calculating or knowing the bias of a simulation

Hello,

I am using Matlab to estimate a probability distribution function using histograms with a bin side of 0.05 on the interval [-10,10]. The density is estimated by varying the number of samples, n. If the number is too few, then it is just a bunch of random impulses that show up in the histogram.

I increased the number of samples, n, in the range from 50 to 50million. I noticed that upon increasing it, the variance of the distribution becomes larger as well. I realized this is part of the 'bias variance trade off'.

My question is, how to calculate bias in this kind of experiment? And I what is the 'right amount of sample' so that bias and variance is just enough so that error is a minimum?

[Tugce TOPRAK]

Hi cgo,

It's been a long time since you asked this question. But, i've tried to find out same problem and found an example demo. I hope it is helpful for everyone. Thanks to Sai Ravela who is the instructor of Quantifying Uncertainty and writer of the code.

http://ecovision.mit.edu/~sai/12S990/bvdemo.html