Aim: Sample

*Y*value using available data.

Let's say I have a function

*which depends on variable*

**Y***and*

**a***.*

**b**1. Data from

*simulated*

**a**is2. Data from

*is from experiments*

**b***3.*is always larger than 1.

**Y**In this image, these are data provided by a journal and

*value is determined from an analytical model provided by the journal. As you can see, the data at high*

**Y***and*

**a***values are sparse and little.*

**b**Initially, I have tried to bin the data into segments and fit a Gaussian distribution into the data which looks like this. The colour plot is a Gaussian fit.

After I have done the binning, I tried to obtain the variance for each bin.

With the analytical model as mean value and the variance for

**and**

*a***I could then sample Y using my own simulation of**

*b,**and experimental value*

**a****As you can expect, if my**

*b.***and**

*a***value is high, this would relate to a large variance. My sampled**

*b***Y**value could be a negative number. So, I have tried to sample my

**with a truncated Gaussian with condition >1. However, this is still not a good result as expected.**

*Y*Is there any suggestion of how I could sample

**with these sparse data that is available?**

*Y*Thank you.