No. Maximum likelihood estimation does not involve a prior over parameters, and the MLE does not depend on how the parameters are represented, nor does it depend on the way the variables are represented.
For example, the maximum likelihood estimate for a variance parameter is just the square of the maximum likelihood estimate for the corresponding standard deviation parameter, as you'd expect. And the maximum likelihood estimate for the parameters of a log-normal distribution for positive data are related in the obvious way to the maximum likelihood estimate for the parameters of a normal distribution for the logs of those data points.
Doing a 1-to-1 continuous transformation of the data causes the probability density (for any given parameter values) to be multiplied by a Jacobian factor, but this factor depends only on the data values, NOT on the probability density (determined by the parameters), so the MLE for the transformed data is the same as for the untransformed data.
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No. Maximum likelihood estimation does not involve a prior over parameters, and the MLE does not depend on how the parameters are represented, nor does it depend on the way the variables are represented.
For example, the maximum likelihood estimate for a variance parameter is just the square of the maximum likelihood estimate for the corresponding standard deviation parameter, as you'd expect. And the maximum likelihood estimate for the parameters of a log-normal distribution for positive data are related in the obvious way to the maximum likelihood estimate for the parameters of a normal distribution for the logs of those data points.
Doing a 1-to-1 continuous transformation of the data causes the probability density (for any given parameter values) to be multiplied by a Jacobian factor, but this factor depends only on the data values, NOT on the probability density (determined by the parameters), so the MLE for the transformed data is the same as for the untransformed data.
Agreed - great reply.