[R] boostrap astronomy problem

From: Gregory Ruchti <gruchti_at_pha.jhu.edu>
Date: Tue 03 Jan 2006 - 04:29:01 EST


I am an astronomer and somewhat new to boostrap statistics. I understand the basic idea of bootstrap resampling, but am uncertain if it would be useful in my case or not. My problem consists of maximizing a likelihood function based on the velocities of a number of stars. My assumed distribution of velocities of these stars is:


where x would be my stellar velocities. (Essentially it is a beta distribution.)

My likelihood function looks something like this:
	log(e) - n*log(k+1) + (k+1)*n*log(e-t)-k*sum(log(e-vg))

The quantities n and t are known, and vg is my velocity data. I am minimizing this function using the function "optim" (BFGS option) to find k and e that minimize this. Also, my data set is small, only about 50 stars. Therefore, I was thinking that I could use the boot function to resample my data and solve the minimization for each resample. This way I believe I'll get better estimates for standard errors and confidence intervals. Is it safe to assume that the distributions for k and e are approximately Normal, therefore making the bootstrap useful? I have actually used the boot function with this set up:

	#Negative Log Likelihood Function
   		log(e) - n*log(k+1) + (k+1)*n*log(e-t) -

	#Gradient of Negative Likelihood Function
   		c(1/e + (k+1)*(n/(e-t)) - k*sum(1/(e-s[b])),-n/(k+1) +
			n*log(e-t) - sum(log(e-s[b])))

optim(c(480.,2.),lm,glm,method="BFGS",control=list(maxit=10000000))$par }

#Compute Bootstrap replicates of escape velocity and kr m2B2=boot(vg,mystat,5000)

Does this appear to be correct for what I'd like to achieve? I have looked at the distribution and it appears to be about Normal, but can I say that this is true for the sampling distribution as well? Also, the bootstrap distribution is fairly biased, should I be using "bca" or tilted bootstrap confidence intervals? If so, I am having some trouble getting the tilted bootstrap to work. Specifically, it is having trouble finding "multipliers".

Also, should I be in some way taking into account my velocity distribution when resampling? Any suggestions would be very helpful, thanks.

Thank you for your time.

Greg Ruchti

Gregory Ruchti
Bloomberg Center for Physics and Astronomy
Johns Hopkins University
3400 N. Charles St.
Baltimore, MD 21218-1216

Tel: (410)516-8520

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Received on Tue Jan 03 04:34:13 2006

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