41–50 of 54 posts
Are there conditions in which a Bayesian reasoner is obliged to make racist decisions? Say you're a Bayesian infant who has never met anyone but Mom, who has blue skin, and has always been very nice to you. You then meet 100 other people of various colors, 97 of who are also nice to you. The other 3 people were mean to you, and they all have purple skin, and only they have purple skin. Person 101 approaches you, and…
And that would be wise.
Earlier quoted context omitted.
This critique might come from the idea that having a good analytic model, or at least some valuable analytic insights, involves much more than assigning some priors. Of course, the two things don't exclude each other, but for some frequentists Bayesians have the wrong perspective - or at least that's the critique, whether it's true or not. Another issue that I personally have with Bayesianism is that I believe that a…
My understanding of physics is that no die toss can be considered "fair" because such a macroscopic system behaves deterministically according to Newton's laws, and isn't even too chaotic to model accurately. No matter the shape or balance of the die, the outcome is determined by the initial conditions and the toss. A skilled gambler can make a fair die land however they want. The only thing I know is that a well-mad…
No, they can't. Dice control is a myth, and there isn't a single study that backs it up.
Earlier quoted context omitted.
This critique might come from the idea that having a good analytic model, or at least some valuable analytic insights, involves much more than assigning some priors. Of course, the two things don't exclude each other, but for some frequentists Bayesians have the wrong perspective - or at least that's the critique, whether it's true or not. Another issue that I personally have with Bayesianism is that I believe that a…
> assigning probabilities to singular events is only meaningful and admissible at all if there is a good analytic explanation for the respective propensity. Wait a minute, you are making a type error here: probabilities are not propensities. They're degrees of belief. (And even if you disagree in general, this is a Bayesian context you're talking about.) If I put a die on a table and hide it with a cup, you could sti…
Some people think that you need to explain why a die can be fair, rather than just assuming it or only looking at it from a frequentist perspective. Of course, die-hard Bayesians don't think so, but that would be begging the question in the context of discussing criticisms of Bayesianism.
> Read the first 2 chapters of Probability Theory: the Logic of Science, by E. T. Jaynes: "Plausible reasoning" and "The quantitative rules". It's very accessible, and you shall see how strong the foundations really are.
I'm an expert on this topic. The only arguments for probabilism are Dutch book arguments, and there is a large number of arguments against these. See for example various articles by Hajek. Alternative representations of graded belief are, among others:
- plausibility theory (Halpern at al.)
- possibility theory (Dubois & Prade)
- Haas-Spohn ranking theory and variants thereof
- various notions of epistemic entrenchment
- Dempster-Shafer belief theory
- almost any quantitative or qualitative representation of belief in belief revision theory not covered by one of the above theories (e.g. belief update by Katsuno & Mendelsohn)
- by a general logical connection, nonmonotonic logics and AAFs can generally represent notions of belief update, such that the underlying qualitative ordering of states is a representation of graded belief
What you probably mean is that the above generalizations (or qualitative theories, in some cases) could be simulated with probabilities, e.g. by using convex sets of probabilities or what Josang is doing in his "subjective logic". That's true, but then we're no longer talking about probabilism in the sense I've used the word.
Of course, you can also try arguing for probabilism like Savage did: Lay out a set of postulates for your subjective plausibility that happen to allow you to proof that this notion of subjective plausibility is in the end probability. Despite the merits of such work, it is in the end a form of cheating (or "reverse engineering"), because you could just as well come up with plausible postulates that yield the weaker axioms of possibility theory.
Are there conditions in which a Bayesian reasoner is obliged to make racist decisions? Say you're a Bayesian infant who has never met anyone but Mom, who has blue skin, and has always been very nice to you. You then meet 100 other people of various colors, 97 of who are also nice to you. The other 3 people were mean to you, and they all have purple skin, and only they have purple skin. Person 101 approaches you, and…
A frequentist assessing probabilities to make decisions about how to respond is in, if anything, a far worse position. The Bayesian would ideally use priors on groups and cross-group correlations to note that the weak evidence that purple -> mean barely shifts from their priors, and the inter-group mean shows that they are likely to be nice, unless your prior is that different colors have nearly independent probabilities of being nice or mean.
