Tagged Questions

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 ...

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Matrix Calculation Significance and Multivariate Bayesian Methods

Suppose I have the matrix given by: $$X = \begin{bmatrix}1 & 0 & 0\\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}$$ This matrix actually represents whether a user interacted with a ...
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Explanation of Aumann's “agreeing to disagree” in modern notation

I'm attempting to understand Aumann's classic 1976 paper Agreeing to Disagree, which claims, under certain assumptions, that if two Bayesian agents share knowledge of each others' posteriors then they ...
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p(a,c) vs p(a∧c)

In this paper: https://www.aclweb.org/anthology/J/J16/J16-2006.pdf, the author breaks the Pointwise Mutual Information of a phrase up into several components: They use the ...
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find the maximum where gamma is attained

I have this problem and I am not figuring the beginning
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Determine probability based on observation

Suppose there is an urn with 100 balls, of two colors, say white and black. Let $p$ be the probability of drawing a white ball. You draw one ball, replacing after the draw. After 100 draws, each with ...
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Making sense out of the method for finding posterior distributions.

I have been recently studying Bayesian statistics and more precisely the problem of finding posterior distributions. I am able to understand the my textbook's problems, but I realize that I understand ...
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Probability that a clumsy boy eats $k$ out of 20 candies

A week or two (or maybe more) ago, the following question was posted and then deleted just as I was getting to the end of my solution. Unfortunately I have now forgotten what my solution was going to ...
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How can we use the Lindley's method to approximate the following expression?

The Lindley's(1980) approximation is one of the most popular methods that is used to obtain Bayes estimates. In this method we need to maximum likelihood estimators(MLEs) of the unknown parameters. ...
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Bridge from Bayesian update to covariance matrix

can somebody please explain me the step from the Bayes' Theorem to the covariance matrix or in a more special case from the Bayesian Update to the Kalman Gain. Best regards.
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implementing particle filters without a priory distribution

i am implrmrnting the particle filter, and i have some problem understanding the algorithm. given the state equations: $$x_k = f(x_{k-1},v_k)$$ $$z_k=h(x_k,u_k)$$ where $v_k, u_k$ are process ...
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Assumptions with Bayes's Theorem

After reading extensively on the subject I would like to clarify this apparent problem with "Bayes Rule". Namely the notation often used P(A and B) = P (B and A) has a big assumption that I will try ...
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Bayesian Nets and weird probability

I have to solve the following problem: Suppose we have a bayesian net in which we have the following variables: R, PA and PR Let: P(R) = 0.1, P(PA) = 0.5, P(PR|R, PA) = 0.6, P(PR|¬R, PA) = 0.4, P(...
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Calculating total probability given some conditions

One machine element is being produced in $3$ series, each series consisting of $20$ elements. In the first series, there are $15$ elements that work correctly, in the second series there're $18$ and ...
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Simple Bayes? Probability of a state at time t in hidden markov model

Suppose we have a HMM with $2$ states -- $A$ and $B$, with $P(A) = 0.4$ and $P(B) = 0.6$. $A$ has a probability of $0.9$ of outputting "hot," and $B$ has a probability of $0.1$ of outputting "hot." ...
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Application of Bayes theorem and Partition Law, total probability

Hi guys, preparing for my finals and trying to get this question out for practice. The exam is in a couple of hours so apologies for being brief. I think I have computed parts 1 and 2 fine. 0.3*...
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OpenBUGS: get a sample from a random variable

I'm working in OpenBugs, and I've defined the next model: $Y\sim {\rm Exp}(\theta)$ so I'm asked to assign different initial distributions to $\theta$: Normal, Gamma and log-normal, to this point ...
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Simple example of “Spike-and-Slab Prior” for Bayesian Inference

I would really like to understand how Spike-and-Slab Priors work in relation to Linearized Models. Can somebody provide a toy example of a Spike-and-Slab Prior with a Bernoulli spike and a Gaussian ...
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How many people should I ask if a statement (A) is true if the same can be inferred by asking two other statements (X and Y implies A)?

I am asking a number of participants if they believe a given statement is valid. I have a number of such statements, some of which can be inferred. In the made up example below, ...
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Approximation of product of Bernoulli with different proportions

I want to update a variable $Y$ with Beta (uniform for simplicity, $Y \sim U(0, 1)$) distribution, with Bernoulli information each period... But each period the proportion parameter of the Bernoulli ...
I have been stragling with figuring out this equality: $\pi(\psi|data)=\int_{\Theta}\pi(\psi|\theta)\pi(\theta|data)d\theta$ Can anyone help me go through the proof? Thanks!
I get a sequence of data that is generated by a distribution with parameter $a_0$ (e.g. $\mathcal{N}(a_0,1)$). I assume a prior distribution $P(a)$, and Bayesian update for the belief according to the ...