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> And even today probability is taught with a lot of empirical examples. (At least it was in my classes, both undergraduate and graduate.) Can you mention some

by nanis 5y ago

> And even today probability is taught with a lot of empirical examples. (At least it was in my classes, both undergraduate and graduate.) Can you mention some of these examples? FYI, I've taught a bunch of Stats/Econometrics classes at grad and undergrad level.

leereeves 5y ago
My university treated stats and probability as separate disciplines, and I didn't have as many empirical examples in stats classes. We did use data sets in exercises, of course, but the focus was on correctly applying statistical methods, not whether the problem was empirically interesting or the answer was empirically correct. We had a lot more empirical work in probability. In introductory probability classes we had, among other things, famous examples like the Chevalier de Méré, birthday, Monty Hall, Bertrand's ballot, and coupon collector's problems; and a lot of calculating probabilities involving coins, dice, cards, and drawing balls from urns in various and increasingly complicated ways. In graduate probability classes we studied mathematical models of things like Brownian motion, birth-death processes, and queuing systems. Our work on these was theoretical, naturally, but grounded in empirical problems from the physical sciences.
- nanis 5y ago
  Thank you for the examples. That shows that we are talking about different things. In all those examples, we are talking about a way to model them using rules enshrined in the _axiomatic_ foundations of probability. Things like, "given that the probability of X is p and the probability of Y is q and X and Y are independent events, probability of X and Y is p times q" etc. That statement and the statements about the actual values of probabilities have no empirical content. Statements like "if there are 10 balls in an urn and three of them are red, the probability of pulling out a red ball is 30%" are _assumptions_ and they are not falsifiable. In practice, this simplifying assumption seems to have worked at least in making it easier think about certain phenomena and so we maintain that assumption, but it is an assumption nevertheless.
  - leereeves 5y ago
    I disagree. Statements like "if there are 10 [well mixed and otherwise indistinguishable] balls in an urn and three of them are red, the probability of pulling out a red ball is 30%" are absolutely falsifiable. An experiment showing that this statement is false is certainly possible. You're right that these are mathematical models and therefore simplifications of reality, but they are useful mathematical models only if their predictions are empirically valid. And if anyone came up with a more empirically useful version of probability, they'd be famous even if mathematicians refused to accept it, because all the scientists, engineers, gamblers, actuaries, etc who rely on the predictions of probability would make it so.

by nanis 5y ago

leereeves 5y ago

My university treated stats and probability as separate disciplines, and I didn't have as many empirical examples in stats classes. We did use data sets in exercises, of course, but the focus was on correctly applying statistical methods, not whether the problem was empirically interesting or the answer was empirically correct. We had a lot more empirical work in probability. In introductory probability classes we had, among other things, famous examples like the Chevalier de Méré, birthday, Monty Hall, Bertrand's ballot, and coupon collector's problems; and a lot of calculating probabilities involving coins, dice, cards, and drawing balls from urns in various and increasingly complicated ways. In graduate probability classes we studied mathematical models of things like Brownian motion, birth-death processes, and queuing systems. Our work on these was theoretical, naturally, but grounded in empirical problems from the physical sciences.

nanis 5y ago
Thank you for the examples. That shows that we are talking about different things. In all those examples, we are talking about a way to model them using rules enshrined in the _axiomatic_ foundations of probability. Things like, "given that the probability of X is p and the probability of Y is q and X and Y are independent events, probability of X and Y is p times q" etc. That statement and the statements about the actual values of probabilities have no empirical content. Statements like "if there are 10 balls in an urn and three of them are red, the probability of pulling out a red ball is 30%" are _assumptions_ and they are not falsifiable. In practice, this simplifying assumption seems to have worked at least in making it easier think about certain phenomena and so we maintain that assumption, but it is an assumption nevertheless.
- leereeves 5y ago
  I disagree. Statements like "if there are 10 [well mixed and otherwise indistinguishable] balls in an urn and three of them are red, the probability of pulling out a red ball is 30%" are absolutely falsifiable. An experiment showing that this statement is false is certainly possible. You're right that these are mathematical models and therefore simplifications of reality, but they are useful mathematical models only if their predictions are empirically valid. And if anyone came up with a more empirically useful version of probability, they'd be famous even if mathematicians refused to accept it, because all the scientists, engineers, gamblers, actuaries, etc who rely on the predictions of probability would make it so.