Statistics

unbiased coin has P(H) = P(T) = 1/2.
To create the event that the question desires, do follow:
first, understand that P(HH) = P(HT) = P(TH) = P(TT) = 1/4

if you flip coin 2 times in a row:
1) HH happens -> do sth
2) HT happens -> do another stuff
3) TH happens -> do other stuff
4) if TT happens -> reroll coin 2 times again and go back .

This guarantees that we only observe 1/3 events.

 
Toss the unbiased coin thrice. Given the outcome is not both tails ( T T) ,
 then the outcome of both heads (H H) has probability 1/3.

Markov chain

https://arxiv.org/pdf/2207.02296.pdf A Tutorial on the Spectral Theory of Markov Chains

https://www.jeremykun.com/2015/04/06/markov-chain-monte-carlo-without-all-the-bullshit/

https://news.ycombinator.com/item?id=43700633 Markov Chain Monte Carlo Without All the Bullshit (2015) (jeremykun.com)

Book

https://www.statlearning.com/ An Introduction to Statistical Learning with Pyton

https://drive.google.com/file/d/1VmkAAGOYCTORq1wxSQqy255qLJjTNvBI/edit?pli=1 Introduction to probability 2nd edition

https://www.thegreatcourses.com/courses/learning-statistics-concepts-and-applications-in-r Learning Statistics: Concepts and Applications in R

Great links to stat resources https://news.ycombinator.com/item?id=37854846

https://jasp-stats.org/

Bayes

https://habr.com/ru/articles/853560/

https://habr.com/ru/articles/802435/

https://xcelab.net/rm/statistical-rethinking/ A Bayesian Course with Examples in R and Stan (& PyMC3 & brms & Julia too

https://users.aalto.fi/~ave/ROS.pdf Regression and Other Stories

https://openintro-ims2.netlify.app/

https://brilliant.org/courses/statistics/

queueing-theory

https://github.com/joelparkerhenderson/queueing-theory

https://news.ycombinator.com/item?id=37532439

https://www.cantorsparadise.com/whats-the-probability-of-1-appearing-as-the-first-digit-of-a-number-41f2fcd781c7 frequency of 1st digit in the number - Benford's law

Hight dimentional probability - Roman Vershinin: https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.pdf

https://mltechniques.com/resources/

Extreme events in dynamical systems and random walkers: A review https://arxiv.org/abs/2109.11219

https://habr.com/ru/post/678604/ Viterbi

https://www.toptal.com/algorithms/metropolis-hastings-bayesian-inference

How to compare distributions:

https://habr.com/ru/company/skillfactory/blog/674880/

https://habr.com/ru/company/X5Tech/blog/679842/

https://habr.com/ru/company/mygames/blog/677074/

https://github.com/matteocourthoud/Blog-Posts

Books

Cook book

https://pages.cs.wisc.edu/~tdw/files/cookbook-en.pdf

P R O B A B I L I S T I C N U M E R I C S
C O M P U TA T I O N A S  M A C H I N E L E A R N I N G

https://www.probabilistic-numerics.org/assets/ProbabilisticNumerics.pdf

https://lukepereira.github.io/notebooks/documents/2021-moduli-attention/main.pdf

Bayes

https://habr.com/ru/post/658707/

https://habr.com/ru/company/otus/blog/658311/

https://towardsdatascience.com/detect-change-points-with-bayesian-inference-and-pymc3-3b4f3ae6b9bb

https://towardsdatascience.com/a-gentle-intro-to-conjugate-priors-8be6ac0d31f6

https://habr.com/ru/post/598979/

https://www.edx.org/bio/elena-moltchanova . Bayes stat with R

https://betterexplained.com/articles/an-intuitive-and-short-explanation-of-bayes-theorem/

P(A/B) = P(A) * P(B/A) / P(B)

posterior = prior * (likelihood /marginal)

Posterior probability (updated probability after the evidence is considered)
Prior probability (the probability before the evidence is considered)
Likelihood (probability of the evidence, given the belief is true)
Marginal probability (probability of the evidence, under any circumstance)
1% of women have breast cancer (and therefore 99% do not).
80% of mammograms detect breast cancer when it is there (and therefore 20% miss it).
9.6% of mammograms detect breast cancer when it’s not there (and therefore 90.4% correctly return a negative result).

