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I do understand that the Gaussian model in the SBM does not necessarily imply that the weights have to be Gaussian distributed overall as it can be a mixture of different Gaussians for within and between … for strongly non-Gaussian weights? …

This question is about how generalized eigenvalues of two covariance matrices relate to the discriminability of their associated Gaussian distributions. … It is clear how the individual $\lambda_i$'s of a pair of covariance matrices reflects how discriminable their 0-mean Gaussians are along the corresponding $\Phi_i$. …

for the mixture, let's split into three components temporarily: The two discrete components The continuous component, which will be a mixture of two beta. … the advantage here is that the probability of each component can be fit wihtout considering the precise value of $Y$, only whether it is $0, 1$ or in-between. we can fit this with any gaussian process …

Assume the two distributions (of differences) are Gaussian, and do a simple Z-test. Is this valid and is there a better approach? … As @whuber implied, the histograms do not look Gaussian. With two big peaks around 0 and some constant which is the result when the probabilities differ at most one element. …

Spike-and-slab: the model parameters are assumed to follow a Mixture of gaussians. However, the posterior is hard to sample from due to the nature of the prior. …

The most popular example that comes up in this regard is the Gaussian Mixture Model: $$p(x, \pi_1, \pi_2, \mu_1, \sigma_1, \mu_2, \sigma_2 ) = \pi_1 \cdot N(x | \mu_1, \sigma_1) + \pi_2 \cdot N(x | \mu … Why cannot MLE be implemented for Gaussian mixture model directly? Why is the marginal likelihood difficult/intractable to estimate? …

I want to produce data with the following generative process which corresponds to a Mixture of Gaussians (MoG): $$ \begin{align} y\sim & Ber(p)\\ \mathbf{x}\sim & \mathcal{N}(\mu_y, \Sigma_y), \end{align …

probability of generating a certain realisation $w_{𝑗^∗}$ This is a product of the probability to propose a death/birth move when having $k+1$/$k$ components and of the density of the proposed new mixture … [Imho, a simpler representation of the moves would be to express the mixture in terms of unnormalised weights divided by their sum.] …

Take a simple case: the data $x$ is a mixture of Gaussians generated by picking a cluster index $z$ (from a categoric distribution $p(z)$) and then sampling from the Gaussian of that cluster $p(x|z)$. … For example, in the mixture of Gaussians case, inferring $z$ identifies the cluster of each data point, which may be semantically meaningful. …

the mixture is over the distribution of $\gamma$. … Lastly, if we specify a distribution (say gaussian) for $\gamma$ in the mixture model thereby allowing for infinite values of $\gamma^{}_{i}$, are we back to a random effects world? …

But, for instance, a sum of $K$ Gaussian random variables, $X_1+\cdots+X_K$, is still a Gaussian, whereas a random variable whose density is the sum of Gaussian densities (as the case in question) is not … Gaussian. …

In discussing Gaussian mixture models (GMMs), https://normaldeviate.wordpress.com/2012/08/04/mixture-models-the-twilight-zone-of-statistics/ highlights the issue of Multimodality of the Likelihood. … variance-covariance matrix for each of the $k$ components separately, and in this case the likelihood has a single maximum and a relatively simple closed-form solution (see Maximum Likelihood Estimators - Multivariate Gaussian …

To get a sample from the mixture, you pick either $X$ or $Y$, with probabilities given by the mixing proportions. … The distribution of the mixture isn't; a mixture of two Normals is bimodal, because you get an observation from one or the other. …

The paper that you refer to by Hans (2011) "broadens the scope of the Bayesian connection by providing a complete characterization of a class of prior distributions that generate the elastic net estimate … $\ell_0$ regularization can be thought (Polson and Sun, 2017) as using a prior that is a mixture of Dirac delta centered at zero $\delta_0$ and a Gaussian $$ \pi(\beta_i) \propto (1 - \theta) \delta_0 …

I use $H$ instead of $F$ because the distributions may belong to different families: for example, if $F$ is Gaussian, $H$ (which is a mixture of Gaussians) will in general be non-Gaussian. … Here is a specific example (although I am interested in the general case described above): $H$ is a mixture of two Gaussians Component 1 has weight $\pi_1 = 0.5$ and is $\mathcal{N}(\mu, \sigma^2_1)$ …