As someone who has a master's degree in statistics and often uses Bayesian statistics, I think we should not focus on whether one is a Bayesian or a frequentist, but rather be pragmatic and take the most practical approach to solving a statistical problem. Moreover, I think statistical education should start with frequentist concepts and then extend them to the Bayesian framework since the likelihood plays also a maj…
One approach gives the right answer. The other approach is more computationally tractable. Computers are pretty powerful now, so we can afford the correct answer much more often than we used to. As for what is more natural… I've seen a (frequentist) introduction to statistics, and it simply did not make sense . Nothing was justified, you just had to learn the stuff by rote and apply it in situations that look like th…
Having used Bayesian stats heavily, I'd note that the hard parts are not gone, they are just located elsewhere - in how to actually do the computations, rather than in how to set up problems. Each can be taught poorly or well, but given that MCMC is certainly harder than least-squares, it seems difficult to argue that using Bayesian statistics is easier. (Unless you're not just applying the methods by rote, and letting the computer spit out answers - and if you are, I don't know why you are better off with Bayesian methods. In fact, if that's what you're doing, please stop doing statistics and pay an expert instead.)
As someone who has a master's degree in statistics and often uses Bayesian statistics, I think we should not focus on whether one is a Bayesian or a frequentist, but rather be pragmatic and take the most practical approach to solving a statistical problem. Moreover, I think statistical education should start with frequentist concepts and then extend them to the Bayesian framework since the likelihood plays also a maj…
I agree, although I respect those who look for deeper justification for the methods we use. Bayesian statistics/decision theory does have axiomatic foundations after all.
As someone who has a master's degree in statistics and often uses Bayesian statistics, I think we should not focus on whether one is a Bayesian or a frequentist, but rather be pragmatic and take the most practical approach to solving a statistical problem. Moreover, I think statistical education should start with frequentist concepts and then extend them to the Bayesian framework since the likelihood plays also a maj…
One approach gives the right answer. The other approach is more computationally tractable. Computers are pretty powerful now, so we can afford the correct answer much more often than we used to. As for what is more natural… I've seen a (frequentist) introduction to statistics, and it simply did not make sense . Nothing was justified, you just had to learn the stuff by rote and apply it in situations that look like th…
On the subject of statistical education: The point I tried to make is that I think it is much easier to study first the likelihood, the central quantity of frequentist inference. One can then go to the Bayesian world simply by allowing the parameters to be random variables. Furthermore, as other commentors have pointed out, technical difficulties arise in the non-conjugate Bayesian setting when MCMC sampling has to be used. In my opinion, MCMC algorithms, convergence diagnostics, etc. are certainly not topics for an intro stats course.
Earlier quoted context omitted.
I agree, although I respect those who look for deeper justification for the methods we use. Bayesian statistics/decision theory does have axiomatic foundations after all.
So does frequentist stats - they are just different axiomatic foundations and assumptions.
Earlier quoted context omitted.
> assigning probabilities to singular events is only meaningful and admissible at all if there is a good analytic explanation for the respective propensity. Wait a minute, you are making a type error here: probabilities are not propensities. They're degrees of belief. (And even if you disagree in general, this is a Bayesian context you're talking about.) If I put a die on a table and hide it with a cup, you could sti…
No, I was not speaking from a Bayesian perspective, I was laying out the propensity-theoretic explanation of probability. The propensity explanation is one of attempts of explaining why singular events might be said to give rise to probabilities, living besides frequentism and Bayesianism. Another perspective worth mentioning is the logical approach, which is in the end purely combinatorial. Some people think that yo…
Unless you can explain this "propensity" in terms of actual physical properties, propensity by itself is… unjustified. The only domain I know of so far where we could possibly argue propensities are a thing is quantum mechanics. And even then it seems to rest on an anthropic argument: which universe am I living in?
