# Tagged Questions

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### Likelihood of Conditional Grouped Continuous Model

I would like to find MLE of the likelihood above by using optim function in $R$. However, I couldn't understand the terms. I couldn't write the likelihood in $R$. I have the data given, some of ...
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### Confusion related to dual problem formulation in sparse inverse covariance matrix estimation

I was reading this paper where they are trying to estimate the inverse covariance matrix of the gaussian. What they are trying to maximize the gaussian log likelihood. The primal problem is maximize ...
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### Given samples from multiple normal RVs, how do we recover the histogram of their means?

Let $X_1,...,X_N$ be independent normal random variables. $X_i$ is normal with mean $\mu_i$ and standard deviation $\sigma_i$. Let $x_i$ be a single random sample from $X_i$. Input: We get all ...
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### pdf of multivariate normal distribution

I have a question concerning some sentences in the book Structural Equations with Latent Variables (Bollen) at page 132 (bottom) and page 133 (top) regarding the pdf of the multivariate normal ...
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### Hypothesis testing of normal distribution, known mean unknown variance

I've been working on review problems, and this one has me completely stumped. Let $X_1 ... X_{10}$ be a random sample from a $N(3,\sigma^2)$ distribution, where $\sigma^2$ is unknown. Using the ...
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### Spherical Gaussian Sigma dimension

I think I am confused with this thing. If we have a 3 dimension Gaussian then the MLE estimate for $\mu$ is a vector with 3 element \mu(1)' = \frac{1}{n}\sum_{j = 1} ^ n x_j\text{ and so on ...
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### Is there a covariance MLE which takes into account independence relationships?

In the extreme case where all of the components of an $M$-variate observation are pairwise independent from each other, a multivariate normal distribution can be decomposed into the product of $M$ ...
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### How difficult is it to train a gaussian mixture model compared to other models?

I have finally been able to wrap my head around the mechanics of how to initialize and train a multivariate Gaussian mixture model using expectation maximization algorithm. So I wonder how difficult ...
Given a univariate sample $\vec X = X_1, ..., X_n$ with standard deviation 1 and a strictly monotone transformation $t: R \to R$ with the property that the standard deviation of $t(\vec X)$ is also 1 ...
Let $Z=(X+Y)/2$, where $X$ and $Y$ are independent normally-distributed random variables with known variances $\sigma^2_X$ and $\sigma^2_Y$ and unknown (and possibly different) means. Given a sample ...