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

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Mixing probabilities in mixture models using EM

Assume we want to estimate the mixing probabilities ($\pi_{k}$) for each member distribution in the mixture model. We know that $\sum_{m}^{K}\pi_{m}=1$, so we can formulate the optimization problem ...
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EM for Mixtures of Bernoulli (M-step)

When applying the M-step for a mixture of Bernoulli distributions, one of the parameters in our maximization is the Bernoulli parameter $\mu_{k}$, where $k$ is the index of the "mixture component", ...
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Finite mixture models - Basic understanding

I have been reading lecture slides about Dirichlet Process. In page 22, there is a picture about the following finite mixture model. $$\phi _{k}\sim H\\ \pi \sim Dirichlet(\alpha /K,\dots,\alpha ...
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How can I partition a distribution into two sub-populations with fixed bias? (simulation)

I am trying to simulate a selection model for a variable $Y$ dependent on covariate vector $X$, so that two groups/sub-sets $S=(0,1)$ of observations on $Y$ are created, which have a fixed difference ...
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non-EM algorithm approach to mixture model?

I have a mixture model and the components are further parameterized by ~200 variables. Originally I use EM-algorithm to get a MLE estimation of the parameters. The algorithm works quite well and ...
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68 views

Binary version of Probabilistic Matrix Factorization in pymc?

I'm a newby in statistics, this is my first post, sorry for any possible mistake. There is a good Bayesian Probabilistic Matrix Factorization model introduced in: Bayesian Probabilistic Matrix ...
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28 views

Evaluate mixture model

I have a question concerning the evaluation of mixture models. Is there a gold standard to compute the goodness of a fit for a mixture model? What I am concerned about is how one would evaluate if ...
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30 views

How to separate distributions from weighted dataset?

I’m trying to separate two component distributions of an apparent finite mixture from a weighted dataset (determined by a weighted.histogram). I've a set of data and weights only for a part of the ...
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Restricted fitting of two-component mixture distribution in R possible?

In fitting a two-component Student's t mixture distribution to some data (standardized GARCH residuals) one of the components has an estimated degree of freedom of 0.6. This means that even the first ...
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Specifying a Normal-Log-Normal Mixture (Skew Normal) in WINBUGS/JAGS

I am an actuary working on a Bayesian loss reserve model using incremental average severity data. Exploratory analysis of the response seems to suggest a skew normal distribution of some sort would be ...
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Good (2d) visualization of a mixture model clustering

I have a specific problem which I'm surprised I don't find answers on-line and I hope somebody here has a good suggestion for me. I'm working with a large data set which I'm clustering into specific ...
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76 views

parameter estimation of a mixture distribution

I have this mixture distribution $f(x) =w \cdot \mathcal{LN}(\mu_1,\sigma) + (1-w)\cdot \mathcal{LN}(\mu_2,\sigma) $ where $\mathcal{LN}(\mu,\sigma)$ is a lognormal distribution. I now have $j$ ...
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Bernoulli mixture models for image classification, pathological cases

I'm trying to use a Bernoulli mixture model to classify MNIST images, and I'm running into pathological cases which screw up my calculations. The pdf of a multidimensional (let's say N dimensions) ...
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38 views

Identifying a mixture model

I am trying to fit a mixture model to a dataset that consists of counts (so every record is a count of something, like the number of attempts by an IP address to connect to a website). I know, a ...
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105 views

Nonparametric mixture model and clusters

I have a question about clusters that I am contemplating to treat with a nonparametric mixture approach (I think). I am working on the explanation of human comportment. Each row of my database ...
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1answer
87 views

How to test against a mixed distribution?

There is a population $D$ in which each data point has two attributes $X$ and $Y$ that are randomly distributed. While they are probably not exactly normally distributed I imagine they are not too ...
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51 views

Probability of data point being from distribution in normal mixtures

Using JMP, I was able to fit a distribution to a set of data, using the normal-2 mixtures model. It returns location (or mean), dispersion (standard deviation) and probability for each of the two ...
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86 views

Automatically fitting a mixture distribution with two univariate scaled noncentral student's t components

So far my own trials to fit such a mixture distribution to simulated or real data in R were unsuccessful (even if the data was simulated from a two-component t mixture!!!). I'm about to try the same ...
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24 views

Library for Bayesian infinite mixture models

Can anyone advise me on a good library in Python, Java or R for constructing an infinite Bayesian mixture model? Other options are also welcome. Thanks.
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Test is data is derived from mixture or just noisy normal

Is there a way to quantify \ test \ describe how likely it is that high dimensional data come from a single Gaussian or a mixture of Gaussians (with different means \ SDs) or not? What I am thinking ...
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93 views

Is there an analytic formula for the kurtosis of a (student t) mixture distribution?

The mixture distribution should be composed of noncentral scaled student t components. The mean of the mixture distribution can be calculated easily just by weighting the component means according to ...
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94 views

How fitting a mixture distribution of noncentral Student t components to a one-dimensional sample in R?

I`d like to extract the parameters of a two-component mixture distribution of noncentral student t distributions which first has to be fitted to a one-dimensional sample. My question is closely ...
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25 views

Is this method for mixing doubly Truncated Normal distribution acceptable?

Say I have to mix n double Truncated Normal distributions $\textit{TNormal(μ,σ$^{2}$,0,1)}$. Furthermore, each distribution has a weight w. w represents the influence of the distribution in the ...
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56 views

Bayesian mixture model for univariate continuous random variable

I'm quite new to the mixture models and I hope you'll help me to understand how they work. Suppose I have a univariate continuous random variable x which represents time of a visit, and suppose that ...
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What is a mixing process?

