12. 02. 02 1 Non-linear Regression Analysis with

12.02.02 2 Agenda Introduction TGA Example NLR Basics Multicollinearity Prediction Testing Bayesian Estimation Conclusions

12.02.02 4 Linear and Non-linear Regressions Close relatives? 2

12.02.02 5 2. Thermo Gravimetric Analysis Example Let’s see it!

12.02.02 6 TGA Experiment and Data TGA Experiment TGA Data

12.02.02 7 TGA Example Variables Small size problem!

12.02.02 8 Plasticizer Evaporation Model Diffusion is not relevant!

12.02.02 9 Fitter Worksheet for TGA Example

12.02.02 10 Service Life Prediction by TGA Data

12.02.02 12 Data and Errors Weight is an effective instrument!

12.02.02 13 Model f(x,a) Presentation at worksheet Rather complex model!

12.02.02 14 Data & Model Prepared for Fitter Apply Fitter!

12.02.02 15 Objective Function Q(a) Parameter estimates Weighted variance estimate Objective function Q is

12.02.02 16 Very Important Matrix A Matrix A is the cause of troubles..

12.02.02 17 Quality of Estimation Matrix A is the measure of quality!

12.02.02 18 Search by Gradient Method Matrix A is the key to search!

12.02.02 20 Multicollinearity: View Multicollinearity is degradation of matrix A Objective function Q(a) 1

12.02.02 22 Data & Model Preprocessing ((a + b) + c) + d 

12.02.02 24 Derivative Calculation and Precision 1) Numerical calculation of difference derivatives

12.02.02 26 Reliable Prediction Forecast should include uncertainties!

12.02.02 27 Nonlinearity and Simulation Non-linear models call for special methods of reliable prediction!

12.02.02 28 Prediction: Example Accelerated aging tests Upper confidence limits Model of rubber aging

12.02.02 30 Hypotheses Testing Test statistics x is compared with critical value t (a)

12.02.02 31 Lack-of-Fit and Variances Tests These hypotheses are based on variances and they

12.02.02 32 Outlier and Series Tests These hypotheses are based on residuals and they

12.02.02 34 Bayesian Estimation How to eat away an elephant? Slice by slice!

12.02.02 35 Posterior and Prior Information. Type I The same error in each portion

12.02.02 36 Posterior and Prior Information. Type II Different errors in each portion of

12.02.02 37 8. Conclusions Mysterious Nature LR Model NLR Model Thank you!

Скачать презентацию 12. 02. 02 1 Non-linear Regression Analysis with

nelin_regressiya_excel_fitter_(1).ppt

Количество слайдов: 37

>12.02.02 1 Non-linear Regression Analysis with Fitter Software Application Alexey Pomerantsev Semenov Institute of 12.02.02 1 Non-linear Regression Analysis with Fitter Software Application Alexey Pomerantsev Semenov Institute of Chemical Physics Russian Chemometrics Society

>12.02.02 2 Agenda Introduction TGA Example NLR Basics Multicollinearity Prediction Testing Bayesian Estimation Conclusions 12.02.02 2 Agenda Introduction TGA Example NLR Basics Multicollinearity Prediction Testing Bayesian Estimation Conclusions

>12.02.02 3 1. Introduction 12.02.02 3 1. Introduction

>12.02.02 4 Linear and Non-linear Regressions Close relatives? 2 12.02.02 4 Linear and Non-linear Regressions Close relatives? 2

>12.02.02 5 2. Thermo Gravimetric Analysis Example Let’s see it! 12.02.02 5 2. Thermo Gravimetric Analysis Example Let’s see it!

>12.02.02 6 TGA Experiment and Data TGA Experiment TGA Data 12.02.02 6 TGA Experiment and Data TGA Experiment TGA Data

>12.02.02 7 TGA Example Variables Small size problem! 12.02.02 7 TGA Example Variables Small size problem!

>12.02.02 8 Plasticizer Evaporation Model Diffusion is not relevant! 12.02.02 8 Plasticizer Evaporation Model Diffusion is not relevant!

>12.02.02 9 Fitter Worksheet for TGA Example 12.02.02 9 Fitter Worksheet for TGA Example

>12.02.02 10 Service Life Prediction by TGA Data 12.02.02 10 Service Life Prediction by TGA Data

>12.02.02 11 3. NLR Basics 12.02.02 11 3. NLR Basics

>12.02.02 12 Data and Errors Weight is an effective instrument! 12.02.02 12 Data and Errors Weight is an effective instrument!

