# Questions tagged [bayesian]

Bayesian reasoning is a probabilistic approach to inductive and abductive reasoning, based on Bayes' rule, that posits when one event implies a second event is likely, that given the second event occurring, that increases the likelihood of the first event.

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### At what point should we suspect unfair game?

In probability theory, there are two primary approaches to interpreting events: the frequentist perspective and the Bayesian perspective. From a frequentist standpoint, each spin of a fair roulette ...
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### What principle protects the objective nature of the prior and the conclusion in Bayes’s theorem?

The Bayesian analysis begins with the "prior": some assumption about the world and the probability that the assumption is true. But the prior seems to be based on nothing. The hypothesis and ...
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### Mario Bunge on Bayesianism

I was reading Bunge's book "Chasing reality" (pg 116-117) and I came across the following text: To appreciate the enormity of the Bayesian attempted counter-revolution, consider, for ...
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### Is there any difference between abduction and induction in Bayesian terms?

In abduction we take some observations and try to find the hypothesis that best explains them. In Bayesian terms this sounds like finding the Maximum A Posteriori (MAP) estimate. To a Bayesian, "...
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### Bayesian conditional probability and material implication

I was reading E. T. Jaynes' Confidence Intervals vs Bayesian Intervals (available here), and I came across this statement regarding Boole's The Laws of Thought: Boole's own work on probability theory....
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### How is this Linda example addressed by Bayesian thinking?

Suppose that you see Linda go to the bank every single day. Presumably this supports the hypothesis H = Linda is a banker. But this also supports the hypothesis H = Linda is a Banker and Linda is a ...
1 vote
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### Does psychophysical harmony strongly point toward theism?

From Psychophysical Harmony: A New Argument for Theism, by Brian Cutter & Dustin Crummett: Abstract This paper develops a new argument from consciousness to theism: the argument from ...
1 vote
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### Is not knowing whether X is true inconsistent with assigning a probability to it?

I have read that it is wise to assign a non zero probability to beliefs, and not 0 or 1. This is because probability represents certainty and you cannot be certain of anything. xxxxxx However, if you ...
117 views

### Does an improbable outcome under a known hypothesis increase the probability of an alternative hypothesis?

Suppose you observe a claimed psychic get 10 guesses right after he says he will guess a number between 1 and 10 that you’re thinking of. After this happens, should your credence in psychism increase? ...
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### Can a zero prior probability for some theories be justified?

Let us assume the case of psychics and call the hypothesis of a “psychic explanation” H. Bayesian theory tells you to never assign a prior of zero. This is because if P(H) = 0, then no amount of ...
1 vote
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### Are there any examples of two theories that accurately describe a phenomenon where the more complex one was found to be correct?

I was reading this answer on how Solomonoff's theory of inductive inference can be used to posit the more correct theory amongst a set that provide the expected "answer", where the shorter, ...
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### Does a 100% degree of belief imply that no amount of evidence can change your mind?

As a reminder, in Bayesian epistemology, given a hypothesis H and new evidence E, it is recommended to update your degree of belief using the formula P (H|E) = (P (E|H) * P(H))/P(E). P (H) is the ...
343 views

### Does this Sleeping Beauty problem show conflicting priors?

Let's say that there are three beauties; Michael, Jane, and Jill. They are put to sleep and assigned a random number from {1, 2, 3}. If the coin lands heads then 1 is woken on Monday. If the coin ...
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### Is there any philosophy that specifically argues against subjective probability?

When I say subjective probability, I am referring to the notion of defining a probability in relation to a credence of belief. For example, one may say that there’s a very high probability that the ...
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### Bayes' Theorem and Science

More than one hypothesis may fit the data (hypotheses generation is the stock-in-trade of science) Choosing a scientific hypothesis is not about truth. People have gone on record that inter alia it's ...
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### Has Occam's Razor famously helped correctly solved some complex problem?

