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Maximum likelihood estimate

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@B.Rabbit wrote:

We use MLE to estimate co-effecients in linear and logistic regression. As far as my understanding The basic intuition is that 'which parameter is most likely given the data'. It is mathematically defined as follows:

L(parameter | data) = P(data | parameter)
where L() is the likelihood function and P() is the probability.

I'm having trouble in understanding the above equation as it goes against the basic intuition. Shouldn't it be P(parameter | data)?

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