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-1
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0answers
76 views

Quantum Bayesian update and Bayesian update of a model category

We know that we can have internal categories in a model category. We also know that there is a notion of Quantum Bayesian update in a monoidal category. Does the Quantum Bayesian update (equation ...
-2
votes
0answers
12 views

Probability of ongoing experiment [migrated]

Suppose, I do a experiment where I have an event 'a' true 1000 times in 1000 trials. So, the probability becomes 1000/1000 = 1. If I am going to do another trial, my prediction about event 'a's ...
2
votes
0answers
52 views

Can truncated/non-smooth distributions be used as priors/posteriors in Variational Bayesian methods?

Variational Bayesian methods can sometimes be a good alternative to Markov Chain Monte Carlo numerical evaluation of probability distributions. They do this, as I understand it, by approximating the ...
0
votes
0answers
42 views

Nice conditional distribution / Closure under noisy observation

Let $X, Y, Z$ be Polish spaces; $M$ a collection of full-support Borel measures on $X$; $\nu$ a Borel measure on $Y$; $f:X\times Y \to Z$ continuous with the property that $f(\cdot,y)$ is injective ...
0
votes
0answers
35 views

Marginalizing GP-LVM

Hello guys, I am taking a look at the "Gaussian Process Latent Variable Models" (GP-LVM) from Lawrence's paper (LINK) and because of my lack of experience in Bayesian modeling I am having some trouble ...
0
votes
2answers
76 views

What is the likehood function in the noise free observation case

In the nonlinear Bayesian Tracking problem, if we consider the noise exists only in the state equation : x[k] = f(x[k-1],v[k-1]) where vk-1 here is an iid process noise sequence And we suppose that ...
0
votes
1answer
193 views

bayes theorem on histogram [closed]

How can we apply Bayes theorem on histogram ?
0
votes
2answers
344 views

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 ...
0
votes
1answer
346 views

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 ...
1
vote
1answer
83 views

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 ...
1
vote
1answer
634 views

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 ...
0
votes
0answers
141 views

Projection of a probability distribution according to another one,

Hi, (Please forgive me if my question is vague or trivial) Let a normal distribution $P(\mu, \sigma)$ and a poisson distribution $Q(\lambda)$. I want to find a distribution $Q'$ that is : a ...
1
vote
1answer
273 views

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 ...
2
votes
0answers
278 views

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, ...
2
votes
1answer
1k views

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 ...
1
vote
1answer
389 views

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 ...
-2
votes
2answers
568 views

In Bayesian statistics, must I use a marginalized prior in conjunction with a marginalized distribution?//

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 ...
4
votes
6answers
1k views

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 ...
5
votes
3answers
926 views

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 ...