# 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).

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### 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 $\theta \sim \pi Beta(\alpha_1, \beta_1) + (1-\pi)Beta(\alpha_2, \beta_2)$. ...
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### 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 (...
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### 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. ...
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### 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 ...
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### How do we obtain the posterior of a beta binomial mixture of continuous and a discrete density?

In section 3.6 of Jim Albert's 2009 book "Bayesian Computation with R" he describes a test of whether a coin is fair using a mixture of priors. The coin tossing follows a binomial ...
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### Flexmix maxima are not where they are expected to be

For my dataset I have plotted the density with ggplot. As the data's density is multimodal (a total of 6 destinct modi) I tried to gain insight on the normal distributions associated to each modus. ...
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### Kolmognorov Smirnov test p values is 0

I am trying to use Kolmogorov-Smirnov test to check the goodness of fit of the distributions for the dataset. I have dataset consisting of 100,000 samples and I apply expectation-maximization ...
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### Cluster based on random effects, STAN

I have a problem where I measure repeated responses in condition A and in condition B for a set of individuals $i=1,...,n$. I am interested in learning about the effect of the condition in the ...
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### Log likelihood of mixture distributions

If I have a gamma mixture distribution represented as, $$f(x;\alpha,\beta) = \sum_{i=1}^{N}\pi_if(x;\alpha_i,\beta_i)$$ Where $\pi$ represents the weights of the $N$ components. For $N=2$ and the ...
1 vote
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### Understanding gamma mixture model

I am trying to understand the gamma mixture models, especially the significance of the 'loc' parameter in scipy.stats. In the code below, I generate a mixture ...
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### Finding subgroups in population, using individual effects of hierarchical model

I want to know how to look for effects both at a population level, and at an individual level in an experiment. I was wondering if I can do this with hierarchical Bayesian models as follows. In a ...
1 vote
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### Bayesian conjugate updating when the likelihood can be approximated by a finite mixture of normals?

I'm facing a situation where I'd like to do Bayesian conjugate updating, but both the prior and the likelihood (a Student-t) can only be approximated by a finite mixture of normals. I know that a ...
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### Are marginal probabilities a mixture model of the conditional probabilities?

In a contingency table, is it correct to say that the marginal probabilities are a mixture model of the conditional probabilities? Also, is it correct to say that these marginal and conditinal ...
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### Maximum likelihood estimate for mixture with components using both cartesian and polar coordinates

I have a set of points (x,y) that were generated from a mixture of two components: one component uses Cartesian coordinates, and the other polar coordinates. For example, with probability $\gamma$ I ...
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### Mixture Model on Time Series with different number of observations on each time point

Suppose that we a dynamic series of values over time points $t=1,2,...,T$ and observations on each time point being $n_{t}$. So, we have a collection of values $y_{i,t}$ with $i=1,2,...,n_{t}$ that ...
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### Approximaion with uniform mixture density

Assume that a RV is drawn from a distribution with PDF $f(x)$. I would like to approximate this distribution as a mixture of infinitely many uniform distributions. Without loss of generality, assume ...
1 vote
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### Are there any fast algorithm to estimate a Bernoulli mixture model?

In a problem I need to estimate a Bernoulli mixture model with 3 mixing components. More specifically, we have a random vector $\mathbf{D}=(D_1,D_2,D_3,D_4,D_5)$. $D_1,D_2,D_3,D_4,D_5$ are drawn ...
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### Loss Function for Neural Network with High density at 0

I am working on a time series project and looking to use a transformer based Neural Network (specifically, temporal fusion transformer). My data is extremely heavily at 0 (the use case is that most ...
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### Is every Compound Poisson distribution a Mixture model?

We have two models: Let $N \sim \hbox Poisson (\lambda)$ and let $(X_k ; k =1,2,3,...)$ be a a sequence of independent and identically distributed random objects (random variables, vectors or ...
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### Extracting distributions from R density function

I am looking for a not terribly complicated solution to deconvolute a series of overlapping distributions. The data may be noisy and I am considering using R's density function. ... 1 vote
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### MLE for a mixture of betas without using EM algorithm

Suppose I have a mixture of two Beta densities say $f_1 = \text{Beta}(1,1)$ and $f_2= \text{Beta}(1,\beta)$ where $\beta$ is unknown. The sample $X_1,....,X_n$ is observed based on latent Bernoulli ...
1 vote
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### What is the best way to calculate the fit of the mixture distribution to the actual data?

I have fitted the mixture of Gaussians to the natural log of the data. I know that the model is not a very good fit to the data in the tail region, however in the high density region the actual data ...
1 vote
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### Is there a way to fit two distributions from exponential family and overcome discontinuity in parameters?

I have data that follows LogNormal distribution in the body (high density region) of the distribution and it seems like it has an Exponential tail after a particular 'cut' point. Given that these two ...
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### Mixtures vs Multi-level models?

I'm confused on how mixture models and multi-level models are different (if at all.) Are there general rules for when to use one and not the other, pros/cons, etc?
Im trying to implement the EM algorithm on mixture model: $pg(x) + (1-p)h(x)$ where the sample $\bar{x} = (x_1, \ldots, x_n)$, is independently generated from the mixture, and $g(x) = e^{-x}$ and \$h(x)...