I wish people would stop conflating “probabilistic/statistical inference” and “Bayesian inference.” Bayesians do not have a monopoly on the use of probability theory.
Bayesians do not have a monopoly on the use of probability theory.
It seems to me that Bayesians do have a ‘monopoly’ on the use of probabilities to express personal uncertainty, which is the topic under discussion. Are you worried that the phrase “Bayesian inference” seems exclusive, or something else?
It seems to me that Bayesians do have a ‘monopoly’ on the use of probabilities to express personal uncertainty.
Are you saying that if I am not sure what the average causal effect is, I better get my Bayesian union card? I am perfectly happy to deal with uncertainty using probability theory without such a card!
Are you saying that if I am not sure what the average causal effect is, I better get my Bayesian union card?
If you express “not being sure” in terms of numerical probabilities assigned to various levels of surety, or a numerical point estimate, then it seems reasonable to describe you as acting in a Bayesian manner.
It does not seem reasonable to insist on identification as a Bayesian to use any piece of the Bayesian toolkit. As I’ve said in the past, Frequentists don’t disagree with Bayes’s law. I hoped to implicitly disavow this view by putting monopoly in quotes.
It wasn’t clear to me what you thought was being conflated. There are ‘fallacies’ which are examples of correct inference using Bayes’s rule, and to object to calling that “Bayesian inference” seems odd to me.
Back when Pearl was arguing for the adoption of probability over logic in AI (for example, in the intro to his 88 book), he was talking about things like “rumor propagation” that logic calculus does not handle well, but probability calculus does. There is not much mention of B vs F in his defense, just properties of probability theory itself.
What Jaynes’ quote is really about is that logic calculus and probability calculus are not the same. Logic obeys locality, probability does not, etc. Bringing issues of epistemology into this is either a confusion of issues or a deliberate bait and switch.
I publish in a conference called “UAI” (Uncertainty in AI) a lot. There is a word “uncertainty” in the title, but I assure you, the community is far from uniformly Bayesian.
What Jaynes’ quote is really about is that logic calculus and probability calculus are not the same. Logic obeys locality, probability does not, etc.
Agreed, and I would go further and say Jaynes is making the claim that probability calculus is superior to logic calculus.
Bringing issues of epistemology into this is either a confusion of issues or a deliberate bait and switch.
I was confused- I flipped “interpret probabilities as beliefs” and “interpret beliefs as probabilities.”
The issue I still haven’t resolved is whether you’re objecting to calling the use of Bayes’ law Bayesian inference instead of probabilistic/statistical inference, and why. I think I see why you would want to, but my speculation is unclear.
I see where you’re coming from, and I agree that probabilistic inference is a more precise term that should be used instead. But I think my sense of shouldness there is much smaller than your sense of shouldness, and I can’t tell if that’s more tolerance for verbal sloppiness on my part or some sort of regret at narrowing the term Bayesian inference. I think I endorse the first but not the second explanation.
I just find LW’s often uninformed “Bayesianism” annoying, that’s all. It’s classic belief as attire—I am willing to bet having an opinion on these sorts of things make zero (0) practical difference in most people’s lives.
In fact, lots of things in the “LW cluster” are like this—MWI for instance.
edit: lest you think I am joking, here’s someone who calls the g-formula “an ad hoc frequentist device”:
which amounts to saying “get more data!” but which starts as follows:
“Bayesian epistemology and decision theory provide a rigorous foundation for dealing with mixed or ambiguous evidence, uncertainty, and risky decisions.”
which is a complete non-sequitur to the main point. I could keep going, but I hope the point is clear. There is an alarming lack of clue coupled with an alarming amount of “rah rah Bayes”. (Note: in case it is not obvious, I have no horse in the B vs F race at all, I am happy to write papers in either formalism. My point is not about B vs F at all.)
I agree that such a reliance is reasonable.
As Jaynes points out, many “logical fallacies” are actually examples of correct Bayesian inference.
