- Six-nines (0.999999) Reliability? Risk
calculations are alluringly simple in principle, but significantly more
complex in practice, making them vulnerable to misuse.
- Probabilistic Life Prediction Isn't as Easy as It Looks
There's much more to it than simply replacing constants with probability distributions.
- Monty Hall Problem explained - It only seems like it shouldn't make a difference to switch doors. Here's why switching doors wins twice as often. No fancy math necessary!
- Bayesian thinking
considers not only what the data have to say, but what your expertise
tells you as well.
- Answer-shopping is the
dubious practice of comparing different approaches to problem-solving
and choosing the answer you like rather than the most plausible.
- Outliers are often infuriating,
but they can be very informative too.
- New animation: How the
LogLikelihood Ratio Criterion Works.
- Probability and Likelihood - looking thorough the other end of the telescope.
(chi-square) and the LogLikelihood
- ExcelTM is a wonderful tool for many things. Statistics is not among them.
- The Weibull model is remarkable for being able to provide insight in so
- "p-values are
dangerous, especially large, small, and in-between ones."
- Frank E. Harrell Jr., Prof. of Biostatistics and
Department Chair, Vanderbilt University
- Generalized Linear Models
Generalized linear models link the independent variable with the
probability of observing the dependent variable.
- Grand Canyon winter snowstorm, 22 December, 2009
NPS webcam images as a sequential collage
POD "floor" and POD "ceiling"
Some data do not support a POD curve that goes to zero on the
left, or to one on the right.
2 + 2 = 5
Just because you can make a statistical statement doesn't make it true,
no matter how much you wish that it were.
Parameter Estimates are NOT parameter values.
There is a profound difference between the mathematical behavior of a
function whose parameter values are
defined (e.g. the FORM/SORM paradigm) and the same function whose
parameter values must be
estimated from data.
How â vs a POD Models Work
POD (Probability of Detection) is the probability that a signal, (â, "ahat")
will be larger than the decision threshold.
How hit/miss POD Models Work
POD (Probability of Detection) as a function of size is less
straightforward for binary (yes/no) data when compared with data having
a continuous response (â).
How WELL do POD Models Work?
In reality we only get to see ONE collection of data, and from that must
estimate the most likely model for the unseen and unknown and unknowable
How the LogLikelihood Ratio Criterion Works
Constructing Confidence Bounds on Probability of Detection Curves based
on how likely some alternatives to the maximum likelihood would
POD Short Course/Workshop
This two-day short course is based on the new (2007) MIL-HDBK-1823 and
mh1823 POD software. The course provides the latest methods for
measuring your NDE system's effectiveness and the workshop will use
these state-of-the-art techniques to analyze your enterprise data.
MIL-HDBK-1823A, "Nondestructive Evaluation System Reliability
2009 release of 2007 Update describes procedures for acquiring NDE data
and statistical methods for analyzing it to produce POD(a)
curves, 95% confidence bounds, noise analysis, and noise vs
detection trade-off curves, and includes worked-out examples using real
Hit/Miss and â data.
... I'm not a philosopher - but I, like you, do occasionally ruminate on
the human condition.
"I don't need to understand your problem to solve it."
The Great Misunderstanding
Both statisticians and engineers recognize the mathematical competence
of the other, and this is the cause of The Great Misunderstanding.
Quantitative Nondestructive Evaluation
It isn't the smallest crack you can find that's important – it's the
largest one you can miss.
False Positives and the ROC Curve ...
The relationship between POD and False Positives depends on more than
the inspection itself. It also depends on the frequency of defectives
in the population being inspected.
If you think you are beaten, you are ...
Probability and Statistics ...
... are not one and the same. The differences are not nuanced.
They are Apples and Oranges.
I am often asked to recommend a "good statistics text." Here are a few
that I refer to often.
Two Secrets of Success
Monte Carlo Oversights
Most Engineering Monte Carlo simulations ignore the distinction between
parameter values, and estimates of parameter values, resulting in
a gross underestimation of the probability of "low-probability" events.
Repeated inspections do not improve Probability of Detection
Central Limit Theorem Fine-Print
Readers have requested further explanation of when the CLT does not
Pseudo-Proof that 2 equals 1
Seemingly logical steps can lead to a silly conclusion. Unfortunately,
not all silliness is as self-evident as this example.
The "Most Probable Point" is a fiction
First Order, and Second Order Reliability Methods (FORM/SORM) are based
on a demonstrably false premise of a "Most Probable Point."
Contrasting the Statistical with the Mathematical Properties of
Engineers see reliability as an optimization problem on a known response
surface. Statisticians view it differently.
"Choosing" the Right Distribution
There is considerable folklore about choosing statistical distributions,
as you might select the appropriate club from your golf bag.
Frequentists and Bayesians
There is a continuing debate among statisticians over the proper
definition of probability.
There is more to Monte Carlo simulation than replacing constants with
Here is a simple algorithm for sampling from a bivariate normal
Did you know ... ?
Goodness-of-Fit tests, like Anderson-Darling, tell you when you don't
have a normal distribution.
... is an often misused goodness-of-fit metric, where bigger isn't
R-squared isn't the only way to judge how well the model works.
Chronology of Crack Initiation
Tongue-in-cheek view contains insights.
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
Joint, Marginal, and Conditional Probability
We engineers often play fast and loose with joint, marginal, and
conditional probabilities - to our detriment.
It's a lot more - and less - than you may think.
Often infuriating, these can be very informative too.
Choosing the wrong grid can undermine your analysis, mislead your
audience, and make you look foolish.
... including an example from
Random Fatigue Limit (RFL) on a P/C
Pascual and Meeker's RFL solves an old problem: how to have a runout
model go through (rather than under) all the runout data.
Not too Statistical, but still Fun! Check it out!
IntraOcular Trauma Test
Sometimes the best Goodness-of-Fit test is the easiest.
Central Limit Theorem
Why is the Average of nearly anything always Normal?
Grand Canyon, rim-to-rim!
Words and pictures are insufficient.
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.
There are myriad probability distributions. But did you know that most
are related to one another, and ultimately related to the Normal?