# Questions tagged [mixture]

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

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### Random Samples from Spliced Distribution

I am studying Clauset, Shalizi, and Newman, Power Law Distributions in Empirical Data (preprint available here) in R. Packages used: ...
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### Modelling a random variable that is mostly zero, but otherwise exponential (PyMC3)

I'm new to probabilistic programming, and have run into problems of this kind a few times now. Simply put: I often find myself wanting to model a random variable that mostly has some nice, continuous ...
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### Clusters keep switching in Gibbs sampling of Dirichlet Process Mixture Model

All the code and data for this question is on GitHub (stackexchange.R script). I've got multivariate Bernoulli data that I'd like to analyse using Bayesian Mixture ...
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### How to latently cluster regressors based on regressors' relationship with the outcome?

What is the best way/method to model patterns across coefficients and reduce number of coefficients based on these patterns? We have hundreds of regressors on the same scale and try to reduce the ...
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### Significance of modes in a distribution

I have several datasets with angular measurements, i.e. circular values from 0 to $2\pi$. These datasets tend to have peaks at 0 and/or $\pi$, and I need to tell if the peaks are detected/significant. ...
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### Estimating two-component mixture of Weibull distributions?

Is there any existing package (preferably in Python or Matlab) to estimate the parameters of a two-component Weibull mixture model? And failing that, I am hoping to get some pointers towards rolling ...
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### Predication of MDN

How to get the prediction of Mixture Density Networks? In MDN one models the conditional density: $P(y^i |x^i) = \sum_{j=1}^{m} \alpha_j(x^i)\phi({y^i|x^j})$, so I guess one just sample from the ...
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### latent variables in EM algorithm are assumed to be i.i.d from multinomial distribution, from what they are idependent

In EM algorithm we introduce a latent variables, say $z_i$, $i=1,...n$, $n$ is the number of the mixture component. These variables ($z_i$) are assumed to be independent and identically distributed ...
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### How to find quantiles and likelihoods of mixture distributions?

My PDF: M was estimated and found to be 5. I need to work out the quartiles for the PDF above. In addition, I need to use different methods of estimation to estimate the parameters. So far I've ...
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### How is jaccard similarity used to find the similarity between Bootstrap samples when measuring stability of EM?

Im reading the answer on "how to determine number of clusters in EM algorithm". How to tell if data is "clustered" enough for clustering algorithms to produce meaningful results? One of the ...
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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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### Can mixture model used as classification prediction

I am learning a prediction model in statistic. I read that we can used mixture model as a classification. My question is, assume we have a data which can be divided into two groups. Can we in this ...
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### Joint posterior for finite mixture with normal components

I currently read the book Finite Mixture and Markov Switching Models by Sylvia Frühwirth-Schnatter and I have a question regarding Section 6.2.1 regarding finite mixtures with normal components. Maybe ...
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### What does it means for “fit a less parsimonious model” in a clustering algorithm?

I'm now trying to implement the algorithm presented in https://www.stat.washington.edu/raftery/Research/PDF/fraley2005.pdf. The algorithm is the following one: First I get a mixture model for ...
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### Mixture of Poissons for positive and negative integers

I'm trying to design a generative model for a random variable $k\in\mathbb{Z}$. The model would work as follows. First draw $b\sim\text{Bernoulli}(p)$. If $b=1$, draw $k\sim\text{Poisson}(c)$. ...
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### Binomial distribution for randomly drawn probabilities

Setting Probability theory can be a weird place sometimes. Here I was, confident in my insane math skills, trying to solve the following problem: Let $N, \alpha$ and $\beta$ be given. ...
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### Is it acceptable in mathematical saying that the E-step is equal to posterior probability

I am studying EM-algorithm for mixture data. I read that some authors said that, the E-step is equivalent to the calculation of the posterior probability (I think this come from Bayesian rule). So, my ...
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### Point mass at zero and a chi square distribution with one degree of freedom

I am unclear about the critical value of a point mass at zero and a chi square distribution with one degree of freedom. How to find this?
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### Equivalent way of rewriting a two-component mixture

I'm confused on the following equivalent way of rewriting a two-component mixture. Consider the two-component conditional mixture $$F(z|x)=\lambda F_1(z|x)+(1-\lambda)F_2(z|x)$$ where all the $F$'...
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### Simulate from a mixture of two beta distribution [closed]

I have this distribution : $X \sim 0.75\mathcal{B}e(\alpha_{X_1}=1,\beta_{X_1}=3)+0.25\mathcal{B}e(\alpha_{X_2}=5,\beta_{X_2}=1.75)$ where the density function is given from this function: ...
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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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### Mixture of two components

Consider a univariate probability density function $p(x)$ that is a mixture of $2$ probability density functions with weights $\eta, 1-\eta$ and $\eta\in (0,1)$:  p(x)=(1-\eta)g(x)+\eta f(x) \...
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### Calculating the probability that an observation comes from either population A or B

If I have two normal distributions A (mean = 0, variance = 4) and B (mean = 0, variance = 16), how can I calculate the probability that an observation with magnitude 2 comes from A?
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### Why we do not accept the result of our simulation study as evidence of a limitation of one method

I am doing a mixture model. I have established a new method using EM-algorithm. I have simulated data from a mixture model. Then, I applied my new method to the data. The result is very satisfying. ...
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### How to build a Bayesian Model to estimate the probability distribution of the parameters given the output?

I'm currently facing a new type of problem, and i have no idea how to solve it, so any suggestion will be really appreciated ! The problem is the following: I have a matrix of temperatures, depending ...
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### Inferring GMM parameters with Gibbs Sampling

On my book, "Machine Learning A Probabilistic Approach". It's stated that is straightforward to derive a Gibbs sampling algorithm to fit a mixture model, especially if we use conjugate priors. So ...
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### Understanding short animation about Dirichlet Process Mixture Model

On the wikipedia page of Dirichlet Process, there is the following video. I don't get the point of the video. My first impression was that the video was showing the fitting of one-dimensional data ...