Conditional sampling from multivariate normal distribution
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From: Peter Perkins on 12 Apr 2010 15:22 On 4/12/2010 1:43 PM, Tomaz wrote: > Could you please just tell > me what would be 'statistical expression' that describes my problem the > best? Is it 'Conditional sampling', 'Conditional distributions' or > something else? Any synonyms/ alternatives? I am asking this to be able > to search for related data more efficiently... I would think either of those, plus perhaps a "multivariate normal". The same simple result does not hold for MVT, for example.
From: Tomaz on 20 Apr 2010 17:46 Peter Perkins <Peter.Perkins(a)MathRemoveThisWorks.com> wrote in message <hpvrtp$iun$1(a)fred.mathworks.com>... > On 4/12/2010 1:43 PM, Tomaz wrote: > > > Could you please just tell > > me what would be 'statistical expression' that describes my problem the > > best? Is it 'Conditional sampling', 'Conditional distributions' or > > something else? Any synonyms/ alternatives? I am asking this to be able > > to search for related data more efficiently... > > I would think either of those, plus perhaps a "multivariate normal". The same simple result does not hold for MVT, for example. I tried really hard to understand the formulas and solve my problem, but I get stuck. Peter (or anybody else), I would really appreciate if you would point out where I go wrong. I tried to follow your directions and Wiki page, but this happens (look below). Should I change anything because of row/ column vector thing? mu=mean (origData) mu1=mu (1) mu2 = mu (2:4) sigma = cov (origData) sigma11 = sigma (1:1, 1:1) sigma12 = sigma (1:1, 2:4) sigma21 = sigma (2:4, 1:1) sigma22= sigma (2:4, 2:4) sigma1_2 = sigma11 - sigma21*(sigma22\sigma12) ??? Error using ==> mldivide Matrix dimensions must agree.
From: Peter Perkins on 20 Apr 2010 18:38 On 4/20/2010 5:46 PM, Tomaz wrote: > sigma1_2 = sigma11 - sigma21*(sigma22\sigma12) > ??? Error using ==> mldivide > Matrix dimensions must agree. My fault, I think. All of these are equivalent: sigma1_2 = sigma11 - sigma12*(sigma22\sigma21) sigma1_2 = sigma11 - (sigma12/sigma22)*sigma21 sigma1_2 = sigma11 - sigma12*inv(sigma22)*sigma21
From: Roger Stafford on 20 Apr 2010 19:56 "Tomaz " <tomaz.bartolj(a)gmail.com> wrote in message <hpvif0$9ih$1(a)fred.mathworks.com>... > ...... > To illustrate: I have 5 attributes (independent variables) all together and I build multivariate normal distribution based on dataset consisting of 999 data points. > ........ > Peter thanks, but is is this also useful when dealing with more than 2 independent variables? > ....... Tomaz, I would like to point out one assertion you made which I don't think you really meant. In the first two articles you said, "To illustrate: I have 5 attributes (independent variables) all together and I build multivariate normal distribution based on dataset consisting of 999 data points" and "is this also useful when dealing with more than 2 independent variables?" I don't think you really meant that these were independent variables. If they were actually independent, then the conditional probability distribution of the one variable given other variables' values would be the same as its unconditional distribution. I suspect you really meant to say "jointly normal". That's the assumption you do need. Roger Stafford
From: Tomaz on 22 Apr 2010 11:30
Peter Perkins <Peter.Perkins(a)MathRemoveThisWorks.com> wrote in message <hqmtpg$pab$1(a)fred.mathworks.com>... > On 4/21/2010 6:13 AM, Tomaz wrote: > > @Peter: so I just change the sequence of calculations so that dimensions > > match. Otherwise I am on the right track. > > As per my most recent post. > > And about sigmas: > > basically sigma11 is the element at coordinates (i,i) - given I always > > condition on n-1 variables. > > sigma12 is row i of sigma without element in column i > > sigma21 is column i of sigma without element in row i > > sigma22 is everything else. > > And there is no issue of column/ row vectors here, since sigma is > > diagonally symmetrical? > > Only that you need the right one in the right place. But yes, sigma12 is just sigma21', and that will be true regardless of how many variables you (don't) condition on. Peter, sorry I don't quite get the meaning of this comment: "Only that you need the right one in the right place." What do you mean by that? I have values for each independent variable in columns of a matrix. Than I simply obtain mu row vector by funtion mean() and I get the covariance matrix with function cov(). I save subsections of the covariance matrix to variables sigmaIJ as described above. Is there something else that I should watch for? |