Poisson errors for the distribution of galaxies?

[taylrl3]

Poisson errors for the distribution of galaxies??

Hi,

I have some data regarding the distribution of galaxies of varying mass in different density regions of the Universe, from which I have a mass functions for each region. I would now like to introduce some errors so I can determine whether changes in the mass function with density are significant or not. I have been told that the errors I need to use are Poisson errors though I am not sure how to implement these. Does anyone have an idea? Your help is most appreciated.

Thanks!
Taylrl

 

[taylrl3]

I am searching around and I think they are Poisson errors due to the fact that my axis use a log scale. Is this the case? :-s

 

[taylrl3]

I have found somewhere in another post on another site that when using binned data such as mine then the Poisson error on counting statistics is sqrt(N). Is it literally as simple as this as some places have very complex explanations of what the Poisson error is?

 

[SW VandeCarr]

I have found somewhere in another post on another site that when using binned data such as mine then the Poisson error on counting statistics is sqrt(N). Is it literally as simple as this as some places have very complex explanations of what the Poisson error is?

The Poisson distribution (PnD) is a single parameter distribution where both the mean and the variance is expressed by the parameter $$\lambda$$. The standard deviation (or error) is just the square root of lambda. The square root of the estimate of lambda from a sample is called the standard error of the mean. The PnD is typically skewed in inverse relation to the number of observations. With a larger number of observations the PnD approaches the binomial distribution, a discrete distribution which approximates the (continuous) Gaussian.

Lambda is easily estimated by:

$$1/n \sum_{i=1}^{n} k_{i}$$

The fact that lambda is both the mean and variance is useful in judging Poisson "noise".

I don't know your specific application but I'm guessing it has to do with using some kind of grid for measuring galactic densities over different regions of space. I don't know what the model is (large scale uniform, lower scale possibly Gaussian) but the PnD would be best suited for small numbers, typically less then 20 observations. One feature of the PnD that could be helpful is that the mass function can assign useful (not vanishingly small) probability estimates to 0 data values of n (no observations in a grid square) .

 

[bpet]

Hi,

I have some data regarding the distribution of galaxies of varying mass in different density regions of the Universe, from which I have a mass functions for each region. I would now like to introduce some errors so I can determine whether changes in the mass function with density are significant or not. I have been told that the errors I need to use are Poisson errors though I am not sure how to implement these. Does anyone have an idea? Your help is most appreciated.

Thanks!
Taylrl

For data of the form "Region 1 has galaxies of masses {x1,...,xm} and Region 2 has galaxies of mass {y1,...,yn}" consider a two-sample KS test (or AD etc).

The Poisson suggestion may have come from an inhomogeneous spatial Poisson model of galaxy coordinates which I'm not sure is immediately applicable here.

 

[SW VandeCarr]

I don't know much astrophysics and I'm not sure if bpet's or my responses were helpful. If the Poisson error is appropriate, I've found a few references relative to galactic distributions, but I think both of us would like to hear from you regarding your question first.