Here’s the thing William, this is one of many definitions of “random”. There’s long-run frequency stability (Frequentist). Then there’s subjective uncertainty (Bayesian). And then there’s algorithmic incompressibility (Kolmogorov). And let’s not forget lack of causal explanation (Philosophy of Science). I’m sure there’s many more. So what’s your flavor of the day? It seems to me this lecture is more about information theory than randomness itself.
Nassim Taleb in his book “Fooled by Randomness” talks about randomness simply being a matter of point of view. What is wholly deterministic from the person generating the numbers, for example, appears random to the person receiving them, as you point out. An example he gives is the 911 attack - seemingly out of nowhere to the government and public of the US, but obviously predictable to the men planning and carrying out the attack.
P.S. Fuzzy logic is the biggest breakthrough in philosophy since Aristotle. Reality does not map neatly to symbols.
Modern day followers on Ayn Rand and Ludwig von Mises ignore this fact and indulge in silly Proof by Definition.
Meanwhile, the East got paralyzed by dwelling on where this mapping fails, and overlooked where logical thinking works for a couple thousand years. Supposedly some of them achieved Nirvanna or something.
Quality of random number generator makes a heap big difference when doing Monte Carlo integrations. Cryptographers will happily give you a verbal spanking as well.
You are on much stronger ground when you question the assumption of Gaussian residuals. The Gaussian bell curve comes from *adding* together a *large number* of *uncorrelated* signals. Fat tails and other "anomalies" happen when the signals are limited in number and/or have couplings (not additive).
Intelligence comes to mind. Intelligence is NOT a simple addition of a huge number of factors. There is a great deal of nonlinearity. People who are good at logic problems are more likely to practice logic problems. People who are good at reading inhale more information. People who could do physics but would be mediocre physicists take on less strenuous fields. (The same holds for athletic prowess. Those who don't make the team work out far less than those who do. Those who make first string get more practice reps than the bench warmers.)
Now here is the question (which I don't have an answer for tonight): does selecting candidates for a clinical trial using an uncorrelated high quality random number generator truly guarantee that residuals should be random and Gaussian distributed? What if there are only a dozen or two significant signals other than what you are controlling for? What if one or more of them is correlated to willingness to participate in the study?
I haven't worked out the details, but it seems that that is where to attack P values. (Apologies if you have already covered this. Sometimes your notation puts me to sleep so I haven't followed all of your lessons.)
My father, an experimental nuclear physicist, opined that nothing is truly random in nature, and physicists use lists of "random" numbers compiled in different ways, knowing that.....
Here’s the thing William, this is one of many definitions of “random”. There’s long-run frequency stability (Frequentist). Then there’s subjective uncertainty (Bayesian). And then there’s algorithmic incompressibility (Kolmogorov). And let’s not forget lack of causal explanation (Philosophy of Science). I’m sure there’s many more. So what’s your flavor of the day? It seems to me this lecture is more about information theory than randomness itself.
Nassim Taleb in his book “Fooled by Randomness” talks about randomness simply being a matter of point of view. What is wholly deterministic from the person generating the numbers, for example, appears random to the person receiving them, as you point out. An example he gives is the 911 attack - seemingly out of nowhere to the government and public of the US, but obviously predictable to the men planning and carrying out the attack.
That's the point. Information theory is about who knows what when and how the information gets there.
P.S. Fuzzy logic is the biggest breakthrough in philosophy since Aristotle. Reality does not map neatly to symbols.
Modern day followers on Ayn Rand and Ludwig von Mises ignore this fact and indulge in silly Proof by Definition.
Meanwhile, the East got paralyzed by dwelling on where this mapping fails, and overlooked where logical thinking works for a couple thousand years. Supposedly some of them achieved Nirvanna or something.
Quality of random number generator makes a heap big difference when doing Monte Carlo integrations. Cryptographers will happily give you a verbal spanking as well.
You are on much stronger ground when you question the assumption of Gaussian residuals. The Gaussian bell curve comes from *adding* together a *large number* of *uncorrelated* signals. Fat tails and other "anomalies" happen when the signals are limited in number and/or have couplings (not additive).
Intelligence comes to mind. Intelligence is NOT a simple addition of a huge number of factors. There is a great deal of nonlinearity. People who are good at logic problems are more likely to practice logic problems. People who are good at reading inhale more information. People who could do physics but would be mediocre physicists take on less strenuous fields. (The same holds for athletic prowess. Those who don't make the team work out far less than those who do. Those who make first string get more practice reps than the bench warmers.)
Now here is the question (which I don't have an answer for tonight): does selecting candidates for a clinical trial using an uncorrelated high quality random number generator truly guarantee that residuals should be random and Gaussian distributed? What if there are only a dozen or two significant signals other than what you are controlling for? What if one or more of them is correlated to willingness to participate in the study?
I haven't worked out the details, but it seems that that is where to attack P values. (Apologies if you have already covered this. Sometimes your notation puts me to sleep so I haven't followed all of your lessons.)
My father, an experimental nuclear physicist, opined that nothing is truly random in nature, and physicists use lists of "random" numbers compiled in different ways, knowing that.....