Questions tagged [bayesian-probability]
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How to deal with this Chicken-And-Egg problem ?
Let's imagine designing an odds pattern for a game, in which players bet for win or lose.
Suppose the probablity of winning is $p$, thus the probablity of losing is $1-p$.
Now imagine $n_1$ people ...
- 99
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Exploiting conditional independence working with covariance matrices
I have a Bayesian network where the number of nodes is potentially large. I've conditioned on some of the nodes (observed data) and I'm trying to draw samples from the distribution remaining nodes (...
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Continuous-time Markov chain to sample Bayesian posterior distribution
Given a Bayesian network and evidence for the values of a subset of the variables, a standard question is to compute the posterior distribution on the remaining variables. The Gibbs sampling technique ...
- 2,453
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A "simple" explanation of the concept of D-separation in a Bayesian Network?
Hello everyone.
I'm looking for a "simple" explanation of the concept of D-separation in a Bayesian Network.
As far as I know the definition is "two variables (nodes) in the network are D-Separated ...
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Conditional probability and independence
Suppose that we have vectors of events $\{H_1,...,H_n\}$ and $\{D_1,...,D_m\}$. Consider the following two sets of conditions:
Condition set 1
(1) $P(H_i H_j)=0$ for any $i\neq j$ and $\sum_iP(H_i)=...
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Estimating Wiener process parameters
Consider a Wiener process with zero drift, infintesimal variance $\sigma^2$, and an unknown starting value $\nu$. That is,
\begin{align}
Y_t \sim \mathcal{N}(\nu, t\sigma^2).
\end{align}
Now, ...
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Derivatives of conditional expectations
Let $X$, $Y$ and $Z$ be independent, real-valued random variables, probably with continuous density functions. Define $A = X + Y$ and $B = X + Z$. Consider the regular conditional expectation $E_Y(a,...
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What can be said about an infinite linear chain of conjugate prior distributions?
We can sample a discrete value from the multinomial distribution.
We can also sample the parameters of the multinomial distribution from its conjugate prior the dirichlet distribution.
Since the ...
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In Bayesian statistics, must I use a marginalized prior in conjunction with a marginalized distribution?// [closed]
Suppose I have some sampling distribution g(x,y,z) which has been marginalized over some variables (say y and z) giving us the marginal distribution which we'll call gx(x).
Suppose I now wish to use ...
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Are all probabilities conditional probabilities? [closed]
We know that $P(A\mid B) = \frac{P(A \cap B)}{P(B)}$. So $P(B) = P(A\mid B)P(A \cap B)$. Thus are all probabilities conditional probabilities? Can one make a probability more accurate by introducing a ...
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Probability estimates for pairwise majority votes
This is related to the rank aggregation question I asked previously.
I have items $I_1, \ldots, I_N$ and the observations of a number of pairwise trials which pit pairs $I_i$ and $I_j$ against ...
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