What is MLE?

Abstract

Chris and Fred discuss the three-letter acronym ‘MLE’ stands for? Well, it stands for ‘maximum likelihood estimate.’ Ever heard of it? Do you know what it means?

Key Points

Join Chris and Fred as they discuss what the MLE or ‘maximum likelihood estimate’ means … usually when using software to conduct data analysis.

Topics include:

What does ‘likelihood’ mean? Most models (like the bell curve, lognormal distribution, and so on) are defined by parameters. For example, the two parameters that define the bell curve are (1) the mean and (2) standard deviation. So these two parameters entirely describe the shape of the bell curve. Now let’s say you have 20 data points from some random process. What is the ‘likelihood’ that a bell curve with a mean of 10 and a standard deviation of 2 ‘fits’ your data? It has been found that if we plot out all 20 data points under this bell curve we think might fit the data, and then draw lines up from each data point to the bell curve shape … and then multiply those heights – we get the ‘likelihood’ that the bell curve fits your data. Or perhaps more correctly, we get a number that represents the ‘likelihood’ that the bell curve models the random process that gave us those 2o data points.
What does ‘maximum likelihood estimate’ mean? Let’s say we are not sure if the bell curve above, or another bell curve with a mean of 9.5 and standard deviation of 1.5 is a good fit. Well … we can go through the same process for the other bell cruve, and come up with another number that represents its ‘likelihood.’ Now we can try all possible combinations of means and standard deviations and come up with likelihoods for each. Computers are good at this, and they can (for example) work out that a bell curve with a mean of 9.76234… and standard deviation of 1.8986… will have the highest likelihood of all possible bell curves. This is the ‘maximum likelihood estimate.’
It’s just another way of coming up with our ‘best fit’ or ‘best guess.’ Other approaches involve ‘regression analysis’ or ‘root mean square analysis’ where we find a line that minimizes the squares of the ‘residual’ distances between candidate lines of best fit and the data points.
So my software package allows me to choose from lots of different options … including MLE … which should we use? WHAT DECISION ARE YOU TRYING TO MAKE? There are no absolute guidelines that work for every scenario. The first question you should ask is … do you need the ‘best guess’ of something or the region within which you are ‘confident’ that something lies? For example, the ‘best guess’ at your item’s time to failure might be 5.4 years. But you might only be 95 % confident that the time to failure will exceed 1.9 years. If you are trying to understand the likelihood that your item will fail within a 2-year warranty period, you might not be interested in your best guess, but instead be interested in a 95 % confidence region.

Enjoy an episode of Speaking of Reliability. Where you can join friends as they discuss reliability topics. Join us as we discuss topics ranging from design for reliability techniques to field data analysis approaches.

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Show Notes

The post SOR 991 What is MLE? appeared first on Accendo Reliability.

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