Suppose you get a positive test result. What are the chances you have cancer?

The chances of a true positive = chance you have cancer * chance test caught it = 1% * 80% = .008

The chances of a false positive = chance you don’t have cancer * chance test caught it anyway = 99% * 9.6% = 0.09504

The chance of getting a real, positive result is .008. The chance of getting any type of positive result is the chance of a true positive plus the chance of a false positive (.008 + 0.09504 = .10304).

So, our chance of cancer is .008/.10304 = 0.0776, or about 7.8%.

http://allendowney.github.io/ThinkBayes2/index.html

https://austinrochford.com/posts/2021-06-10-lego-pymc3.html

https://pub.towardsai.net/bayesian-inference-beyond-estimating-statistical-models-4b2f78c7f090

https://www.cs.ox.ac.uk/people/nando.defreitas/publications/BayesOptLoop.pdf Bayes

http://www.numericalexpert.com/blog/online_stat/ single pass for (variance, skewness, kurtosis, covariance)

http://www.numericalexpert.com/tutorials.php

precision and recall https://habr.com/ru/post/661119/

https://sakshamgulati123.medium.com/an-intuitive-guide-to-various-statistical-tests-d8148105eeca

Permutations

The number of permutations of n distinct objects is n!

combinations = сочетание

сочетанием из n по k называется набор из k элементов, выбранных из n-элементного множества, в котором не учитывается порядок элементов.

combination is a selection of items from a set that has distinct members, such that the order of selection does not matter

If the set has n elements, the number of k-combinations, denoted as C_{k}^{n}} C_{k}^{n}, is equal to the binomial coefficient C= n!/k!(n-k)!

Размещение = k-permutations of n

размеще́нием (из n по k) называется упорядоченный набор из k различных элементов из некоторого множества различных n элементов. В отличие от сочетаний, размещения учитывают порядок следования предметов.

A= n!/k!(n-k)!

Python

https://patsy.readthedocs.io/en/latest/ Describing statistical models in Python

https://habr.com/ru/post/681218/. statmodels

if we have some variable y, and we want to regress it against some other variables x, a, b, and the interaction of a and b, then we simply write:

patsy.dmatrices("y ~ x + a + b + a:b", data)

https://cdanielaam.medium.com/essential-mathematical-equations-for-predictive-models-fcb79630ec96

https://habr.com/ru/post/585232/ Получаем кривую плотности распределения вероятности

https://habr.com/ru/post/587372/ Получаем кривую плотности распределения вероятности случайного процесса

https://habr.com/ru/post/556856/ Python и статистический вывод: часть 4

https://habr.com/ru/post/562380/ Погружаемся в статистику вместе с Python

https://towardsdatascience.com/probability-distributions-with-pythons-scipy-3da89bf60565

https://towardsdatascience.com/statistical-modelling-with-python-the-three-must-know-s-modules-79fa393e5640

https://www.kdnuggets.com/2021/09/advanced-statistical-concepts-data-science.html

https://www.kdnuggets.com/2021/09/determine-best-fitting-data-distribution-python.html

https://towardsdatascience.com/a-practical-introduction-to-9-regression-algorithms-389057f86eb9

https://towardsdatascience.com/deep-diving-statistical-distributions-with-python-for-data-scientists-a0a4badc8d1a
https://towardsdatascience.com/random-seed-numpy-786cf7876a5f

https://towardsdatascience.com/practical-guide-to-common-probability-distributions-in-machine-learning-487f6137625

https://towardsdatascience.com/practical-guide-to-common-probability-distributions-in-machine-learning-part-2-5bcb910218c0

https://towardsdatascience.com/statistics-in-python-generating-random-numbers-in-python-numpy-and-sklearn-60e16b2210ae

https://towardsdatascience.com/mathematical-statistics-a-rigorous-derivation-and-analysis-of-the-wald-test-score-test-and-6262bed53c55

https://towardsdatascience.com/union-of-probabilistic-event-groups-b415d23e1a62

Stat

https://www.statlearning.com/

https://www.crosstab.io/

https://xcelab.net/rm/statistical-rethinking/

http://bayes.cs.ucla.edu/WHY/ The Book of why

five number summary in statistics: mean, median, standard deviation, 25th percentile and 75th percentile.

