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AliceInWonderland said: 

Bayesianism is fundamentally an epistemic study of belief.

As such you can come to the completely wrong conclusion and then say my belief in the wrong conclusion is justified.

Furthermore it seems to make a lot of assumptions that transcendental realists and empirical idealists make, so it could be said all considering that it's epistemologically flawed but that is a very complicated subject I am not ready to flesh out.

I would argue that this is not the fault of Bayesianism but rather it's an unfortunate fact of reality that we do not have access to all conceivable information. I.e., your world-view is not perfect. Once you learn that there's something that conflicts your current world-view, you build and modify your model.

Science doesn't make proclamations about the truth, but it makes tentative statements based on the best information and models available to us.

Before we learned that Newtonian laws of gravity are incorrect, it made perfect sense for us to assume that Mercury traced an ellipse. Once we discovered new information that conflicted with that world view, we revised our models.

Bayesianism just happens to be the best method, currently, to learn about the natural world. If you can come up with an example of another epistemology which can show that something we both accept as true is true, but which Bayesian analysis states is false, I'll be very surprised.

AppleGenius said: 

AliceInWonderland said: 

Bayesianism is fundamentally an epistemic study of belief.

As such you can come to the completely wrong conclusion and then say my belief in the wrong conclusion is justified.

Furthermore it seems to make a lot of assumptions that transcendental realists and empirical idealists make, so it could be said all considering that it's epistemologically flawed but that is a very complicated subject I am not ready to flesh out.

I would argue that this is the fault of Bayesianism but rather it's an unfortunate fact of reality that we do not have access to all conceivable information. I.e., your world-view is not perfect. Once you learn that there's something that conflicts your current world-view, you build and modify your model.

I wouldn't place any fault with Bayesianism as it is merely a system and as a system I think it's perfectly fine at what it does. I am pointing out that as a system that purely functions on updating a belief it is purely a system of what knowledge can be stated about a system given some observation, as such it can be said to be a kind of empirical epistemic realism which has its benefits as a theory of knowledge but also has its disadvantages. 

Science doesn't make proclamations about the truth, but it makes tentative statements based on the best information and models available to us.

Before we learned that Newtonian laws of gravity are incorrect, it made perfect sense for us to assume that Mercury traced an ellipse. Once we found new information that conflicted with that world view, we revised our models.

I completely agree with you here. 

It's interesting because it was really the ontology that was incorrect in this instance, it just so happened that the ontology determined the language of our epistemic language. 

This is what really makes Bayesian tricky and it's really all up to the human in reality as the system cannot be inherently wrong if one accepts its empirical epistemic realist (transcendental realist/empirical idealist, I am combining the two into this new phrase) base; only the human being who chooses the wrong priors and hypothesis can be wrong. 

Bayesianism just happens to be the best method, currently, to learn about the natural world. If you can come up with an example of another epistemology which can show that something we both accept as true is true, but which Bayesian analysis states is false, I'll be very surprised.

 Here I am not sure but it makes a very strong case for itself. 

 I am going to put a lot of thought into this though given it's important and also will deeper my understanding of the system as a   whole. 

AliceInWonderland said: 

I wouldn't place any fault with Bayesianism as it is merely a system and as a system I think it's perfectly fine at what it does. I am pointing out that as a system that purely functions on updating a belief it is purely a system of what knowledge can be stated about a system given some observation, as such it can be said to be a kind of empirical epistemic realism which has its benefits as a theory of knowledge but also has its disadvantages. 

I can accept that there are limitations to Bayesian analysis insofar as it can not prove its own axioms (and neither can any other system) and there are questions that science can not answer or test. However, when you say it has its own `disadvantages`, do you mean limitations in the questions it can answer, or do you mean to say that there are other methodologies that are better at answering those questions (i.e., would have an advantage over Bayesianism)? If the former, I'd agree with you but simply state that I know of no other epistemology that is any better; if the latter, then I'd be interested in an example.

I've been doing Bayesian analysis for years, and I have yet to find any other competing methodology that is as reliable. The continued reliability is why Science as a whole employs largely Bayesian philosophy. The frequentist philosophy is a subset of Bayesianism in many ways, so I don't consider it a competitor (you can derive it from Bayesian principles).

This is what really makes Bayesian tricky and it's really all up to the human in reality as the system cannot be inherently wrong if one accepts its empirical epistemic realist (transcendental realist/empirical idealist, I am combining the two into this new phrase) base; only the human being who chooses the wrong priors and hypothesis can be wrong. 

Indeed, if a person employs Bayesian analysis incorrectly or is missing some information necessary to draw conclusions, then the result is incorrect.

