# PCE - Method to calculate coefficients

When I decrease the sample size each method to calculate the polynomial coefficients shows improvement (i.e., better agreement between the Ypc and Ytrue). Why? That was unexpected.

Dear @Pilgrim

There are many reasons why this could happen. The information you present is too little to make a clear statement. Please provide more information about your experimental design:

• size
• input distributions
• how you obtained/collected the data

You can also provide information about the problem you are solving and the output you are collecting.

Best regards
Styfen

Dear Styfen,

I believe I answered those questions in the previous post. I am trying to use the PCE method to predict the ignition delay time based on a temperature input. I want to include the uncertainty in the temperature measurements, the uncertainty in A and the uncertainty in E. Note that A and E are determined from the measured data and using a curve fit. After a curve fit is applied the y-intercept is the ln(A) and the slope is -E/R.

I noticed that when I decreased the sample size the approximations of the ignition delay time from the PCE method are in better agreement with the true value as calculated using the Arrhenius equation. This is true for each method used to calculate the coefficients of the PCE.

Pilgrim

Dear Styfen,
I was wondering if you had suggestions on possible solutions based on the additional information I provided. Also, I noticed the PCE will provide approximations that are negative values (physically impossible). Is it possible to limit the PCE approximations to only positive values?
Pilgrim

Dear @Pilgrim

I am trying to use the PCE method to predict the ignition delay time based on a temperature input.

To me it looks like you’re confusing inverse and forward uncertainty quantification.
You gave analytical expression for this here: PCE - Why is coefficient of variance and standard deviation so high?. If I understand your goal correctly, then there is no need to construct a PCE. Please have a look at inverse UQ and reconsider if what you’re trying to do/you’re describing makes sense. You may find this UQLab manual helpful:

Best regards
Styfen