Normal Snap

Illustrates the concept of maximum likelihood estimation of the parameters of a univariate normal distribution.

Scroll down below the applet for more background and details.

Some things to try:

• Drag your mouse up to decrease the standard deviation of the distribution (i.e. increase “sharpness”)
• Drag your mouse down to increase the standard deviation of the distribution (i.e. spread it out more)
• Drag your mouse left to decrease the mean of the distribution (i.e. move it to the left)
• Drag your mouse right to increase the mean of the distribution (i.e. move it to the right)
• Letting go of the mouse button causes the app to “snap” back to the maximum likelihood estimates of mean and standard deviation

You will note that dragging the distribution away from the maximum likelihood estimates (MLEs) causes the background to become increasingly red. This increasing redness corresponds with the decreasing log-likelihood shown below the plot. The log-likelihood measures the fit of the distribution to the data. Notice that lower log-likelihoods are associated with the sampled points being closer to the baseline (i.e. their probability density is lower than it would be if the mean and standard deviation were at their MLEs).

Acknowledgements

This applet makes use of the excellent d3js javascript library. Please see the GitHub site for details about licensing of other libraries that may have been used in the source code for this applet.

Licence

Creative Commons Attribution 4.0 International. License (CC BY 4.0). To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.