What does this mean? Asset prices follow a mixture of normal distributions with a mixing process dependent on the unobservable information arrival process.
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Is there other types of mixture distribution besides the normal mixture

There are quite a lot of study on the normal mixture distributions, say, $X=Y*Z$,where $Z$ is a normal r.v. and Y is a r.v. follows other distributions and $Y$ and $Z$ are independent. Some well-known ...
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64 views

Inverse CDF of Mixture of Gaussians Without Sampling

It is fairly straightforward to compute the inverse cdf a gaussian mixture model by doing sampling (first selecting a component of the mixture according to the coefficient of the component, then ...
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Negative binomial distribution mixture model with R

I have two data vectors of observed count data: $A$ and $B$, where count $A_n$ and $B_n$ refer to the same observation point. $A$ is assumed to follow a negative binomial distribution. $B$ is assumed ...
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98 views

Parameter Estimation of a Poisson mixture model

I want to estimate the parameters for a Poisson mixture model with 2 (and later 3) Poisson distributions. I want to use Matlab and have numerical problems to solve the loglikelihood of the mixture ...
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55 views

Separating mixture with little a priori knowledge

I have a dataset (time series data) of measured signal power values from a radio receiver. The data does not originate from a controlled experiment. I have limited knowledge of the underlying ...
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470 views

Manually fitting a mixture distribution in matlab

I am trying to fit a mixture model containing a gamma and an exponential distribution: The general form, using the pdfs, is: p * gammapdf + (1-p) * exponentialpdf. The pdfs for the Gamma and ...
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Ranking undergrad students by their future income - Mixture distribution

I would be very grateful for some advice on how to model mixture distributions with R. Given a problem to create a ranking of graduate students by their yearly income after completing their ...
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31 views

Single-class vs two-classes hypothesis testing

Consider a Gaussian mixture model of unknown parameters, having just one or two components. I would like to design a statistical test to decide the number of classes ($H_0$: single component model vs. ...
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138 views

Dirichlet process mixture model with Bayesian hierarchical clustering

I am doing Bayesian hierarchical clustering. From my understanding, there are three basic points for this algorithm. Use marginal likelihoods to decide which clusters to merge Asks what the ...
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Fitting a “pseudo” discrete dataset

I'm working with a dataset that contains information about consumption of apples. The dataset contains the amount of apple consumed in g/day. The problem with this is that the data points fall into 3 ...
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35 views

Multivariate student t distribution as a mixture of distribution

I would like to derive the likelihood function corresponding to a student t model as a mixture of distribution, but there is one point which is not completely clear to me. It is usually written that ...
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43 views

Approximating a binomial distribution with a mixture normal

This is purely a theoretical question (I legitimately can't think of a real application), but if you wanted to approximate a binomial distributed variable with a two-component mixture normal, is there ...
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40 views

Rayleigh fading from finite mixture exponential

I want to plot Rayleigh fading mixture. can any one give me help in how i can do this by matlab or R ??? this is the link of Rayleigh fading mixture : ...
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How to mix probability estimators of the same phenomenon?

Also posted here and here. I have the following problem: I have N models that give me an estimation of the probability distribution function p(x) of a certain phenomenon x. Let's call them: ...
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error of the mean in presence of background

Suppose I have a normal distribution, $N[\mu,\sigma]$, and I have a sample of size $n$. It is well know that the error (std deviation) of the mean is $\sigma/\sqrt{n}$. Now suppose that my ...
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how to show the following consistency?

It is well-known that maximum likelihood estimate for a mixture model, with the mixture distributions known, and the estimation is done for the mixture coefficients is consistent (I think) -- the ML ...
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when is an estimator consistent?

Say there are parameters $\theta$ such that $\theta_i > 0$ and $\sum_i \theta_i = 1$ and a model such as $p(x) = \sum_{i=1}^n \theta_i p_i(x)$ where $p_i(x)$ are fixed and defined over a domain of ...
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144 views

Inverse transformation sampling for mixture distribution of two normal distributions

I am confused by the special way required to use inverse method in the following problem, Here is the problem: Consider a mixture distribution of two normal distributions, where the desired PDF ...
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Evaluating Gaussian PDF when det(Sigma)-->0

I want to evaluate a Gaussian PDF that does not exist because the determinant of sigma is either approx 0 or -inf (depends on parameters), and the condition number is of order 10^20. I need this ...
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1answer
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Flipping identifiable coins in batches

I have collected data to estimate a parameter and am now puzzled about how to generate confidence intervals: Setup: 1) We have a bag with $N$ coins. 2) Each coin $i \in N$ has a known probability ...
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Simulating random variables from a mixture of Normal distributions

How can I sample from a mixture distribution, and in particular a mixture of Normal distributions in R? For example, if I wanted to sample from: $$ ...
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Akaike criterion for gaussian mixtures

I am trying to estimate a multimodal gaussian mixture model with an unknown number of nodes. I wish to use a model selection strategy and iteratively test whether incremental modes leads to ...
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2answers
121 views

How to accomplish unsupervised separation of subpopulations?

I have a dataset drawn from a social network that looks Bimodal on logarithmic scales for all attributes (I'll demonstrate only one here): I know the variable that would give me a clean separation ...
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4answers
153 views

Can a function be split into sub-function to prove it is a probability mass function? And how to find variance of such function?

I have a question that requires to prove if the following function whether is it a PMF with poisson random variable. The function is as follows... $f(x) = \pi \frac {\lambda_1^x}{x!} e^{-\lambda_1} + ...
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How to approximate 0 in transition probability matrix without loss of generality?

In trying to implement Mixture Markov Model, (see question here), I have extreme cases ( e.g. 0's in the Transition Probability Matrix). I have approached this with replacing 0 with 1e-17. However, I ...