# Questions tagged [mixture]

A mixture distribution is one that is written as a convex combination of other distributions.

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### Help me understand the Bayesian kernel density estimation (Sibisi and Skilling, 1996)

Sibisi and Skilling (1996, also mentioned in the 1997 paper) define Bayesian kernel density as $$f(x) = \int dx' \,\phi(x')\, K(x, x') \tag{2}$$ Here the kernel $K$ is an assigned smooth ...
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### How to predict state probabilities or states for new data with DepmixS4 package, for Hidden Markov Models

It seems like I can learn the parameters just fine and find the posterior probabilities for the training data but I have no clue on how to make new predictions on new data. The problem in particular ...
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### Label Switching in WinBugs/JAGS

I am using JAGS to estimate a Dirichlet Process Mixture of Normals. The code works well and the estimated density is accurate. However, I would like to know which component each observation is ...
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### Relationship of Poisson regression to determining proportions in a mixture distribution

I am a particle physicist, and a very frequent task is: given data sampled from a distribution mixture $$Z \sim \sum_i \phi_i F_i,$$ where $\phi_i$ are the mixture proportion / prior probabilities ...
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### Estimate fraction of a known distribution in a mixture with unknown second distribution

Suppose I have a set of bulbs, which are known to be healthy. For each bulb I have a value of its brightness. The underlying distribution is not necessarily normal, and possibly have some complex ...
101 views

### Sampling from mixture of *unnormalized* densities

Suppose I have $n$ unnormalized densities $g_1(\textbf{x}), \ldots, g_n (\textbf{x})$, for $\textbf{x} \in \mathbb{R}^d$, and $n \gg 1$, which largely overlap but in a nontrivial way. I need to sample ...
583 views

### Expectation and variance of sample mean with random sample size

I have a question regarding sampling where the sample size itself is a random variable. Say I have two sub-populations $A$ and $B$ from which I can sample a real valued random variable with ...
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### Closed form posterior for product of inverse Gamma and Normal distribution

I am currently reading a book about mixture analysis, and in the textbook a posterior for the parameters $\mu1,\mu2,\sigma_1^2,\sigma_2^2$ of a two-component gaussian mixture is derived as follows (S ...
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### Ideas for fixing manual misclassification

Imagine the following problem. Mechanics fix cars and use a set of parts which is recorded on invoices. They also write down a classification of the work that was done from a fixed set of possible ...
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### A 2 component mixture is symmetric if and only if $\lambda\in \{0,1,\frac{1}{2}\}$

Consider the following mixture of two densities $$f(x)=\lambda g(x-\mu_1)+(1-\lambda)g(x-\mu_2)$$ with $\lambda\in [0,1]$, $g(\cdot)$ symmetric around zero, $\mu_1<\mu_2$. Claim: the mixture is ...
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### How to implement Exponential Power distribution in JAGS

I would like to fit a simulated data to Exponential Power likelihood using uniform mixture with gamma mixing presented in "Scale Mixtures Distributions In Statistical Modelling" by Choy and Chan: \$EP(...