## [ai-geostats] maximum likelihood

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• Hi One of methods to estimate variogram or covariance parameters is maximum likelihood. Likelihood function contains the term logarithm of determinant of
Message 1 of 2 , Jul 8, 2005
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Hi

One of methods to estimate variogram or covariance parameters is maximum likelihood. Likelihood function contains the term logarithm of determinant of covariance matrix.
My question:
Is it natural logarithm or base 10 log?

Recep

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• ... Apologies if anyone else has replied to the above and I ve overlooked it. 1. If you have a logarithm of that determinant then you are looking at the
Message 2 of 2 , Jul 14, 2005
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On 08-Jul-05 Recep kantarci wrote:
> Hi
>
> One of methods to estimate variogram or covariance parameters is
> maximum likelihood. Likelihood function contains the term logarithm of
> determinant of covariance matrix.
> My question:
> Is it natural logarithm or base 10 log?
>
> Recep

Apologies if anyone else has replied to the above and I've overlooked it.

1. If you have a logarithm of that determinant then you are looking
at the logarithm of the likelihood function, not the likelihood
function itself.

2. Usually it is the natural logarithm (to base e), but for maximisation
it doesn't matter what base it is since they differ by a constant
factor:

log_10(X) = log_e(X) x log_10(e)

so if you maximise one form you maximise the other.

3. However, when it comes to interpreting rates of variation of
the likelihood function in order to assess the precision of
estimates (e.g. minus the second derivatives of the log LF)
then it does matter: here you must use the batural logarithm
for the usual methods to be valid.

Hoping this helps,
Ted.

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Date: 14-Jul-05 Time: 20:16:11
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