Relevant: http://lesswrong.com/lw/aq2/
Thanks, that was interesting, although didn’t specifically address my question.
I wish people would stop conflating “probabilistic/statistical inference” and “Bayesian inference.” Bayesians do not have a monopoly on the use of probability theory.
It seems to me that Bayesians do have a ‘monopoly’ on the use of probabilities to express personal uncertainty, which is the topic under discussion. Are you worried that the phrase “Bayesian inference” seems exclusive, or something else?
Are you saying that if I am not sure what the average causal effect is, I better get my Bayesian union card? I am perfectly happy to deal with uncertainty using probability theory without such a card!
If you express “not being sure” in terms of numerical probabilities assigned to various levels of surety, or a numerical point estimate, then it seems reasonable to describe you as acting in a Bayesian manner.
It does not seem reasonable to insist on identification as a Bayesian to use any piece of the Bayesian toolkit. As I’ve said in the past, Frequentists don’t disagree with Bayes’s law. I hoped to implicitly disavow this view by putting monopoly in quotes.
It wasn’t clear to me what you thought was being conflated. There are ‘fallacies’ which are examples of correct inference using Bayes’s rule, and to object to calling that “Bayesian inference” seems odd to me.
Back when Pearl was arguing for the adoption of probability over logic in AI (for example, in the intro to his 88 book), he was talking about things like “rumor propagation” that logic calculus does not handle well, but probability calculus does. There is not much mention of B vs F in his defense, just properties of probability theory itself.
What Jaynes’ quote is really about is that logic calculus and probability calculus are not the same. Logic obeys locality, probability does not, etc. Bringing issues of epistemology into this is either a confusion of issues or a deliberate bait and switch.
I publish in a conference called “UAI” (Uncertainty in AI) a lot. There is a word “uncertainty” in the title, but I assure you, the community is far from uniformly Bayesian.
Agreed, and I would go further and say Jaynes is making the claim that probability calculus is superior to logic calculus.
I was confused- I flipped “interpret probabilities as beliefs” and “interpret beliefs as probabilities.”
The issue I still haven’t resolved is whether you’re objecting to calling the use of Bayes’ law Bayesian inference instead of probabilistic/statistical inference, and why. I think I see why you would want to, but my speculation is unclear.
Yes I do (because Bayes’ law is a triviality—it’s like saying any use of fractions is frequentist).
I see where you’re coming from, and I agree that probabilistic inference is a more precise term that should be used instead. But I think my sense of shouldness there is much smaller than your sense of shouldness, and I can’t tell if that’s more tolerance for verbal sloppiness on my part or some sort of regret at narrowing the term Bayesian inference. I think I endorse the first but not the second explanation.
I just find LW’s often uninformed “Bayesianism” annoying, that’s all. It’s classic belief as attire—I am willing to bet having an opinion on these sorts of things make zero (0) practical difference in most people’s lives.
In fact, lots of things in the “LW cluster” are like this—MWI for instance.
edit: lest you think I am joking, here’s someone who calls the g-formula “an ad hoc frequentist device”:
http://lesswrong.com/lw/hwq/evidential_decision_theory_selection_bias_and/9crr
Here’s a post by Nyan Sandwich
http://lesswrong.com/lw/irj/crush_your_uncertainty/
which amounts to saying “get more data!” but which starts as follows:
“Bayesian epistemology and decision theory provide a rigorous foundation for dealing with mixed or ambiguous evidence, uncertainty, and risky decisions.”
which is a complete non-sequitur to the main point. I could keep going, but I hope the point is clear. There is an alarming lack of clue coupled with an alarming amount of “rah rah Bayes”. (Note: in case it is not obvious, I have no horse in the B vs F race at all, I am happy to write papers in either formalism. My point is not about B vs F at all.)
Do you also get annoyed when people say “prior” when they mean “probability estimate”? As in, “my priors have been updated”.
One could affirm probabilism while denying (especially stronger forms of) Bayesianism (without contradiction), and, in fact, many philosophers do.