# Questions tagged [finite-mixture-model]

a model that represents the presence of subpopulations within an overall population and describes the data in terms of a mixture distribution.

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### Is omitting the mixture components with small weight enough to select the number of mixture components

I had a discussion with one of my colleagues and he told me that if we fit k- mixture components and some of them are very small, then we can remove them and hence we select the number of the mixture ...
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### EM-algorithm for spatial data

I am very new to Geostatistics (Modeling spatial data) and have some questions: 1- I found that in many literature, the spatial random field is divided into spatial bins. That is, suppose I am ...
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### Hypothesis Test Finite Sample Spatial Gaussian Mixture Model

I have $n$ observations of pairs $(x, y)$ and three different models I would like to compare. Model0 is nested within Model1. Model0 is also nested within Model2. I would like to do hypothesis ...
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### Example of nonidentification mixture

Consider a continuous r.v. $X$ with pdf $f$ obeying the following finite mixture model for each $x\in \mathbb{R}$: $$f(x)=\sum_{k=1}^K \lambda_k f_k(x) \quad \lambda_k\geq 0, \sum_k\lambda_k=1$$ ...
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### Distribution of sum of $n$ random variables with mixture of two exponential distributions

Suppose that the random variable $Y$ follows a mixture of two exponential distributions, that is $$f_Y(y) = \sum_{i=1}^{2}\pi_i f(y| \lambda_i)$$ where $\pi$ stands for ...
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### Simultaneous Bayes Estimation

Given $\theta_i$, $0 < \theta_i < 1$, a sequence of independent Bernoulli ($\theta_i$) random variables from i subpopulations, that are also independent across subpopulations. Suppose i=2 (2 ...
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### Anomaly detection with strong prior assumptions about data generating process

I have data that can be described using the model $$y \sim \mathcal{N}\big(f(x; \Theta), \, \sigma^2)$$ where $f$ is some function with known functional form, but unknown parameters. I also can make ...
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### Expectation maximization: does the likelihood always increase monotonically?

When working with (gaussian) mixture models, I always took it for a mathematical fact that the marginal likelihood increases with every iteration step. If it were not the case, it always meant an ...
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### Using regression to both estimate and attribute a single value to a subset of established categories

I am using Stata 15.1 I have a dataset with some 12,000 observations with a continuous dependent variable and 4 continuous independent variables. Each observation is also prior assigned to one of ...
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### What is truncated gaussian mixture model?

I am interested in the Gaussian mixture model. I read about it and I think I am good with it. However, found that there is something called truncated Gaussian mixture model, which I do not understand. ...
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How could I fit data with observations from one Dirac delta component and $n$ normal distributed components? Where $n$ usually is between 1 and 5. My prior knowledge is that one component really is a ...