I just answered one of the user's questions. The user's question I answered didn't get involved in frequentist versus Bayesian and, thus, neither did my answer.
I started my post by quoting the user's question; that's the question I answered.
I never used the word frequentist and made only minimal use of the word Bayesian. I avoided all political fights.
Note: Possibly of special interests to Bayesian, I touched on E[X|Z] for an infinite collection of random variables Z. This will be important in conditioning (the core of Bayesian) in statistics of stochastic processes.
Also of interest in conditioning, I did mention that if events A and B are independent, then B gives no more information about A because
P(A|B) = P(A)
Anyone working with conditioning needs to know this concept.
More generally, I mentioned the sense in which conditioning gives the best possible non-linear least squares estimate; so, here we begin to see the power of conditioning, of which Bayes Rule is the most elementary case.
Also you may find that my touching on the Radon-Nikodym theorem is a first step to high end versions of Bayesian, e.g., the old idea of sequential testing (A. Wald) and the concepts of stopping times, optimal stopping, the strong Markov property, etc. I wrote out an earlier response, longer, I didn't post, that did go back to
sigma algebras, measurability, etc. I did omit measurable selection, sufficient statistics, etc. For such concepts, the Radon-Nikodym theorem and sigma algebras are crucial, and my post may be the only one here that mentioned either.
Also, comparing my response to others, you may find that my response was comparatively clear, precise, understandable, for such a short post without poorly defined or undefined terms, correct, and from a mature view.
By the way, I hold a Ph.D. in applied math from one of the world's best and best known research universities. My research was on stochastic optimal control and passed an oral exam from a Member, US National Academy of Engineering. I've published as sole author peer-reviewed original research in mathematical statistics. Once I did a statistical estimation of expected revenue growth for the BoD of FedEx; my work got two Board representatives from investor General Dynamics to change their mind and stay and, thus, saved FedEx. I've worked in statistical consulting in finance, marketing, etc., including in computing and statistical consulting for the faculty at Georgetown University. My work in statistical power spectral estimation got my company sole source on an important contract from the US Navy. Once I did a Monte Carlo estimation of a statistical estimation I did of the survivability of the US SSBN fleet under a special scenario of global nuclear war limited to sea -- the US Navy was pleased. My work passed review from J. Keilson, a world class expert in statistics.
Maybe, instead of what I wrote, some readers were looking for something else.
I started my post by quoting the user's question; that's the question I answered.
I never used the word frequentist and made only minimal use of the word Bayesian. I avoided all political fights.
Note: Possibly of special interests to Bayesian, I touched on E[X|Z] for an infinite collection of random variables Z. This will be important in conditioning (the core of Bayesian) in statistics of stochastic processes.
Also of interest in conditioning, I did mention that if events A and B are independent, then B gives no more information about A because
P(A|B) = P(A)
Anyone working with conditioning needs to know this concept.
More generally, I mentioned the sense in which conditioning gives the best possible non-linear least squares estimate; so, here we begin to see the power of conditioning, of which Bayes Rule is the most elementary case.
Also you may find that my touching on the Radon-Nikodym theorem is a first step to high end versions of Bayesian, e.g., the old idea of sequential testing (A. Wald) and the concepts of stopping times, optimal stopping, the strong Markov property, etc. I wrote out an earlier response, longer, I didn't post, that did go back to sigma algebras, measurability, etc. I did omit measurable selection, sufficient statistics, etc. For such concepts, the Radon-Nikodym theorem and sigma algebras are crucial, and my post may be the only one here that mentioned either.
Also, comparing my response to others, you may find that my response was comparatively clear, precise, understandable, for such a short post without poorly defined or undefined terms, correct, and from a mature view.
By the way, I hold a Ph.D. in applied math from one of the world's best and best known research universities. My research was on stochastic optimal control and passed an oral exam from a Member, US National Academy of Engineering. I've published as sole author peer-reviewed original research in mathematical statistics. Once I did a statistical estimation of expected revenue growth for the BoD of FedEx; my work got two Board representatives from investor General Dynamics to change their mind and stay and, thus, saved FedEx. I've worked in statistical consulting in finance, marketing, etc., including in computing and statistical consulting for the faculty at Georgetown University. My work in statistical power spectral estimation got my company sole source on an important contract from the US Navy. Once I did a Monte Carlo estimation of a statistical estimation I did of the survivability of the US SSBN fleet under a special scenario of global nuclear war limited to sea -- the US Navy was pleased. My work passed review from J. Keilson, a world class expert in statistics.
Maybe, instead of what I wrote, some readers were looking for something else.
Sorry some people were offended.