deinst

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	725 reputation	bio	website		visits	member for	2 years, 10 months
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Jul 19	awarded	Yearling
Apr 7	answered	Minimum of two exponential variates: What's wrong with this derivation?
Apr 7	comment	Minimum of two exponential variates: What's wrong with this derivation? The distribution of $X$ conditional on the fact that it is less than $Y$ is not the same as the distribution of $X$.
Apr 1	comment	What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix? @Xi'an You are correct, I did not process them as parameters of the exponential family. Doing so would have made the family no longer a natural family, and including them would have just muddled the algebra for comuting the moment equations (which was muddled enough to begin with).
Apr 1	comment	What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix? @xian There are the 6 exponents $e_i$ and $f_i$ as well.
Apr 1	answered	What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix?
Mar 31	comment	What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix? One way of slighly extending this is to consider the natural exponential family $$f(\mathbf{X}\|\mathbf\theta)=h(\mathbf{x})e^{\mathbf\theta^T\mathbf{X}-A(\mathb‌f\theta)}.$$ Then the mean and covariance are the gradient and Hessian of $A$. If $h$ is a polynomial (with real exponents > -1) then $A$ is the log of a polynomial (with real exponents), and the variance and Hessian are rational functions. I think this gives enough freedom to represent any mean and covariance matrix.
Mar 22	comment	Results on Monte Carlo estimates produced by importance sampling @Xi'an You are quite welcome. (In case it is not clear, I meant no offense. Quite the opposite).
Mar 22	revised	Results on Monte Carlo estimates produced by importance sampling fixed typos and lunch addled grammar
Mar 22	comment	Results on Monte Carlo estimates produced by importance sampling @BerkUstun The capital G is a typo for a small that I will fix promptly. X/Y is just a generic ratio of random variables. IIRC all this is explained in Liu's Monte Carlo book (something with scientific in the title.)
Mar 22	comment	What is the probability of rolling all faces of a die after n number of rolls this is crossposted to math.se. Also the fractions in brackets are flipped.
Mar 21	answered	Results on Monte Carlo estimates produced by importance sampling
Mar 21	comment	Results on Monte Carlo estimates produced by importance sampling Even if this was not the OP's intention, I would be interested in some pointers on how to figure out when self-normalization will go horribly wrong.
Mar 21	comment	Results on Monte Carlo estimates produced by importance sampling I suspect, given that the OP is reporting small variance estimators that are biased, but seem to have small variance, that he may be asking about self normalized importance sampling. See Radford Neal's rant on the Harmonic mean estimator for a good example, that takes what would be an importance sampling estimate with 0 variance, and returns nonsense. I am not certain that this does not ever occur in regular importance sampling, but it is certainly rare.
Mar 4	comment	Need help on Gibbs sampling with truncated normal and gamma In your case with mean $\beta$ and variance $1/\lambda$, you truncate at 0 and $\infty$. So after translating to the standard normal your $a$ and $b$ are $-\beta\sqrt{lambda}$ and $\infty$ respectively. You will note that $1-\Phi(-\beta\sqrt{\lambda})$ occurs in the denominator of your function. Just as an aside, it would probably be well worth your while spending a week or so reviewing your probability. If you are playing in this swamp without a good knowledge of the distributions and transformations, the alligators are going to eat you alive.
Mar 4	comment	Need help on Gibbs sampling with truncated normal and gamma Yes, sort of. I am working with standard normals, it is just a linear transformation to get to any other normal.
Mar 4	answered	Need help on Gibbs sampling with truncated normal and gamma
Feb 27	comment	How to compute importance sampling? @Xi'an Sorry to bother you again, but your definition of `h` contain the t distribution, when it should just have the $\sqrt{\|x/(1-x)\|}$. This causes all the estimates to be off because you are multiplying by f^2 instead of f. The approximations should be around 1.015, while they are around 0.25.
Feb 25	comment	How to compute importance sampling? The problems with the variance are akin to the game where you win $2^n/n$ dollars with probability $2^{-n}$. The expected payout may be infinite, but I am not about to sell my house to play. With the folded gamma there will be large excursions, but they will be extremely rare. In practice using $\frac{\sum hf/g}{\sum f/g}$ with the folded gamma performs worse, although in theory it has finite variance.
Feb 25	comment	How to compute importance sampling? Here the definition of `sam3` takes 5 times as many samples as the other tests. This makes the folded Gamma look better than the Cauchy-power mixture, while the reverse is true. The folded Gamma estimator has infinite variance, while the Cauchy-power mixture does not.