Hi Phil, 2012/10/19 Phil Steitz <phil.ste...@gmail.com>: > On 10/19/12 12:20 AM, Sébastien Brisard wrote: >> Hi Phil, >> >>> that might also force us to implement some useful multivariate >>> integration algorithms :) >>> >> Is there any, general purpose multidimensional integration algorithm? >> MC would be flexible enough, but I doubt this would be efficient enough... >> How would you define the domain? Would you restrict it to products of >> intervals, or more general domains? > > I have not really looked into multivariate integration algorithms. > Note that we do not provide this convenience now for univariate > distributions (though I did recently add some integration tests that > verify consistency of the distribution and density impls). I would > define the cdf to take dimension vectors are arguments, so F(x_1, > ..., x_n) = P(X_1 <=x_1, ..., X_n <= x_n). Other things to > consider are marginal and conditional densities and distributions. > Here again, defaults could in theory be provided; but without > actually hacking some examples, I am not sure it is practical. > Even in one-d, I would not recommend that we implement a default integration scheme to be used in *all situations* on an unbounded integration domain (-infty, x]. Indeed, I think it will always be possible to find a distribution with a pdf which goes to zero so slowly as x tends to -\infty that our integration scheme fails (or is grossly in error). Or am I missing something?
Sébastien > > Phil >> >> Sébastien >> >> >> --------------------------------------------------------------------- >> To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org >> For additional commands, e-mail: dev-h...@commons.apache.org >> >> > > > --------------------------------------------------------------------- > To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org > For additional commands, e-mail: dev-h...@commons.apache.org > --------------------------------------------------------------------- To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org For additional commands, e-mail: dev-h...@commons.apache.org
