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I strongly disagree. Bayesian inference is the only known self-consistent formal system for doing science, i.e. updating our belief system about the world based

I strongly disagree. Bayesian inference is the only known self-consistent formal system for doing science, i.e. updating our belief system about the world based on the current evidence.

bo1024 8y ago
The problem with that reasoning is: whose belief system? Where do you come up with a prior that everyone agrees with?
- KirinDave 8y ago
  Actually, it's the strength of Bayesian inference that these assumptions are made apparent. Coming to consensus on priors is the same process for arriving at consensus that all scientific inquiry must engage in. Anyone who says frequentist methods somehow more accurately represent an underlying reality are pulling a fast one.
  - bo1024 8y ago
    Hmm, I think part of the question is where this debate and consensus should occur. I believe in firmly separating rigorous science from opinion and belief. To me, it follows that scientific research should focus on presenting evidence and leave it to Bayesian individuals to update their beliefs based on this evidence. Similarly I think argument or discussion about priors is not in scope for scientific research (except maybe a bit in the "motivation" subsection). (edit: I see now the top post here on this article also discusses this point.)
    - KirinDave 8y ago
      I can't help but feel like this is a fundamental definition problem. Science is not actually distinct from consensus forming. Science does not work with raw facts, it forms models based off human observations which are themselves a kind of consensus. Bayesian research is just more honest about what's already the case.
      - bo1024 8y ago
        I wouldn't agree, at any given time there is a lot of disagreement and non-consensus in given fields. So we need to new research to gather additional evidence. If every research paper tried to argue for a particular prior and posterior, rather than just gathering evidence, we would never make progress toward consensus either...
        KirinDave 8y ago
        > I wouldn't agree, at any given time there is a lot of disagreement and non-consensus in given fields. That's precisely my point. The act of presenting and refining research IS the act of building that consensus. My statement here is not a novel thought. It's pretty much the modern philosophy of science for over a decade. > So we need to new research to gather additional evidence. This is simply data gathering though. Every approach starts here. I'm not sure why you suggest that people using Bayesian approaches to analysis are somehow forbidden from being informed by data (or informing priors by data). That's exactly the same process folks use when selecting non-bayesian models. They don't spring from absolute truth, they're selected as well. > If every research paper tried to argue for a particular prior and posterior Given the replication crisis that's in part due to mis-application of existing models along with a lack of rigor in data collection, having research focus more tightly on the methodology for presenting data and conclusions doesn't seem like a bad outcome at all.
- abdullahkhalids 8y ago
  You are not supposed to agree on a prior. That's one of the fundamental insights of the Bayesian inference framework. That different people know different things about a given situation, so they initially disagree, and therefore their priors are different. This should not be surprised. People disagree all the time, and the Bayesian framework just formalizes it. The different people can then go on and do lots of experiments, collect lots of data and update their priors to posteriors. And the guarantee is that as long as each person's prior was not a mathematically weird function, after enough evidence has been collected all these people will have the same posterior function i.e. they will agree [1]. [1] The famous Aumann's agreement theorem https://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem https://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem is a related result that you might like to read about.
  - bo1024 8y ago
    Exactly. This is why (in my view) scientific research should focus on presenting evidence, not on arguing for certain posteriors or priors. The meta-science process then steers Bayesian beliefs correctly and the evidence-gathering process efficiently. (edit: I see now the top post here on this article also discusses this point.)
aaronblohowiak 8y ago
And if you believe Friston, Active Inference is how biological systems work!

I strongly disagree. Bayesian inference is the only known self-consistent formal system for doing science, i.e. updating our belief system about the world based on the current evidence.

bo1024 8y ago

The problem with that reasoning is: whose belief system? Where do you come up with a prior that everyone agrees with?

KirinDave 8y ago
Actually, it's the strength of Bayesian inference that these assumptions are made apparent. Coming to consensus on priors is the same process for arriving at consensus that all scientific inquiry must engage in. Anyone who says frequentist methods somehow more accurately represent an underlying reality are pulling a fast one.
- bo1024 8y ago
  Hmm, I think part of the question is where this debate and consensus should occur. I believe in firmly separating rigorous science from opinion and belief. To me, it follows that scientific research should focus on presenting evidence and leave it to Bayesian individuals to update their beliefs based on this evidence. Similarly I think argument or discussion about priors is not in scope for scientific research (except maybe a bit in the "motivation" subsection). (edit: I see now the top post here on this article also discusses this point.)
  - KirinDave 8y ago
    I can't help but feel like this is a fundamental definition problem. Science is not actually distinct from consensus forming. Science does not work with raw facts, it forms models based off human observations which are themselves a kind of consensus. Bayesian research is just more honest about what's already the case.
    - bo1024 8y ago
      I wouldn't agree, at any given time there is a lot of disagreement and non-consensus in given fields. So we need to new research to gather additional evidence. If every research paper tried to argue for a particular prior and posterior, rather than just gathering evidence, we would never make progress toward consensus either...
      - KirinDave 8y ago
        > I wouldn't agree, at any given time there is a lot of disagreement and non-consensus in given fields. That's precisely my point. The act of presenting and refining research IS the act of building that consensus. My statement here is not a novel thought. It's pretty much the modern philosophy of science for over a decade. > So we need to new research to gather additional evidence. This is simply data gathering though. Every approach starts here. I'm not sure why you suggest that people using Bayesian approaches to analysis are somehow forbidden from being informed by data (or informing priors by data). That's exactly the same process folks use when selecting non-bayesian models. They don't spring from absolute truth, they're selected as well. > If every research paper tried to argue for a particular prior and posterior Given the replication crisis that's in part due to mis-application of existing models along with a lack of rigor in data collection, having research focus more tightly on the methodology for presenting data and conclusions doesn't seem like a bad outcome at all.
abdullahkhalids 8y ago
You are not supposed to agree on a prior. That's one of the fundamental insights of the Bayesian inference framework. That different people know different things about a given situation, so they initially disagree, and therefore their priors are different. This should not be surprised. People disagree all the time, and the Bayesian framework just formalizes it. The different people can then go on and do lots of experiments, collect lots of data and update their priors to posteriors. And the guarantee is that as long as each person's prior was not a mathematically weird function, after enough evidence has been collected all these people will have the same posterior function i.e. they will agree [1]. [1] The famous Aumann's agreement theorem https://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem https://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem is a related result that you might like to read about.
- bo1024 8y ago
  Exactly. This is why (in my view) scientific research should focus on presenting evidence, not on arguing for certain posteriors or priors. The meta-science process then steers Bayesian beliefs correctly and the evidence-gathering process efficiently. (edit: I see now the top post here on this article also discusses this point.)

aaronblohowiak 8y ago

And if you believe Friston, Active Inference is how biological systems work!