Sampling of data by applying Kernel Density Function to a sparse set of data

Dear all

Aim: To have a stochastic value of Y by sampling it using available data.

Let's say I have a function Y which depends on variable a and b.

1. Data from a is simulated

2. Data from b is from experiments

3. Y must be larger than 1 (However some values are lesser than 1)

In these images, these are data provided by a journal and Y value is determined from an analytical model provided by the journal. As you can see, the data at high a and b values are sparse and little. This leads to high variance if I were to sample a random value of Y with given values of a and b.

From what I understood of Kernel Density Estimation, a Guassian could be set for the kernel. From this gaussian, I will be able to sample Y from a given a and b value. But I'm not sure on how to go about doing this.

I took a look at Zdravko Botev scripit on Kernel Density Estimation, but sadly to say, I do not konw how to implement it. What it returns is a estimated density at a point, so how can I make use of this estimated density to sample a Y value?

https://www.mathworks.com/matlabcentral/fileexchange/58312-kernel-density-estimator-for-high-dimensions

Is there any reccomendation on how to approach this problem?

Many Thanks!!!