# Questions tagged [statistical-inference]

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

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### Bayesian Network for wordle

Intro In preparation for stuyding AI, I'm currently studying probability and bayesian inference. As a first challenge in the subject, I want to model and train a Bayesian network that is able to solve ...
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### How does One Come Up with Confidence Intervals For Fermi Estimation Problems?

A common question is estimate some quantity $X$, and give a 95% confidence interval for it. The estimation part, I understand how to think about and attack, but I'm always lost when it asks for a ...
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### Bagging Linear Model?

I have a question regarding bagging linear models. Suppose you wanna do linear regression on data X and y. Alice directly implements (OLS) Linear Regression on it. The model is A1. Bob applies bagging....
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### Statistical estimator of expected value of the gradient of an unknown function

Fix a probability space $(\Omega, \mathcal{A}, \Bbb P),$ a continuously differentiable function $f:\Bbb R^n \rightarrow \Bbb R,$ and a random vector $X: \Omega \rightarrow \Bbb R^n.$ Furthermore, we ...
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### Simplifying a Kullback-Leibler divergence

I want to find an approximation of a mixture of probability distributions that minimises the Kullback-Leibler divergence (KLD). I need to verify my result, as it seems suspect. We have a joint ...
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### Confused about interpretation and intuition behind Mcnemar's Test

I've always been under the impression that Mcnemar's Test is for paired categorical data, just like paired t-tests are for paired continuous data. However, I was looking at the Wikipedia article for ...
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### Is this a binomial experiment?

I ran a survey where I asked respondents to say how much they liked a certain game. They could choose one of five possible options. I calculated the sample proportion of all five options (say A, B, C, ...
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### Method of Moment Estimator of Normal Distribution

The sample r.v. $X_1, X_2,\ldots, X_n$ i.i.d. $N(\mu, \sigma^2)$, find the moment estimator of $P\{X>1\}$, where $X\sim N(\mu, \sigma^2)$. Here is my answer. I want to know whether it is right, thx....
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### Let a random experiment be the casting of a pair of fair six-sided dice and let X equal the minimum of the two outcomes . [closed]

the problem is I am suffering a lot in my journey,I cant even determine where I must start solve mathematical problems: Let a random experiment be the casting of a pair of fair six-sided dice and let ...
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### How to prove multivariate Bayesian Cramér-Rao inequality?

I came cross multivariate Bayesian Cramér-Rao inequality as follow recently, but I don't know how to prove it. Let $\{f(\cdot ; \theta): \theta \in \Theta\}$ be a family of probability density ...
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### Proof of the information bottleneck equations

In The Information Bottleneck Method, the third term of Eq.(31) is $P_{t+1}(y|\tilde{x})=\sum_yp(y|x)p_t(x|\tilde{x})$, which minimizes the term $D_{KL}[p(y|x)|p(y|\tilde{x})]_{<p(x,\tilde{x})>}$...
So imagine we take $n$ random samples from a Bernoulli Trial. Thus our random samples are composed by binary random variables $X_1, X_2, ..., X_n$. So by central limit theorem we know that the ...