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The updates on that page come from belief propagation (a special case of EP). The general formula for belief propagation messages is: $$ m_{a \rightarrow i}(x_i) \propto \int_{\mathbf{x} \backslash x …

The paper The Kernel Gibbs Sampler by Graepel and Herbrich (2001) describes how to do Gibbs sampling over a sphere. They had a special likelihood function that gave piecewise constant conditionals, b …

There is no commonly used conjugate distribution for $\beta$ in this problem.

It depends a lot on the details of the problem being solved. You can find a tabular comparison between them here, which links to more information. You are right about VB generally requiring more ite …

Here are two examples. $x$ is normally distributed around mean $\theta$. The likelihood for $\theta$ is a normal distribution with mean $x$. $x$ is Gamma distributed with rate $\theta$. The likeli …

Logistic regression already has some slack but if you want even more slack you can use a softer link function. For example, replace the logistic function $\sigma(x)$ with $\sigma(\lambda \tanh(x/\lam …

The integral becomes a sum over the possible values of $\theta$.

I think the question is asking "how many parameters would be required to choose among any probability distribution compatible with this Bayesian network?". …

Since the domain is bounded by 0 and 1, in order for the mean to be 0.25 and the variance to be large, most of the mass has to be pushed up against the boundaries. There's simply no other way for the …

You are almost right. Use the sum of the two integrals rather than the product.

If you want the derivation of this result, read Bayesian inference, entropy, and the multinomial distribution. I have written several papers on exactly this topic. … If you want more examples, check out: Pathologies of Orthodox Statistics, Inferring a Gaussian distribution and Bayesian inference of a uniform distribution. …

You are right that the paper is saying the wrong thing. You certainly can evaluate the posterior distribution of $x$ at a known location using $O(n)$ operations. The problem is when you want to comp …

Yes, you can use different exponential families to approximate the marginal for different variables. You only need all messages into a variable to have the same type, so that they can be multiplied to …

I would use a first-order hidden Markov model. The transition distribution of the model corresponds to the room topology, as well as the probability of lingering in the same room. I would learn that …

The algorithm that you describe is treating $D$ like a variable in the problem, but using a method other than Bayesian inference to deal with $D$. … A Bayesian solution requires handling $D$ in a Bayesian manner, i.e. giving it a prior and integrating it out to get the marginal for $p_i$. …