Bayesianism relates probabilities with information and lays out the framework to test hypotheses. However, information is what enters the prior, not belief, technically speaking. In situations where we don't know what the prior is, we require the Bayes factor in support of a given hypothesis to be extraordinarily large to offset the unknown prior interpretation. Otherwise, the result should be considered inconclusive.

At the very least, that is how it is employed in research.

Bayesianism just happens to be the best method, currently, to learn about the natural world. If you can come up with an example of another epistemology which can show that something we both accept as true is true, but which Bayesian analysis states is false, I'll be very surprised.

 Here I am not sure but it makes a very strong case for itself. 

 I am going to put a lot of thought into this though given it's important and also will deeper my understanding of the system as a   whole.

Right; if we're talking about epistemology or how to gather knowledge, I have knowledge of no alternative methods that can really compete with Bayesianism. There are questions that science does not answer / can not answer. However, I do not know of any epistemology that can answer those questions.

Phillip V of Macedon vs Inquirer

AppleGenius said: 

So the constant re-definitions were certainly an issue, and as you point out, that will essentially make the analysis useless because his framework doesn't have any predictive power and indeed the priors are useless then.

I re-defined once to re-explain, my point never changed.

One other problem I pointed out is that he is presuming that anecdotal evidence is equivalent to personal experience, which is simply not correct.

If we lack personal experience then multiple sources of anecdotal experience can still give us a sense of what's true. That's not evidence in a strict sense but it's still a valid basis for an opinion, which was my argument.

Had he accepted that something you've seen with your own eyes should count as much better evidence than hearsay, he would've needed to admit that John Johnson evidence is better than Inquirer evidence (because it was based on personal experiences/data accessible to Inquirer and the other one was not).

I asked you to give me sufficient John Johnson evidence for a list of people. You chose to give it only for the easiest one, Sensy. A person we never disagreed on. That's not proving my point wrong, it's disingenuously trying to circumvent it.

Dragoon said: 

Phillip V of Macedon vs Inquirer

 Did you watch the full two hours of it?

Oh shit part two incoming. 

I am finally clearly seeing cracks inherent to Bayesian Inference, they are not only problematic but run to its very foundations. 

AliceInWonderland said: 

I think I understand and I can see the utility of this form of analysis. 

let there be events A and B and conditional probabilities P(A|B) and P(B|A). 

P(A|B) = P(A∩B)/P(B) → P(A∩B) = P(A|B)*P(B) 

P(B|A) = P(A∩B)/P(A) → P(A∩B) = P(B|A)*P(A) 

Hence, P(A|B)*P(B) = P(B|A)*P(A) 

→ P(A|B) = (P(B|A)*P(A))/P(B) and P(B|A) = (P(A|B)*P(B))/P(A) 

Bayes theorem is then a statement of the relationship between two inverse conditional probabilities. The relationship can then be explored my assumption is that this is what Bayesian Analysis is used for, exploring this relationship and using it to make inferences. 

That analysis would begin with replacing the marginal probabilities P(A) and P(B) with their joint equivalents. 

That is, 

P(A) = P(A∩B) + P(A∩~B) and P(B) = P(A∩B) + P(~A∩B)

So, 

P(A|B) = (P(B|A)*P(A))/(P(A∩B) + P(A∩~B))

P(B|A) = (P(A|B)*P(B))/(P(A∩B) + P(~A∩B))

Now we sub the joint probabilities with there conditional probabilities, 

P(A∩~B) = P(A|~B) * P(~B)

P(~A∩B) = P(~A|B) * P(~A)

So, 

P(A|B) = (P(B|A)*P(A))/(P(B|A)*P(A) + P(B|~A)*P(~A))

P(B|A) = (P(A|B)*P(B))/(P(A|B)*P(B) + P(A|~B)*P(~B))

The expressions convey that P(A|B) and P(B|A) are therefore ratios between the product of some conditional and prior probability divided by the sum of that product and the sum of some of its conditional in relation to its negation. 

In statistical terms, specifically the use case of analyzing Hypothesis as you've stated, where A and ~A are hypothesis and B is a observation, 

P(B|A) is the probability of observation B given hypothesis A

P(A) is the probability of hypothesis A before observation B 

P(B|~A) is the probability of observation B given hypothesis ~A 

P(~A) is the probability of hypothesis ~A before observation B

Finally, 

P(A|B) is the probability of A given observation B

As such we can compare hypothesis A and ~A given some set of observations B (We can account for a set of observations by summating the denominator) and verify the validity of a given hypothesis through the ratio of these hypothesis when observations B are given. 

Is this correct and do you have anything to add? 

 

 

 Cool, you learn probabilities basics in highschool and again in college in Statistics I

Congrats

You guys do think you are somewhat intelligent, that’s cute