# Questions tagged [bayesian]

The approach and interpretation of probability associated with Bayes' theorem; usually used as opposed to the frequentist approach. It can be seen as an extension of logic that enables reasoning with propositions whose truth or falsity is uncertain. A Bayesian probabilist starts with some prior probability, and evaluates the evidence in favour of a hypothesis by combining the prior with the likelihood function of the observed data.

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### How to use Bayesian Inference in this problem? [closed]

I've just learned Bayesian Inference and encountered this math problem: "A box contains 20 of both red anh black balls. Hypothetically, 40% <= the ratio of red balls <= 75%. Pick 5 balls ...
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### Bayesian Approach to Hypothesis Testing: Posterior Probability that Two Distributions Differ

I'm trying to take a Baysian approach to Hypotheisis testing but I need a bit of help formalizing what claims I can actually make. Let's assume I have two datasets $X$ and $Y$ that each consist of $N$ ...
1 vote
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### Notation for probability density function in Bayesian context

The Bayes theorem is often quoted as, $$P(\theta|X) = \frac{P(X|\theta)P(\theta)}{P(X)}.$$ In my use case, I'm dealing with Gaussian continuous variables. So, by $P(X|\theta)$ I'm referring to the sum ...
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### How do we derive the conditional distribution for a Poisson whose rate is the product of two Gamma distributed rv?

This question is motivated by Gopalan et al. "Content-based recommendations with poisson factorization." Advances in neural information processing systems 27 (2014). https://proceedings....
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### Mathematical Definition of "Improvement"?

In the context of Bayesian Optimization, we model the Objective Function we are trying to optimize using a Gaussian Process. The location at which we evaluate the Objective Function at next is decided ...
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### a simple question about conditiona probability

known conditions: $$P(b|a) = 0.6 \\ P(c|b) = 0.8 \\ P(c|\neg b) = 0.7$$ What I want to solve: $$P(b\cup c|a )$$ (in the condition of "a" happen, at least one of b and c happen. ) I tried ...
1 vote
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### bayesian gauss prior prove

given zero mean Gaussian prior as $\beta~ \sim(0,\Sigma p)$ inference is given by $\log p(\beta \mid y, X)=\log p(y \mid X, \beta)+\log p(\beta)-\log (y\mid X)$ I can't understand how to get the ...
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### Necessary conditions for $P(A|B)=P(A|C)P(C|B)$?

Suppose we know $P(A|C)$ and $P(C|B)$ and we want to find $P(A|B)$. What are the necessary conditions under which the $C$ "cancels out" and we have the equality $P(A|B)=P(A|C)P(C|B)$? I have ...
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### Naive Monte Carlo Sampling vs. Importance Sampling

Can someone help me understand this paragraph: The naive Monte Carlo estimator introduced in the last section performs well if the prior and posterior distribution have a similar shape and strong ...
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### What is a latent spatial process?

What is a latent spatial process in the context of Bayesian hierarchical models? For intensity, we model daily precipitation above a high threshold at 56 weather stations with the generalized Pareto ...
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### Modeling dependent events

Say we have event A (saving a life) and event B (person living after initially getting saved). A and B are dependent events as p(A|B) = 1. I want to model the probability of a person living which is p(...
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### Dropping Conditioning in the Prior for the Posterior Distribution Linear Regression

In linear regression, we have the following formula $$p(w | X, Y) \propto P(Y | X, w) P(w)$$ where $X$ is a sample vector input data (and is random). $Y$ is the corresponding vector of output data. ...
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### probability of rolling a consecutive 1, 2, 3, 4, 5, 6 on a die

Questions I was wondering what the probability of rolling a consecutive $1 ,2, 3, 4, 5, 6$ on a dice is? For realism, is there any way to calculate an 'extra' factor, such as someone kicking the table ...
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### Reference request: multi-armed bandit problems with analytical solutions

Is there a book/survey on (multi-armed) bandit problems that yield analytical solutions? I.e. has an exactly optimal closed-form solution (e.g. derived using dynamic programming).
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1 vote
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