# Tag Info

## New answers tagged mathematical-statistics

### Bayesian Posterior distribution for binomial distribution with uniform prior

To answer your last question first - the way you have written it, the $p$ is the same in the two distributions, so they share the same prior. Your calculation is indeed correct; you've found the ...
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### Understanding multiple linear regression residuals

Its been a long time since I've had to do some linear algebra, so forgive me if I've forgotten some of it. Let's begin by assuming that $X$ is full rank and $\operatorname{rnk}(X)=p<n$. Minimizing ...
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### When the sample mean converges to the population mean, does the probability that the sample mean is equal to the population mean tend to 0?

It's possible set it up so that $\hat{\bar{y}}_N$ equals $\bar y_N$ at most finitely often. Make all the $y$ binary 0/1 and choose $n$ coprime to $N$,eg by taking $n$ to be the smallest prime greater ...
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### How can I back transform a log data to interpret t-test and get original CI?

First of all, I have to highlight that you used log10, which is unusual (although it doesn't affect anything) and the natural log is preferred and usually assumed ...
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### Prove E[Y|X] = f(X)

$\mathbb{E}[Y|X] = \mathbb{E}[f(X)+\epsilon|X] = \mathbb{E}[f(X)|X]+\mathbb{E}[\epsilon|X] = \mathbb{E}[f(X)|X]+\mathbb{E}[\epsilon] = f(X)+0$
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### How can I back transform a log data to interpret t-test and get original CI?

I can log-transform it to be normally distributed, and then perform a t-test and get confidence intervals (CI). But how do I interpret the results of the t-test and the CIs? If you want to compare 2 ...
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### If mean is so sensitive, why use it in the first place?

We use the mean more than the median because it is additive, in two senses. (I am surprised that in 11 years, no one has really said this!) If data on a population is broken down into data about men ...
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### hypothetical statistical test - type I and type II errors

You don't say it explicitly, but assume that the random number between 0 and 1 has a uniform distribution.Let's be more realistic and assume that you hope that it's uniform, but not sure, so you take ...
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### Structural Causal Models with cycles

Well, the fundamental rule of causality is that causes must precede effects - that is a strict inequality in time. So it is not permissible to have $X_i(t)=f_i(X_j(t),\dots,U_i(t)),$ but then turn ...
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### How to compare the mean to the mean of mean values of dummy variables?

Suppose you have v1 = 0 1 v2 = 1 1 0 0 0 0 Total mean = 3/8 meanv1 = 1/2 meanv2 = 1/3 mean(meanv1, meanv2) = (1/2 + 1/3) / 2 = 5/12 3/8 is not equal to 5/12 Only if v1 and v2 have the same number of ...
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### What are some good blogs for Mathematical Statistics and Machine Learning?

An Outsider's Tour of Reinforcement Learning by Ben Recht gives a short introduction into RL and draws connection to control theory.
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### When is a statistic not a statistic?

The statistic is defined as A statistic is a function $T (X^n )$ of the data. (Larry Wasserman All of Statistics, p. 137) A statistic (singular) or sample statistic is any quantity computed from ...
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### What are some good blogs for Mathematical Statistics and Machine Learning?

Towards data science a collection of articles focussing on data science, machine learning, artificial intelligence and programming. It is written by various authors. The articles often focus on ...
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### How to determine interventional distributions from observational data?

In general, observational data is not sufficient to obtain the interventional distributions. You will "only" obtain the Markov equivalence class (e.g. with the ...
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### What are some good blogs for Mathematical Statistics and Machine Learning?

In the last couple of years I have warmed up to using geometry to understand deep learning models, and indeed various types of statistical models. While I recommend the book Geometric Deep Learning: ...
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### What are some good blogs for Mathematical Statistics and Machine Learning?

This is neither really a blog nor just about statistics and many times very basic, but I found many good advices and ideas in there so I decided to add it as an answer https://chrisalbon.com/#...

### If $F_X, F_Y$ agree for all $x \in \mathbb{R}$, Do their distributions $\mu_X, \mu_Y$ agree on $\mathcal{B}$?

Observation $1.$ Let $\mathbf P_1, ~\mathbf P_2$ be two probability measures on $(\Omega, \mathcal F).$ Let $\mathcal P$ be a $\pi$-system such that \mathbf P_1(A) =\mathbf P_2(A), ~~~\forall A\in \...
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### What are some good blogs for Mathematical Statistics and Machine Learning?

https://statisticaloddsandends.wordpress.com/ reminds me of Gunderson blog, nicely written with code and clear explanations.

### What are some good blogs for Mathematical Statistics and Machine Learning?

ICLR recently introduced its Blog Track and its taken inspiration from some blogs like Bach's. Best thing is that it's peer-reviewed and contains diverse topics from diverse authors (often a group of ...

### What are some good blogs for Mathematical Statistics and Machine Learning?

Andrew Gelman: https://statmodeling.stat.columbia.edu. Gelman is a professor of statistics and political science at Columbia, and has co-authored several statistics books, including Bayesian Data ...

### What are some good blogs for Mathematical Statistics and Machine Learning?

Francis Bach's Machine Learning Research blog is an "easy to digest" introduction to some of his research works and related topics ("easy" as in easier than reading the original ...
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### I need help clarifying what (R1,..RN) is in this context

Your statement will make a bit more sense if you use more standard notation to differentiate vectors of values from sets. I would write it as follows: Let $\mathscr{R}$ be the space of all $N!$ ...
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