Comments on: Diversity of Opinion, and Stats http://www.thinktoomuch.net/2007/07/12/diversity-of-opinion-and-stats/ Pondering the South African Memesphere - Looking for the Good in Everything Sat, 11 Feb 2012 15:43:45 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Steve http://www.thinktoomuch.net/2007/07/12/diversity-of-opinion-and-stats/#comment-821 Steve Mon, 23 Jul 2007 08:35:16 +0000 http://thinktoomuch.net/2007/07/12/diversity-of-opinion-and-stats/#comment-821 The question is if you use your axioms rationally. Generally, axioms are the basis of a framework built from the axioms, including axioms with regard to logic. If the logic axioms are questionable (i.e. axioms aren't used rationally), the results of the framework are entirely questionable. The question is if you use your axioms rationally. Generally, axioms are the basis of a framework built from the axioms, including axioms with regard to logic. If the logic axioms are questionable (i.e. axioms aren’t used rationally), the results of the framework are entirely questionable.

]]> By: Hugo http://www.thinktoomuch.net/2007/07/12/diversity-of-opinion-and-stats/#comment-797 Hugo Mon, 16 Jul 2007 07:59:07 +0000 http://thinktoomuch.net/2007/07/12/diversity-of-opinion-and-stats/#comment-797 Coming from an applied sciences discipline (uh, that the correct description?), doing pattern recognition, we use Bayesian probability, "of course". I suppose I could point out "it's not the axioms that matter, it's what you <em>do</em> with them that counts". Hehe. And this whole, uh, allegory?, isn't even that far-fetched, considering Bayesian probability is named after <em>Reverend</em> Thomas Bayes, who I suspect would have applied it in thinking about religious beliefs. (He was a nonconformist as well.) """Some regard Bayesian inference as an application of the scientific method because updating probabilities through Bayesian inference requires one to start with initial beliefs about different hypotheses, to collect new information (for example, by conducting an experiment), and then to adjust the original beliefs in the light of the new information. Adjusting original beliefs could mean (coming closer to) accepting or rejecting the original hypotheses.""" I've wondered if I should blog about "stuff I know about", i.e., pattern recognition? Don't think that's really of interest to the "lay person". Hehe. Anyway, you failed in your attempted invocation of Godwin's law. Here's a better attempt... As I claimed above, it depends on what you do with your axioms, not what your actual axioms are. (Might argue against that, sure, but bear with me long enough to invoke Godwin's law.) While many people complain about the evils committed by the "church" in the name of "religion", there are also complaints about evils supposedly committed in the name of atheism or in the name of evolution. I'm not even sure which one is relevant - Nazi's used evolution-inspired arguments, but I think they also had some warped form of Christianity? Never mind their axioms, they did terrible things with them... Coming from an applied sciences discipline (uh, that the correct description?), doing pattern recognition, we use Bayesian probability, “of course”. I suppose I could point out “it’s not the axioms that matter, it’s what you do with them that counts”. Hehe.

And this whole, uh, allegory?, isn’t even that far-fetched, considering Bayesian probability is named after Reverend Thomas Bayes, who I suspect would have applied it in thinking about religious beliefs. (He was a nonconformist as well.)

“”"Some regard Bayesian inference as an application of the scientific method because updating probabilities through Bayesian inference requires one to start with initial beliefs about different hypotheses, to collect new information (for example, by conducting an experiment), and then to adjust the original beliefs in the light of the new information. Adjusting original beliefs could mean (coming closer to) accepting or rejecting the original hypotheses.”"”

I’ve wondered if I should blog about “stuff I know about”, i.e., pattern recognition? Don’t think that’s really of interest to the “lay person”. Hehe.

Anyway, you failed in your attempted invocation of Godwin’s law. Here’s a better attempt… As I claimed above, it depends on what you do with your axioms, not what your actual axioms are. (Might argue against that, sure, but bear with me long enough to invoke Godwin’s law.) While many people complain about the evils committed by the “church” in the name of “religion”, there are also complaints about evils supposedly committed in the name of atheism or in the name of evolution. I’m not even sure which one is relevant – Nazi’s used evolution-inspired arguments, but I think they also had some warped form of Christianity? Never mind their axioms, they did terrible things with them…

]]> By: Steve http://www.thinktoomuch.net/2007/07/12/diversity-of-opinion-and-stats/#comment-796 Steve Mon, 16 Jul 2007 06:58:41 +0000 http://thinktoomuch.net/2007/07/12/diversity-of-opinion-and-stats/#comment-796 This is all semantics, once again, as I understand it. Bayesians consider one concept, which they call probability. It behaves in a certain way. Frequentists consider a different concept, which they also call probability (but they called it probability first!). It also behaves in a certain way. The frequentist concept and the Bayesian concept tend to follow similar axioms, but the frequentist interpretation is more narrow. All the problems would go away if one spoke of F-probability and B-probability, and proved various results based on that. That would unite a lot of the work (general results could be proved to hold for both types). Frequentists have no beef with Bayesian results which apply in a Bayesian setting, since it's then a different framework. The problem is their axioms are being attacked, and since axioms are "self-evident truths", it's hardly likely one will ever win out over the other. I reference religious debates here *cough* Godwin's law? *cough*. So, the B-probability approach works great, but the problem with it for frequentists is that the results depend on the person doing the analysis. Proponents of F-probability say that their framework doesn't suffer from that. This is all semantics, once again, as I understand it. Bayesians consider one concept, which they call probability. It behaves in a certain way. Frequentists consider a different concept, which they also call probability (but they called it probability first!). It also behaves in a certain way. The frequentist concept and the Bayesian concept tend to follow similar axioms, but the frequentist interpretation is more narrow.

All the problems would go away if one spoke of F-probability and B-probability, and proved various results based on that. That would unite a lot of the work (general results could be proved to hold for both types). Frequentists have no beef with Bayesian results which apply in a Bayesian setting, since it’s then a different framework. The problem is their axioms are being attacked, and since axioms are “self-evident truths”, it’s hardly likely one will ever win out over the other. I reference religious debates here *cough* Godwin’s law? *cough*.

So, the B-probability approach works great, but the problem with it for frequentists is that the results depend on the person doing the analysis. Proponents of F-probability say that their framework doesn’t suffer from that.

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