> Some people think that you need to explain why a die can be fair,
A die by itself is not fair, right? A die might be balanced, and the way it is thrown it might have enough unpredictable variability to cause everyone in the room to think "uniform distribution over [1..6]".
Likewise, a cryptographic pseudo random generator is unpredictable (and thus "fair"), to anyone who doesn't know its internal state. Even though the process itself is deterministic, it's just not computationally feasible to guess its output just from the observation of past inputs. (Though for this one I'm relying on the fact we're not logically omniscient.)
> I'm an expert on this topic.
Good. Then you know that any inference strategy that falls prey to Dutch Books is not rational. Right?
To be fair, probability theory is not computationally tractable. I did not verify, but I guess any feasible approximation is vulnerable to some more or less subtle Dutch Books.
Now the way you talk about Dutch Books sound like all the other strategies you mention are vulnerable, not just in practice, but in theory as well. They are thus not perfectly rational. Do their authors at least have the grace to admit this is a flaw that should be corrected?
But then I suspect that correcting the flaw inevitably leads to probability theory itself: if you accept Jaynes three "desiderata" as required for any kind of rational reasoning, as he shows, the result is necessarily equivalent to probability theory as we know it (where probabilities are subjective assessments of plausibility, otherwise known as "degrees of belief").
I can only conclude that you do not accept Jayne's desiderata as necessary for correct inference. And this is the point where I look at you like you're not quite sane.
For reference, Jaynes Desiderata:
(1) Degrees of plausibility are represented by real
numbers. (And a continuity assumption.)
(2) Qualitative correspondence with common sense.
(explained in more detailed in the book)
(3a) If a conclusion can be reasoned out in more than
one way, then every possible way must lead to the
same result.
(3b) The robot always takes into account all of the
evidence it has relevant to a question. It does
not arbitrarily ignore some of the information,
basing its conclusions only on what remains. In
other words, the robot is completely non
ideological.
(3c) The robot always represents equivalent states of
knowledge by equivalent plausibility assignments.
That is, if in two problems the robot’s state of
knowledge is the same (except perhaps for the
labeling of the propositions), then it must assign
the same plausibilities in both.
I don't care it's reverse engineering, those desiderata match the way I think. I accept the conclusion that probability theory is the correct (albeit intractable) way to think, because I ultimately agree with the postulates it rests on. Vehemently so. They're not just true, they're obvious.
If you don't accept them, then I can only give up, and remember what Yudkowsky once wrote: "How do you argue a rock into becoming a mind?"
Earlier quoted context omitted.
One approach gives the right answer. The other approach is more computationally tractable. Computers are pretty powerful now, so we can afford the correct answer much more often than we used to. As for what is more natural… I've seen a (frequentist) introduction to statistics, and it simply did not make sense . Nothing was justified, you just had to learn the stuff by rote and apply it in situations that look like th…
Having taught frequentist stats as a TA to grad students, I understand why frequentist stats seems not to make sense. On the other had, my prior on teaching quality, and my data on the relative difficulty of understanding the approaches says with near-certainty that your experience has nothing to do with the approach taken. Having used Bayesian stats heavily, I'd note that the hard parts are not gone, they are just l…
Actually, I am not saying Bayesian statistics are easier to use. I was saying they looked easier to understand. Though I must point out that "Bayesian" may be the wrong word here. What truly makes sense to me is Probability Theory, which Edwin T. Jaynes describes pretty well.
(That does not make me any more capable at applying MCMC, which I don't even know of. Searching… Ah, Markov Chain Monte Carlo, yeah that's not easy. Plus, this sounds like an approximation of probability theory… not that we have anything better, mind you: I know that applying probability theory directly is often computationally intractable.)