>12.02.02 13 Model f(x,a) Presentation at worksheet Rather complex model! 12.02.02 13 Model f(x,a) Presentation at worksheet Rather complex model!

>12.02.02 14 Data & Model Prepared for Fitter Apply Fitter! 12.02.02 14 Data & Model Prepared for Fitter Apply Fitter!

>12.02.02 15 Objective Function Q(a) Parameter estimates Weighted variance estimate Objective function Q is 12.02.02 15 Objective Function Q(a) Parameter estimates Weighted variance estimate Objective function Q is a sum of squares and may be more…

>12.02.02 16 Very Important Matrix A Matrix A is the cause of troubles.. 12.02.02 16 Very Important Matrix A Matrix A is the cause of troubles..

>12.02.02 17 Quality of Estimation Matrix A is the measure of quality! 12.02.02 17 Quality of Estimation Matrix A is the measure of quality!

>12.02.02 18 Search by Gradient Method Matrix A is the key to search! 12.02.02 18 Search by Gradient Method Matrix A is the key to search!

>12.02.02 19 4. Multicollinearity 12.02.02 19 4. Multicollinearity

>12.02.02 20 Multicollinearity: View Multicollinearity is degradation of matrix A Objective function Q(a) 1 12.02.02 20 Multicollinearity: View Multicollinearity is degradation of matrix A Objective function Q(a) 1 N(A) = 2 4 5 6 7

>12.02.02 21 Multicollinearity: Source 12.02.02 21 Multicollinearity: Source

>12.02.02 22 Data & Model Preprocessing ((a + b) + c) + d  12.02.02 22 Data & Model Preprocessing ((a + b) + c) + d  a + (b + (c + d)) as 1+10 –20 = 1

>12.02.02 23 Example: The Arrhenius Law 12.02.02 23 Example: The Arrhenius Law

>12.02.02 24 Derivative Calculation and Precision 1) Numerical calculation of difference derivatives 12.02.02 24 Derivative Calculation and Precision 1) Numerical calculation of difference derivatives

>12.02.02 25 5. Prediction 12.02.02 25 5. Prediction

>12.02.02 26 Reliable Prediction Forecast should include uncertainties! 12.02.02 26 Reliable Prediction Forecast should include uncertainties!

>12.02.02 27 Nonlinearity and Simulation Non-linear models call for special methods of reliable prediction! 12.02.02 27 Nonlinearity and Simulation Non-linear models call for special methods of reliable prediction!

>12.02.02 28 Prediction: Example Accelerated aging tests Upper confidence limits Model of rubber aging 12.02.02 28 Prediction: Example Accelerated aging tests Upper confidence limits Model of rubber aging

>12.02.02 29 6. Testing 12.02.02 29 6. Testing

>12.02.02 30 Hypotheses Testing Test statistics x is compared with critical value t (a) 12.02.02 30 Hypotheses Testing Test statistics x is compared with critical value t (a) Test don’t prove a model! It just shows that the hypothesis is accepted or rejected!

>12.02.02 31 Lack-of-Fit and Variances Tests These hypotheses are based on variances and they 12.02.02 31 Lack-of-Fit and Variances Tests These hypotheses are based on variances and they can’t be tested without replicas! Lack-of-Fit is a wily test!

>12.02.02 32 Outlier and Series Tests These hypotheses are based on residuals and they 12.02.02 32 Outlier and Series Tests These hypotheses are based on residuals and they can be tested without replicas Series test is very sensitive!

>12.02.02 33 7. Bayesian Estimation 12.02.02 33 7. Bayesian Estimation

>12.02.02 34 Bayesian Estimation How to eat away an elephant? Slice by slice! 12.02.02 34 Bayesian Estimation How to eat away an elephant? Slice by slice!

>12.02.02 35 Posterior and Prior Information. Type I The same error in each portion 12.02.02 35 Posterior and Prior Information. Type I The same error in each portion of data!

>12.02.02 36 Posterior and Prior Information. Type II Different errors in each portion of 12.02.02 36 Posterior and Prior Information. Type II Different errors in each portion of data!

>12.02.02 37 8. Conclusions Mysterious Nature LR Model NLR Model Thank you! 12.02.02 37 8. Conclusions Mysterious Nature LR Model NLR Model Thank you!