fit of the model to actual data Modification of the model according to the results of the experimental evaluation

Mathematical Modeling of Serial Data Criteria of Fit of the Model Least Sum of Squares Shape of the curve

Mathematical Modeling of Serial Data Examination of Residuals Residual = Actual Y - Predicted Y Ideally there is no pattern to the residuals. In this case there would be a horizontal normal distribution of residuals about a mean of zero. However there is a clear pattern indicating the lack of fit of the model.

Mathematical Modeling of Serial Data Ideal Characteristics of a Model Simple Fits the experimental data well Has biologically meaningful parameters

Modeling Growth Data

Mathematical Modeling of Serial Data National Centre for Health Statistics (N.C.H.S.)1970’s revamped as Center for Disease Control C.D.C. charts, 2001 Most often used clinical norms for height and weight Cross-sectional Clinical Growth Charts

Mathematical Modeling of Serial Data Preece-Baines model I where h is height at time t, h 1 is final height, s 0 and s 1 are rate constants, q is a time constant and h q is height at t = q.

Smooth curves are the result of fitting Preece- Baines Model 1 to raw data This was achieved using MS EXCEL rather than custom software

Examination of Residuals

Caribbean Growth Data n =1697