In an earlier post, I have explained how a Bayesian based method can replace standard chi-square technique. Since a Bayesian method is solely based on statistics, having a very few data points then has a significant consequence on the fit quality. To evaluate how reproduceble are the fit parameters (for a parabolic function),

I performed the following test: I created 10 data points and assumed given values for {** a**,

**,**

*b**}. The resulting y-values then formed a parabola. I added normal noise to both x and y axis. I let the PyMC run the Bayesian fit for 100 times. That means we have 100 solutions for each parameter. Then I repeated the identical experiment but this time, I assumed 100 data points rather than 10. The following plot show the scatter of data points for parameter*

**c***.*

**b**It is clear that with more input information, we can better constrain the parameters. In this particular example, the solutions with ten data points (blue circles) returned on average ** b**=4.39±0.78 while the ones with hundred data points (red circles) return a more accurate solution of

**=4.41±0.25.**

*b*