My thinking is that it is not something like Bayes' Rule -- I do not see it as being counter-commonsense. (I think Bayes Rule is almost fundamentally not commonsense.) If that is not true, that there ...
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### Bayesian argument for combining extraordinary claims

This is an improved version of Backwards Bayesian argument for alien visitation? It is said that extraordinary claims require extraordinary evidence and therefore this criterion is applied to every ...
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### How to accomodate hyperintensionality in a Bayesian framework?

Generally, propositions are modelled as sets of possible worlds, and Bayesians define a credence function on the set of those propositions. They then adopt new credence functions in response to new ...
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### What approaches are there to resolving the problem of new theories in Bayesian epistemology?

Bayesianism is thought to have a problem accounting for the development of new theories/beliefs. Since Bayesians would like to proceed by updating prior credences in response to new evidence via ...
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### Backwards Bayesian argument for alien visitation?

Let A = the hypothesis that aliens are visiting Earth Let E = evidence that aliens are visiting Earth The posterior probability that aliens are visiting Earth, given some evidence, P(A|E), can be ...
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### Consequences and importance of the "No Free Lunch Theorem"?

So I was watching this and was wondering about the consequences and importance of the "No Free Lunch Theorem" David Wolpert: that if I have any particular reasoning algorithm be it in say ...
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### Does Aumann's agreement theorem extend to moral propositions?

Aumann's agreement theorem says: two perfectly rational agents with the same prior estimate of an event's probability and common knowledge of one another's posterior estimates cannot come to ...
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### Is Occam's Razor a Prior?

In Bayesian statistics, the posterior probability of a hypothesis is composed of two parts: the prior, reflecting our initial belief in a certain hypothesis, and the likelihood, which represents how ...
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### Is modal logic too coarse-grained? [closed]

Modal logic has "necessary" operators (true in all worlds) and "possible" operators (true in some world). Compare this to probability, where only probabilities of 1 would be "...
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1 vote
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### Absolute confirmation of Carnap and consistency condition

In formal epistemology, consistency condition states that: An evidence E can't confirm both H and its negation, not-H. Carnap states that for the concept of absolute confirmation, the consistency ...
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### Questions on "Bayes or Bust?" by Earman

In bayesian epistemology, we usually find the bayesian theorem expressed in relation with three proposition: H, hypoyesis, E, evidence, K, background knowledge. In particular, in "Bayes or Bust?&...
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### Probability vs Possiblity vs gambling knowledge gap for a beginner

Probability is a difficult subject for me to grasp. I watch many religious vs atheist vs philosopher debates on YouTube where probability is often brought up, and because of my poor understanding I ...
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### Term for this bias kind of probability bias related to choosing the wrong reference class to calculate prior from? [closed]

Let's say that you want to calculate the prior for a woman in her 40s getting breast cancer. P(H) But instead of using the base rate from women in their 40s getting breast cancer, you use the base ...
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### Guessing the past - Bayes - Throwing Dart

I'm trying to understand how Bayes formula helps us make guesses about the past. What are your thoughts about the following philosophical metaphor regarding claims about events in the past? Whenever ...
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### What is my fallacy? LSAT Reasoning Question: Titanium Ink

I have a question regarding an LSAT Reasoning question and it drives me crazy Question is: Until recently it was thought that ink used before the sixteenth century did not contain titanium. However, ...
1 vote
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### Using Bayes Theorem in a Court Case - dementia and testamentary capacity

I'm trying to learn how to use Bayes theorem to explain probabilities in court cases related to dementia and testamentary capacity. Let's say that we are trying to explain the probability for a person ...
1 vote
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### Does Bayes' Theorem justify rejecting an argument for the supernatural from a well-supported miracle?

Suppose you have really good evidence for a miracle. Let's say that given the evidence, the probability of the miracle having occurred is about 80%. Now, you also know that miracles can only occur if ...
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### Logical Interpretations of Probability

According to Wikipedia's page on probability interpretations... Logical probabilities are conceived (for example in Keynes' Treatise on Probability) to be objective, logical relations between ...
1 vote