This video introduces the maximum likelihood estimator (MLE) technique
as a way of determining a good estimator for a given probabilistic
problem. This method is very straightforward and intuitive, and the
video motivates the approach by considering again how the likelihood
function is formed. The properties of the MLE is discussed, and it is
noted that many of the caveats and tricks used in optimisation theory
simply apply to maximising the likelihood function. An example is shown
for finding the MLE for estimating the mean of a Gaussian distributed
set of data. This, of course, equals the minimum variance unbiased
estimator (MVUE) since, as we know from a previous video, the MVUE
exists. Finally, the video considers the MLE for a transformed
parameter, and its application to, for example, calculating the
signal-to-noise ratio (SNR) (although a detailed solution is saved for
other exercises for the viewers).
PGEE11164 Probability, Estimation Theory, and Random Signals Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
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