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From: Peter Perkins on 22 Apr 2010 13:19
On 4/22/2010 11:30 AM, Tomaz wrote:

>> 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?

All I meant was "sigma11 - (sigma12/sigma22)*sigma21", and not "sigma11 - sigma21*(sigma22\sigma12)". And that even when you are generating conditional random values for more than one variable, sigma12 and sigma21 are always transposes of each other. Just not necessarily vectors.
From: Peter Perkins on 21 Apr 2010 09:15
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.

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