I think too that Jaynes failed in his attempt, but just because he died too, too soon. Otherwise, have he lived a long life, I believe we would have had much more advancement in the field. To the present moment, nobody seems interested in bringing forward his vision, not even his closest student (Bretthorst, who edited the printed version of Jaynes’ book).
Having said this, I believe you are wrong, because while it’s true that two different agents can come up with two different prior for the same problem, they can do so only if they have different information (or, being the same thing, have different beliefs about it). Otherwise one is violating either common sense or coherence or basic logic. There lies, I believe, all the meaning of objective Bayesian probability: a collection of methods, possibly with a unifying framework such as minxent, that allow to uncover the information hidden in a problem formulation, or to reveal why two different subjective priors actually differ.
two different agents can come up with two different prior for the same problem, they can do so only if they have different information
Sure, but agents almost always have different background information, in some cases radically different background information.
Let’s say a pharma company comes out with a new drug. The company claims: “Using our specially-developed prior, which is based on our extensive background knowledge of human biochemistry, in combination with the results of our recent clinical trial, we can see that our new drug has a miraculous ability to save lives!” An outsider looks at the same data, but without the background biochemical knowledge, and concludes that the drug is actually killing people.
You can partially alleviate this problem by requiring the pharma company to submit its special prior before the trial begins. But that’s not what Jaynes wanted; he wanted to claim that there exists some ideal prior that can be derived directly from the problem formulation.
Sure, but agents almost always have different background information, in some cases radically different background information.
In that case, it’s the correct situation that they come up with different prior.
he wanted to claim that there exists some ideal prior that can be derived directly from the problem formulation.
Yes, but he also made a point to always include all background information in the problem formulation. He explicitly wrote so, and his formulas had a trailing term P(...|...,X) to account for this. It might be interesting to explore what happens to models if you change part of the background information, but I think it’s undeniable that with the same information you are bound to come up with the same prior. This is why I think objective Bayesian probability is a better framework than subjective Bayesian: objectivity accounts for and explains subjectivity.
I think too that Jaynes failed in his attempt, but just because he died too, too soon.
Otherwise, have he lived a long life, I believe we would have had much more advancement in the field. To the present moment, nobody seems interested in bringing forward his vision, not even his closest student (Bretthorst, who edited the printed version of Jaynes’ book).
Having said this, I believe you are wrong, because while it’s true that two different agents can come up with two different prior for the same problem, they can do so only if they have different information (or, being the same thing, have different beliefs about it). Otherwise one is violating either common sense or coherence or basic logic.
There lies, I believe, all the meaning of objective Bayesian probability: a collection of methods, possibly with a unifying framework such as minxent, that allow to uncover the information hidden in a problem formulation, or to reveal why two different subjective priors actually differ.
Sure, but agents almost always have different background information, in some cases radically different background information.
Let’s say a pharma company comes out with a new drug. The company claims: “Using our specially-developed prior, which is based on our extensive background knowledge of human biochemistry, in combination with the results of our recent clinical trial, we can see that our new drug has a miraculous ability to save lives!” An outsider looks at the same data, but without the background biochemical knowledge, and concludes that the drug is actually killing people.
You can partially alleviate this problem by requiring the pharma company to submit its special prior before the trial begins. But that’s not what Jaynes wanted; he wanted to claim that there exists some ideal prior that can be derived directly from the problem formulation.
In that case, it’s the correct situation that they come up with different prior.
Yes, but he also made a point to always include all background information in the problem formulation. He explicitly wrote so, and his formulas had a trailing term P(...|...,X) to account for this.
It might be interesting to explore what happens to models if you change part of the background information, but I think it’s undeniable that with the same information you are bound to come up with the same prior.
This is why I think objective Bayesian probability is a better framework than subjective Bayesian: objectivity accounts for and explains subjectivity.