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Probability and Statistics ... |
| ... are not one and the same. The differences are not nuanced. They are Apples and Oranges.
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Reading List |
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I am often asked to recommend a "good statistics text." Here are a few that I refer to often. |
| R-squared ... |
| ... is an often misused goodness-of-fit
metric, where bigger isn't always better. |
| Other Measures |
| R-squared isn't the only way to
judge how well the model works. |
| Curse
of Dimensionality |
| Direct-sampling Monte Carlo
requires the number of samples per variable to increase exponentially with the number of
variables to maintain a given level of accuracy. |
| convergence in
distribution |
| We engineers are familiar with
convergence to a point, but what of convergence to a distribution? |
| extreme value
distributions |
| The largest, or smallest,
observation in a sample has one of three possible distributions. This is another
example of "convergence in distribution." |
| Joint,
Marginal, and Conditional Probability |
| We engineers often play fast
and loose with joint, marginal, and conditional probabilities - to our detriment. |
Correlation |
When the correlation between two variables is zero, they're not realted.
Right? Wrong! |
Outliers |
Often infuriating, these can be very informative too. |
Wrong Grid? |
Choose wisely - to avoid embarrassment. |
Bayesian Thinking |
| ... including an example from NDE |
| InterOcular Trauma
Test |
| Sometimes the best
Goodness-of-Fit test is the easiest. |
| Central
Limit Theorem |
| Why is the Average
of nearly anything always Normal ? |
| Bayesian Updating |
| We use Bayesian Statistics
every day without knowing it. |
| Sums
of Random Variables |
| Sometimes you need to know the
distribution of some combination of things. Here's an example. |
| Distributional
Inter-relationships |
| There are myriad probability
distributions. But did you know that most are related to one another, and ultimately
related to the Normal? |
| Goodness-of-Fit |
| We engineers often use a
statistical distribution without checking to see if it's doing a good job. Here's
how to fix that. |
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