[R] boostrap astronomy problem

Gregory Ruchti gruchti at pha.jhu.edu
Mon Jan 2 18:29:01 CET 2006


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
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])))


#Compute Bootstrap replicates of escape velocity and kr
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

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

gruchti at pha.jhu.edu
Tel: (410)516-8520

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