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“Bayesian decision making” it’s not very common in med research, as far as I can see. And it is also not very commonly meant in intro statistics books
The fact that a decision theory perspective is mostly absent from medical research and intro stat books I see as an important cause of poor research conduct and misinterpretation of statistical methods.
I have not seen any rebuttal to the claim that the maximization of utility, when applied to the scientific research domain is simply the maximization of information to reliably estimate or predict the state of nature . That is how IJ Good conceptualized it, and I find much value to that perspective.
The maximization of information is implied by Harry Crane’s premise in The Fundamental Principle of Probability
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If you assign a probability to an outcome happening, then you must be willing to accept a bet offered on the other side (that the outcome will not happen) at the correct implied odds.
Another excuse against the testing by betting philosophy is the use of gambling to model concepts. If recreational gambling is objectionable, consider the important issue of risk management in a modern economy – life insurance, health, pensions, etc. That involves calculation of probabilities of propositions occurring or not, their costs when they do occur, and the correct value an insured needs to pay to transfer that risk.
In the U.S, “value based healthcare” really means shifting economic risk onto providers. Medical stats is not prepared for this.
The notion of information as utility to be maximized in principled scientific research can be extended to the idea of markets for information explored by Robin Hanson a physicist who became an economist.
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Information markets are institutions for accomplishing this task [of information aggregation] via trading in speculative markets, at least on topics where truth can be determined later. Relative to simple conversation, it is harder to say any one thing by market trading, and there are fewer things one can say. When people do not know whom to believe, however, the fact that a trader must put his money where his mouth is means that the things people do say in information markets can be more easily believed. Those who know little are encouraged to be quiet, and those who think they know more than they do learn this fact by losing.
Compare the notion of information markets to this description of scientific activity by statistician Paul Rosenbaum in his book Observational Studies.
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Scientific evidence is commonly and properly greeted with objections, skepticism, and doubt. Some objections come from those who simply do not like the conclusions, but setting aside such unscientific reactions, responsible scientists are responsibly skeptical…This skepticism is itself scrutinized. Skepticism must be justified and defended. One needs “grounds for doubt” in Wittgenstein’s phrase. Grounds for doubt are themselves challenged. Objections bring forth counter-objections and more evidence. As time passes arguments on one side or the other become strained, fewer scientists are willing to offer them … In this way, questions are settled.
I find them to have much in common.