Many of us, especially those in business, have to make decisions. We know that our "models" are imprecise, we know that tomorrow everything we based our data on may change, we know that people and their choices/decisions are fickle and irrational, yet we have to make a decision.
At some future date we will be called to account for those decisions. If all goes well we get praise and hopefully financial rewards. When it goes wrong we get canned.
We have only two defences.
1) All the data pointed to our decision being right and we performed more than sufficient due diligence.
2) We formed a committee.
Any person with intelligence hates committees more than they hate being canned.
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An insightful lecture, Dr. William! It is remarkable to consider how much of the statistical theory we learned, foundational concepts included, relies on the notion of infinity, an abstract construct that is unattainable. Perusing Casella and Berger’s Statistical Inference, one encounters the Central Limit Theorem as a cornerstone, permeating the text, its development intricately tied to the elusive infinity. Every significance test and CI count on something unattainable.
The binomial also has parameters. And arises from letting letting N → infinity in the example today.
Something better as mentioned last time would be something more like a parameterless multinnomial. Something that gives probability to just those values, and only those values, in the finite discrete set of possible GPAs.
Does the Mandelbrot set exist? What do we mean when we say the solution to a differential equation “exists”?
Not saying you’re wrong, but the concept of “exists”, I think, is quite deep and the word is not without ambiguity.
Ultimately (if you take my meaning), it would seem to me that we have to qualify “exists” with “relative to what?”. Can we actually say that any *thing* (or concept) has absolute existence?
"My heart soars like a hawk." I shall christian you Old Lodge Skins.
Many of us, especially those in business, have to make decisions. We know that our "models" are imprecise, we know that tomorrow everything we based our data on may change, we know that people and their choices/decisions are fickle and irrational, yet we have to make a decision.
At some future date we will be called to account for those decisions. If all goes well we get praise and hopefully financial rewards. When it goes wrong we get canned.
We have only two defences.
1) All the data pointed to our decision being right and we performed more than sufficient due diligence.
2) We formed a committee.
Any person with intelligence hates committees more than they hate being canned.
Hence models
No parameters...but I still like that word.
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An insightful lecture, Dr. William! It is remarkable to consider how much of the statistical theory we learned, foundational concepts included, relies on the notion of infinity, an abstract construct that is unattainable. Perusing Casella and Berger’s Statistical Inference, one encounters the Central Limit Theorem as a cornerstone, permeating the text, its development intricately tied to the elusive infinity. Every significance test and CI count on something unattainable.
It’s far from easy. I don’t think anybody alive today, that I know of, has it all figured out.
That is for sure. Always loved it though. Pity most of it doesn't really work.
Sure, using a normal distribution to model a discrete set can give some absurd values. But that's why we have the binomial distribution.
The binomial also has parameters. And arises from letting letting N → infinity in the example today.
Something better as mentioned last time would be something more like a parameterless multinnomial. Something that gives probability to just those values, and only those values, in the finite discrete set of possible GPAs.
Exist. Hmmm.
Does the Mandelbrot set exist? What do we mean when we say the solution to a differential equation “exists”?
Not saying you’re wrong, but the concept of “exists”, I think, is quite deep and the word is not without ambiguity.
Ultimately (if you take my meaning), it would seem to me that we have to qualify “exists” with “relative to what?”. Can we actually say that any *thing* (or concept) has absolute existence?
Numbers don’t exist either, in the way I’m using the word. Have being.
Things exists, substance exist, and these have natures and powers. Probability has none.
Yes, I understand, and thank you for permitting me my little tangent.