# deinst

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 Jul19 awarded Yearling Jul19 awarded Yearling Apr7 answered Minimum of two exponential variates: What's wrong with this derivation? Apr7 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 $X$. Apr1 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). Apr1 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. Apr1 answered What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix? Mar31 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 $$f(\mathbf{X}|\mathbf\theta)=h(\mathbf{x})e^{\mathbf\theta^T\mathbf{X}-A(\mathb‌​f\theta)}.$$ 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. Mar22 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). Mar22 revised Results on Monte Carlo estimates produced by importance sampling fixed typos and lunch addled grammar Mar22 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.) Mar22 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. Mar21 answered Results on Monte Carlo estimates produced by importance sampling Mar21 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. Mar21 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. Mar4 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. Mar4 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. Mar4 answered Need help on Gibbs sampling with truncated normal and gamma Feb27 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. Feb25 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.