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Parameter Estimation & Model Fitting

Parameter Estimation & Model Fitting. More SAAMII Applications & Intro to DIMSUM. Experiment. Experimental point z is the sum y and z Variable y is the output of your model; deterministic Variable e is the error at any given point in time; stochastic. Parameters.

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Parameter Estimation & Model Fitting

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  1. Parameter Estimation & Model Fitting More SAAMII Applications & Intro to DIMSUM

  2. Experiment • Experimental point z is the sum y and z • Variable y is the output of your model; deterministic • Variable e is the error at any given point in time; stochastic

  3. Parameters • Microparameters: kij’s, Vi’s so far have been given • Macroparameters: Ai’s, lambdai’s derived from our kij’s, Vi’s and knowing the structure of the model

  4. DIMSUM • W3dimsum available online at http://biocyb.cs.ucla.edu • If working from home, must first d/l Java Start up and turn off proxy servers • Using a set of data (which one: z, y, or e?) finds the best macroparams (which are?) via WRSS (which is?)

  5. Curve peeling v. Marquardt • Used to fit the model to data • Curve peeling: page 353 in your reader; basically strips away the individual exp curves composing the composite curve • Marquardt: requires initial guesses, more expensive in computation time but more robust.

  6. WRSS as a determination of goodness of fit • Weighted Residual Sum of Squares • Minimizes residuals from the expected curve(s) (which is z,y,or e??)

  7. Information Criteria • Akaike Info Criterion • Schwartz Criterion • Also…F-test…RMS….see pps 357+ AIC and SC are closely related but weight residuals differently.

  8. Ready, set, go! • After starting W3DIMSUM, click on data and enter to start entering data values. • Enter number of data points and the t & z values. • Enter error model to be used….

  9. HUH? WHAT’S AN ERROR MODEL • Given z’s, the error model assigns how much “credit” should be given to the z’s, I.e. how closely they should match the y • Also, determines how points are weighted – why would more allowance, for example, be given to earlier data points??

  10. CV v. Var, Constant or not • CV: sd/mean • Var: sd squared • When would we choose to have error same for all data points? When no? • CV<10% is ok, <5% is even better.

  11. Now run the algorithms • Go to Models on the top bar and select automated modeling. • The program will automatically find the best macroparameters for 1, 2, 3, and 4 exponential models using the Curve-Peeling algorithm, followed by the Marquardt algorithm.

  12. Expert System • Expert system is like a little statistician in the program – analyzes AIC, etc and determines best fit • Notice that when you ran the error model you were given the Ai’s and lambdai’s.

  13. SAAMII and parameter estimation • Given a compartmental layout and ranges for your microparameters, you can determine microparameters that best fit your model • Again, uses CV, var, etc to determine how closely the model should fit the data

  14. How to do it… • Lay out model in compartments and fluxes. • Assign fixed or adjustable ranges (with an intial value) for all microparameters, including volume. • Open data window…

  15. Entering data • First line: DATA • Second line: error model (FSD f) for fractional standard deviation – 5% cv is equivalent to f=.05 • Third line: headers of columns: t, smple, etc • …data separated by spaces & enters • Last line: END • Close the window

  16. Fitting • Associate: go to show, then choose associations. Choose to associate s1, etc with whichever column you want. • Fit: click the red bar, and then the blue “fit” icon on the taskbar. • Clicking the values icon on gives your best fit parameters. Clicking on the sigma looking icon gives statistical breakdown.

  17. One last note about fit • Given a set of errors, the line best fit through them should ideally look like what? ?

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