interquartile range - IQR is 75th - 25th, aka, the middle-50%

https://habr.com/ru/post/548104/ ТЕСТ МАННА-УИТНИ-УИЛКОКСОНА И SCORE-ФУНКЦИИ

https://seeing-theory.brown.edu/index.html

http://www.jerrydallal.com/LHSP/LHSP.HTM

https://www.stat.berkeley.edu/~aditya/resources/AllLectures2018Fall201A.pdf

https://habr.com/post/265321/ . statistical disributions

https://seeing-theory.brown.edu/index.html . Visual probability and stat

https://textbooks.opensuny.org/introduction-to-the-modeling-and-analysis-of-complex-systems/

https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf

https://github.com/Quanteeks/Statistics-lectures/blob/master/book.pdf

https://queueing-tool.readthedocs.io/en/latest/

https://www.youtube.com/watch?v=pYxNSUDSFH4 Probability vs likehood

https://www.dynatrace.com/news/blog/why-averages-suck-and-percentiles-are-great/

https://www.youtube.com/watch?v=coNDCIMH8bk

"How NOT to Measure Latency"

https://www.infoq.com/presentations/latency-response-time/

https://github.com/astralord/Statistics-lectures/blob/master/book.pdf

https://openintro-ims.netlify.app/ Modern stat book

https://www.dynatrace.com/news/blog/why-averages-suck-and-percentiles-are-great/

https://www.infoq.com/presentations/latency-response-time/

https://towardsdatascience.com/all-probability-distributions-explained-in-six-minutes-fe57b1d49600

https://www.maa.org/sites/default/files/pdf/ebooks/GTE_sample.pdf

https://github.com/telmo-correa/all-of-statistics

In the case of normally distributed data, the three sigma rule means that roughly 1 in 22 observations will differ by twice the standard deviation or more from the mean, and 1 in 370 will deviate by three times the standard deviation

https://statmodeling.stat.columbia.edu/2020/12/09/what-are-the-most-important-statistical-ideas-of-the-past-50-years/

How percentile approximation works and why it's more useful than averages

https://news.ycombinator.com/item?id=28526966

survival analysis

https://www.crosstab.io/topics/survival-analysis

https://www.crosstab.io/articles/survival-analysis-applications

Z-score

https://www.codingthepast.com/2024/11/28/Python-z-score.html

https://habr.com/ru/companies/otus/articles/793678/

https://statisticsbyjim.com/basics/z-score

Correlation

https://towardsdatascience.com/a-new-coefficient-of-correlation-64ae4f260310

https://gwern.net/doc/statistics/order/2020-chatterjee.pdf

https://habr.com/ru/post/683442/

Casual inference

https://habr.com/ru/company/glowbyte/blog/686398/

https://arxiv.org/abs/2206.15475

https://habr.com/ru/company/ods/blog/544208/

BOOK: Causal Inference for The Brave and True

https://matheusfacure.github.io/python-causality-handbook/landing-page.html

BOOK: Causal Inference in Python https://www.oreilly.com/library/view/causal-inference-in/9781098140243/

https://microsoft.github.io/dowhy/

https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/

https://www.bradyneal.com/which-causal-inference-book

https://yanirseroussi.com/causal-inference-reading-list/

https://www.inference.vc/causal-inference-4/

Мир статистических гипотез

https://habr.com/ru/post/558836/

https://habr.com/ru/companies/X5Tech/articles/807001/ T-test

Anova

https://davidbergkamp.com/two-way-anova-tukeys-honest-difference-test/

https://towardsdatascience.com/statistics-in-python-using-anova-for-feature-selection-b4dc876ef4f0

Statistics

Casual inference

DAU, CLV, etc

Основные типы распределений вероятностей в примерах

Statistical process control

How to generate uniformly random pointson n-spheres and in n-balls

краткий обзор методов выбора случайной точки на диске, на окружности, на сфере и на шаре.

Unfair coin - simulate any probability

How do you create an event with a probability of 1/3 using an unbiased coin?

Markov chain

Book

Bayes

queueing-theory

How to compare distributions:

Books

Bayes

Permutations

combinations = сочетание

Размещение = k-permutations of n

Python

Stat

survival analysis

Z-score

Correlation

Casual inference

Мир статистических гипотез

Anova