I've often meant to ask whether you've come across Stephen Toulmin's discussion of probability in ch 2 of his Uses Of Argument, and if so what you think of it. "To say that a statement is a probability-statement is *not* to imply that there is some one thing which it can be said to be about or express. There is no single answer to the questions, ‘What do probability-statements express?...Some express one thing: some another" (p65) "whether backed by mathematical calculations or no, the characteristic function of our particular, practical probability-statements is to present *guarded* or *qualified* assertions and conclusions." (p86) (https://johnnywalters.weebly.com/uploads/1/3/3/5/13358288/toulmin-the-uses-of-argument_1.pdf)
I have never understood the desire to call frequencies probabilities. It introduces an unnecessary confusion that students rarely escape. Why not keep the concepts of frequency and probability distinct? A probability is something that we assign in order to represent a state of knowledge. A frequency is a factual property of the real world that we measure or estimate. Probabilities change when we change our state of knowledge; frequencies do not. The probability that we assign to an event can be equal to its frequency only for certain states of knowledge. Intuitively, one would expect this to be the case when the only information we have consists of observed frequencies. Probabilities are something we assign to frequencies. Keeping the concepts distinct avoids the slippery transmutation you describe. Jaynes makes a very convincing argument for taking this position.
Your Probability 0 explains why frequencies obey Kolmogorov's axioms. A relative frequency is a normalized measure on a finite population, which is Probability 0 with a physical referent. Household budget shares satisfy the same axioms, and nobody has proposed calling them Probability 3. Is there a good argument for a numbered family of probabilities beyond deference to Carnap and Meehl?
Hi professor, thanks for sharing the blog and video. I never deeply think about the hidden link between probability and psychology but this reminds me about Persi Diaconis' story of being a statistician. I twice dropped my undergrad forecasting course as I was unable to sense enough math to secure my own validity. I hope I would be able to keep up this time XD
I've often meant to ask whether you've come across Stephen Toulmin's discussion of probability in ch 2 of his Uses Of Argument, and if so what you think of it. "To say that a statement is a probability-statement is *not* to imply that there is some one thing which it can be said to be about or express. There is no single answer to the questions, ‘What do probability-statements express?...Some express one thing: some another" (p65) "whether backed by mathematical calculations or no, the characteristic function of our particular, practical probability-statements is to present *guarded* or *qualified* assertions and conclusions." (p86) (https://johnnywalters.weebly.com/uploads/1/3/3/5/13358288/toulmin-the-uses-of-argument_1.pdf)
Millennia of religious testimony provide strong evidence that math is not a required model for belief. And some people don’t even believe in math.
I have never understood the desire to call frequencies probabilities. It introduces an unnecessary confusion that students rarely escape. Why not keep the concepts of frequency and probability distinct? A probability is something that we assign in order to represent a state of knowledge. A frequency is a factual property of the real world that we measure or estimate. Probabilities change when we change our state of knowledge; frequencies do not. The probability that we assign to an event can be equal to its frequency only for certain states of knowledge. Intuitively, one would expect this to be the case when the only information we have consists of observed frequencies. Probabilities are something we assign to frequencies. Keeping the concepts distinct avoids the slippery transmutation you describe. Jaynes makes a very convincing argument for taking this position.
Your Probability 0 explains why frequencies obey Kolmogorov's axioms. A relative frequency is a normalized measure on a finite population, which is Probability 0 with a physical referent. Household budget shares satisfy the same axioms, and nobody has proposed calling them Probability 3. Is there a good argument for a numbered family of probabilities beyond deference to Carnap and Meehl?
Hi professor, thanks for sharing the blog and video. I never deeply think about the hidden link between probability and psychology but this reminds me about Persi Diaconis' story of being a statistician. I twice dropped my undergrad forecasting course as I was unable to sense enough math to secure my own validity. I hope I would be able to keep up this time XD
"Yeah man, they call gambling a disease, but it’s the only disease where you can win a bunch of money." -Good ol' Norm