Questions tagged [mixture-distribution]
A mixture distribution is one that is written as a convex combination of other distributions. Use the "compound-distributions" tag for "concatenations" of distributions (where a parameter of a distribution is itself a random variable).
495
questions
0
votes
1
answer
39
views
Example of nonidentification mixture
Consider a continuous r.v. $X$ with pdf $f$ obeying the following finite mixture model for each $x\in \mathbb{R}$:
$$
f(x)=\sum_{k=1}^K \lambda_k f_k(x) \quad \lambda_k\geq 0, \sum_k\lambda_k=1
$$
...
- 889
3
votes
2
answers
198
views
Mixture distributions: an intuition on why we cannot infer the number of mixture components by visual inspection
I am studying mixture models and I would like your help with this question:
Consider the distribution $\Gamma$ and assume it is a finite mixture distribution, i.e., $\Gamma=\sum_{k=1}^K \Gamma_k \...
- 889
0
votes
0
answers
11
views
Continuous mixture distribution
I am currently working on the derivation of the negative binomial distribution as a result of a continuous mixture of Poisson and Gamma distribution for regression purposes.
To obtain the entire ...
- 623
0
votes
0
answers
67
views
Posterior distribution of shape & rate parameter in Poisson-Gamma Mixture
Currently I'm struggling to handle the following question.
Suppose $x_i,(i=1,2,\dots,n)$ follows Poisson distribution:
$$p(x_i|\theta) = \frac{\theta^{x_i}e^{-\theta}}{x_i!}, \quad x_i\in\mathbb N,\...
- 311
1
vote
1
answer
44
views
Minimum entropy decomposition of probability distributions
Say you want to decompose a probability distribution (a PDF) into a mixture of distributions in such a way as to minimize the mean entropy of the component distributions. I have an idea that this is ...
- 11
2
votes
1
answer
61
views
Estimating an unknown distribution from a mixture
I have two data sets, $\{x_i\}$ and $\{y_i\}$. I know that data set $\{x_i\}$ was sampled from some distribution $X$, and that data set $\{y_i\}$ is sampled from a mixture of the $X$, and some other ...
- 43
2
votes
1
answer
49
views
linear Combination of Normal and T-Distributions
Consider the following probability distribution function (PDF):
\begin{equation}
p(x) = a\mathcal{N}(x; \mu, \sigma^2) + b \mathcal{T}(x; \mu, \tau^2, v) \; \; st. \; \;a + b = 1
\end{equation}
$p(x)$ ...
- 331
0
votes
0
answers
13
views
Online mixture inference; better alternatives than windowed EM?
I have an online Gaussian mixture estimation problem that I would appreciate some input on. To be more precise, I have a stream of scalar observations $x_1, x_2, \dotsc$ arriving over time which are ...
- 145
8
votes
3
answers
284
views
Sampling from $P(x) \propto \cosh^{m}(a x) e^{-x^{2}/2}$
Is there an efficient algorithm to draw samples $x \sim P(x)$ from the PDF:
$$
P(x) \propto \cosh^{m}(a x) e^{-x^{2}/2}
$$
where $a\ge0$ is a real parameter, and $m$ a positive integer?
Since this is ...
- 4,440
3
votes
0
answers
20
views
Feature importance in expectation maximization
The context is using EM algorithm for a mixture model - more precisely Dirichlet Multinomial Mixture, as discussed in Dirichlet Multinomial Mixtures: Generative Models for Microbial Metagenomics. One ...
- 4,439
0
votes
1
answer
50
views
EM algorithm for mixture with latent regression?
I have in the past implemented the EM algorithm for certain cases of mixture distributions. However, I'm attempting to implement it now for a given problem that's exposing my lack of understanding of ...
- 2,842
1
vote
2
answers
88
views
Posterior of binomial and mixed prior
I'm currently studying posterior distribution with likelihood $y|\theta \sim B(n,\theta)$ and mixture of prior distribution $\theta \sim \pi Beta(\alpha_1, \beta_1) + (1-\pi)Beta(\alpha_2, \beta_2)$. ...
- 311
1
vote
1
answer
124
views
Generate marginally dependent (with predetermined covariance) but conditionally independent data from a Mixture of Gaussians
Suppose you have three variables $y\in\{0,1\}$ and $x_1\in\mathbb{R}$ and $x_2\in\mathbb{R}$. I want to produce data with the following generative process which corresponds to a Mixture of Gaussians (...
- 336
0
votes
0
answers
15
views
Calculating Mean Vector and Covariance Matrix of Mixture of Multivariate Normal Distributions [duplicate]
In an effort to better understand multivariate normal distributions, I am attempting to derive the mean vector and covariance matrix of multivariate random vector defined by a mixture distribution. ...
0
votes
0
answers
12
views
Combining factors, represented as normal distributions, to one combined factor, normally distributed
I'm trying to combine the different factors that may affect running pace, such as GPS-measured distance, grade, terrain, heat and other factors (such as wind etc.). Each factor is represented as a ...
