The bayesian tag has no wiki summary.

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### Expectation of a random variable with respect to a distribution in variational Dirichlet methods

I have a problems calculating the expectation of a random variable over some distribution.
More specifically my current problem is the following:
I am trying to implement the algorithm regarding ...

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### In what sense is the Bayesian posterior mean a “convex combination”?

I asked this on math.stackexchange with no response, I'm hoping someone here might have something.
Suppose I want to estimate $x \in \mathbb{R}^n$ from two signals with zero mean, normally ...

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### Probability spaces involved in using Bayesian Inference

I am currently reading "Statistical and Inductive Inference by Minimum Message Length" by C.S. Wallace. In this, Wallace gives a fairly informal account of Bayesian Inference which, in the case ...

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### Simultaneous multiple perturbations in Markov chain Monte Carlo

I'm coding a McMC algorithm for geophysical applications.
Using the Metropolis-Hastings scheme to accept/reject the proposed models is smth that i thought i completely understood, but i don't. To be ...

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### What is the problem with this model parameter estimation algorithm?

In a statistical model with parameters $\theta$ and unobserved laten variables $Z$, the model likelihood is
$$L(\theta;X)=Pr(X|\theta)=\sum_ZPr(X,Z|\theta)$$
The standard way to estimate $\theta$ ...

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### Doubts about Bayes' Theorem [closed]

I meet one problem on the probability and statistic theory.
"Assume given a measure space $(X,S)$ with three probability measure $\mu_1,\mu_2,\lambda$ on the space. And there exsit functions ...

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128 views

### Parameter estimation using bayesian update on moduli space?

Scientists take a set of data points, say in ${\mathbb R}^2$, and, assuming that this data should fit a polynomial of degree $d$ (or an exponential, etc.), they estimate parameters.
I would think ...

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### 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 ...

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### 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 ...

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### 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 ...

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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 ...

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439 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 ...

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87 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 ...

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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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162 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 ...

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282 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 ...

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342 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, ...

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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 ...

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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?//

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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931 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 ...