Likelihood of some points fitting a derived function....

[Silviu]

Hello! I have some concentrical spheres with many points inside. And I need to plot the total mass of points in each shell (so between 2 spheres) versus the radius of that shell (defined as (r1+r2)/2, where r1 and r2 are the radius of the 2 spheres forming the shell). I have 10 shells so my plot has 10 points and I want to fit them with a certain function and I need to calculate the likelihood associated with this fitting function. But for this, I need a sigma and I don't know what exactly would that be. So i know the mass, radius and number of points in each shell. I thought to take the error something like sqrt(number of particles) but I am not sure. What should I do to calculate the likelihood?

Thank you!

 

[Stephen Tashi]

I need to calculate the likelihood associated with this fitting function.

What is the probability model for the situation ?

Unless you can state a mathematical model, you'll only get vague and general advice.

"Liklihood" is technical term in statistics, and I don't know whether you intend to use it in a technical sense. It isn't clear what random variable you are talking about when you speak of "sigma". If the data in each shell follows a different probability distribution, the data in different shells might be realization of different random variables, each with its own standard deviation.

 

[chiro]

Hey Silviu.

You should provide the model you want to use to fit the data and then provide the assumptions for the original data you are using.

After that, it's a matter of going through the steps [either using things like Central Limit Theorem if you have lots of data or using specific techniques if this is isn't the case].