Questions tagged [mixture]

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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Mixture Models and Dirichlet Process Mixtures (beginner lectures or papers)

In the context of online clustering, I often find many papers talking about: "dirichlet process" and "finite/infinite mixture models". Given that I've never used or read about dirichlet process or ...
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Mixture model and Pymix (python package for mixture models)

I have a data set that behaves approximately Standard normal. It is an image where each observation is a pixel intensity. I want to cluster this into three different sets by fitting a 3-gaussian ...
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Algorithms for 1D Gaussian mixture with equal variance and noise cluster

I would like to fit a Gaussian mixture model to some data. The data is 1D and I want to constrain all the Gaussians to have equal variance. I would also like to have a uniform background noise cluster ...
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Goodness of fit test for a mixture in R [duplicate]

Possible Duplicate: Goodness of fit test for a mixture in R I just estimated the parameters for a mixture of two gaussians with different means and different sigmas, I would like to test if the ...
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Goodness of fit test for a mixture in R

I just estimated the parameters for a mixture of two gaussians with different means and different sigmas, I would like to test if the data adjusts well to the explicit form of the mixture, do I ...
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Fitting an exponential mixture model with interval constraints on the mixture weights

What methods are there to fit a model of the form $y=A\mathrm e^{Bx}+C\mathrm e^{Dx}+E$? Here is the actual scientific data to be fitted: http://dl.dropbox.com/u/39499990/Ben%2C%20real%20data.xlsx ...
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Variance of median from the mixture distribution

Consider iid samples from a fixed distribution function $F(x)$ and consider its median. Now consider another median from iid samples where one half is drawn from $F_1(x)$ and the other is drawn from $...
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Separating the populations in a bimodal distribution

I have a data set which displays a bimodal distribution. This was determined by plotting a histogram of the frequency vs number. I now need to separate the two original populations and therefore ...
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Generative modeling of a mix of continous and discrete variables

I'm trying to build a generative model to run a Monte Carlo simulation. The existing data consist of a combination of discrete and continuous variables. Suppose I have a number of people... ...
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Python packages for working with Gaussian mixture models (GMMs)

There seem to be several options available for working with Gaussian Mixture Models (GMMs) in Python. At first glance there are at least: PyMix - http://www.pymix.org/pymix/index.php Tools for ...
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Simple problem formulation for EM algorithm

I understand the EM algorithm, I understand for example how we get $Q(\theta, \theta^t)$, but I have trouble translating a real-world problem into the EM framework. For example, I'm given this ...
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Quick and simple cluster analyses for univariate data

Can you suggest any quick and simple clustering analyses, for univariate real-valued data? In other words, I have $n$ real numbers, $x_1,\dots,x_n$ where $x_i \in \mathbb{R}^+$, and I want to cluster ...
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Detect outliers in mixture of Gaussians

I have a ton of univariate samples ($x_i \in \mathbb{R}^+$). I'd like an automated method to check for outliers and identify the outliers, if any are present. A reasonable model for the distribution ...
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Minimum-Distance estimation of mixed/mixture distributions

Please note: I posted this first on Mathoverflow. Someone there advised me that on stats.stackexchange the question might fit better here. This is the link to the original post. I currently have to ...
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Can I use correlated variables in a mixture model?

I want to fit a mixture model with continuous (input) variables to cluster my data. Some of the variables are correlated with each other. Should I remove the correlated variables and retain only one ...
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Fitting a pdf against Weibull pdf

I have a pdf function as follows: $$\dfrac{1}{s+a-b} [bs e^{-bt} + (a-b)(s+a)e^{-(s+a)t}]$$ I want to fit this against a weibull pdf with shape=1.12 and scale=461386. I want to calculate the values of ...
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Proper use and interpretation of zero-inflated gamma models

Background: I am a biostatistician presently wrestling with a dataset of cellular expression rates. The study exposed a host of cells, collected in groups from various donors, to certain peptides. ...
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What is the variance of the weighted mixture of two gaussians?

Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and $...
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Generative model that penalizes clumping of data

I'm interested in modeling a generative process that encourages data to be "evenly distributed" over its support, i.e. clumping of data points is penalized. For example, if I have a mixture ...
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Analysis hierarchical circular mixture data

I have circular data such that multiple human participants were, each shown a color from a color wheel, asked to remember it for a "retention interval", then report it back by clicking a color wheel. ...
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Computing Gaussian mixture model probabilities

I was looking over the solution to this question on SO and it got me thinking about computing probabilities for a Gaussian mixture model. Let's assume you've fit some Gaussian mixture model so that ...
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How to differentiate two subgroups from a histogram?

I have a set of samples in which I assume there are 2 definite subsets in it. I plotted their values in a histogram and found that there are two distinct modes as shown in the figure below. My ...
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What's a component in gaussian mixture model?

What is the relation between a dimension and a component in a Gaussian Mixture Model? And what are the meanings of dimension and component? Thank you. Please correct me if Im wrong: my understanding ...
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Fitting 4-moment distribution with mixture gaussian

I know that Mclust does the fit on its own but I am trying to implement an optimization with the aim to generate a mixture of 2 gaussians with the combine moments as closed as possible to the moment ...
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Understanding expectation maximization for simple 2 linear mixture case

I would appreciate some help getting some EM stuff straight. So, say I generate data in R as follows: ...
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Data Augmentation Examples

I am looking for applied references to data augmentation (preferably with some written code). Either online references are books would be great. I found this book online: http://www.amazon.com/...
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Discerning between two different linear regression models in one sample

Suppose I observe a sample $(y_i,x_i)$, $i=1,...,n$. Suppose that I know the following: $y_i=\alpha_0+\alpha_1x_i+\varepsilon_i$, $i \in J\subset\{1,...,n\}$ $y_i=\beta_0+\beta_1x_i+\varepsilon_i$, ...
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Modeling a gamma-mixture waiting model in BUGS

I'm analyzing a noisy time series where where the inter-event interval is known to follow a two-gamma mixture distribution. If there was a simple model that would generate that kind of thing, it ...
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Using the EM Algorithm for unimodal distributions?

I've really only seen EM used for mixtures where one can point out multiple modes visually - e.g, the classic mixture of gaussians example. I would like to use EM for a mixture of an empirically ...
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Optimization of MLE for mixture problems

I have about 1000 data points from some thick tailed distribution that I would like to fit a parametrized distribution to. From my data, I've made some adjustments and constructed an empirical ...
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Learning parameters of a mixture of Gaussian using MLE

It seems that MLE (via EM) is widely used in machine learning / statistics to learn the parameters of a mixture of Gaussians. I'm assuming we're given random samples from the mixture. My question is:...
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How to identify points and an unknown distribution in a two type clustering problem?

I have a data set that contains two types of points. The first type of points come from an N(0,1) distribution. The second type of points come from an N(m,v) distribution for some real m and some ...
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Series expansion of a density function

Here's something I've wondered about for a while, but haven't been able to discover the correct terminology. Say you have a relatively complicated density function that you suspect might have a close ...
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Is there a standard method to deal with label switching problem in MCMC estimation of mixture models?

Label switching (i.e., the posterior distribution is invariant to switching component labels) is a problematic issue when using MCMC to estimate mixture models. Is there a standard (as in widely ...

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