#probability — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #probability, aggregated by home.social.
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I have a habit of cutting an onion in half and putting one half in the fridge in a container, then using the other in cooking. In the past the container was a round Tupperware thing; lately it's a jar. No matter, result is the same.
I always put the half onion cut side up in the container, to reduce contact. For many years now, 19 times out of 20 when I tip the half onion onto a chopping board, it lands cut side up.
This used to be cute, then frustrating. Now I have acceptance. This is what the universe wants.
-
I have a habit of cutting an onion in half and putting one half in the fridge in a container, then using the other in cooking. In the past the container was a round Tupperware thing; lately it's a jar. No matter, result is the same.
I always put the half onion cut side up in the container, to reduce contact. For many years now, 19 times out of 20 when I tip the half onion onto a chopping board, it lands cut side up.
This used to be cute, then frustrating. Now I have acceptance. This is what the universe wants.
-
Alright, future engineers!
**Expected Value (E[X]):** The long-run average outcome of a random variable.
Ex: For a fair 6-sided die, E[X] = (1+2+3+4+5+6)/6 = 3.5.
Pro-Tip: Crucial for evaluating risks & rewards in projects & decision-making!
#Probability #Stats #STEM #StudyNotes -
Alright, future engineers!
**Permutations:** Ways to arrange 'r' items from 'n' where order *matters*.
Ex: Arranging 3 books from 5 on a shelf: P(5,3) = 5! / (5-3)! = 60.
Pro-Tip: Think P for POSITION (order matters)! Crucial for sequencing tasks.
#Combinatorics #Probability #STEM #StudyNotes -
**Normal Distribution:** A bell-shaped curve showing how data clusters around the mean.
Ex: Natural phenomena (heights, errors). Z-score: `(X - mean) / SD`.
Pro-Tip: Key for inferential stats! `+/- 1 SD` contains ~68% of data.
#StatsBasics #Probability #STEM #StudyNotes -
Греческий, древнегреческий язык
грецька, давньогрецька мова
Ελληνικά, Αρχαία Ελληνικά
Greek, Ancient Greek
#греческий, #древнегреческийязык
#грецька, #давньогрецькамова
#Ελληνικά, #Αρχαία Ελληνικά
#Greek, #Ancient Greek
t.me/scilib_yura15cbx/664Аюрведа
#Аюрведа
t.me/scilib_yura15cbx/663t.me/Avraam_Edelberg_archive
Канал где большинство книг и статей слиты в корневую директорию, терабайты книг, поэтому их можно найти по поиску названия. В поиске надо учитывать, что многие файлы названы латиницей, подчёркиваниями, сокращениями, поэтому можно использовать умный поиск, по автору, ключевым словам названия.Алексиевич, Анни Эрно Annie Ernaux, Ольга Токарчук
t.me/scilib_yura15cbx/659Sbírka knih v češtině a slovenštině (1868-2021)
Собрание книг на чешском и словацком языках (1868-2021)
Collection of books in Czech and Slovak (1868-2021)
Збірка книг чеською та словацькою мовами (1868-2021)
#чешский, #словацкий, #книги, иностранные языки, литература на иностранных языках #Čeština, #slovenština, #knihy, cizí jazyky, literatura v cizích jazycích чеська, #словацька, книги, іноземні мови, література іноземними мовами #Czech, #Slovak, books, foreign languages, literature in foreign languages
t.me/scilib_yura15cbx/657Владимир Высоцкий
t.me/scilib_yura15cbx/656диафильмы
filmstrips діафільми
#диафильмы
#filmstrips #діафільми
t.me/scilib_yura15cbx/653ajedrez, libros en español
шахматы, книги на испанском
chess, books in spanish
#ajedrez, #libros en #español
#шахматы, #книги на испанском
#chess, #books in #spanish
t.me/scilib_yura15cbx/651ветеринария
#ветеринария
t.me/scilib_yura15cbx/650Судебная медицина
t.me/scilib_yura15cbx/649Math Collection 5
Books in english
#Математика, #точныенауки, #алгебра, #анализ, #геометрия, #фрактальнаягеометрия, #вычисления, #статистика, #вероятность, #алгоритмы и пр.
#Mathematics, #algebra, #analysis, #geometry, #fractal geometry, #calculations, #statistics, #probability, #algorithms, etc.
#Математика, #точнінауки, #алгебра, #аналіз, #геометрія, #фрактальнагеометрія, #обчислення, #статистика, #ймовірність, #алгоритми та ін.
t.me/scilib_yura15cbx/644Mythology myth
in English
t.me/scilib_yura15cbx/643Собрания сочинений
Collected works, Зібрання творів
t.me/scilib_yura15cbx/641Тибет.
Тибетский язык, литература, культура, религия
Tibet. Tibetan language, literature, culture, religion
Тибет. Тибетська мова, література, культура, релігія
西藏。 藏語、文學、文化、宗教
#Тибет.
#Тибетскийязык, #литература, культура, #религия
#Tibet. #Tibetan language, #literature, #culture, #religion
#Тибет. #Тибетськамова, #література, #культура, #релігія
#西藏。 #藏語、#文學、#文化、#宗教
t.me/scilib_yura15cbx/636Китайский язык, литература
на китайском языке
Chinese language, literature in Chinese
Китайська мова, література китайською мовою
漢語、漢語文學
t.me/scilib_yura15cbx/635Майя. Древняя история, язык
Майя. Давня історія, мова
Mayan. ancient history, language древние языки
#Майя. #Древняяистория, #язык
#Майя. #Давняісторія, #мова
#Mayan. #ancient history, #language #древние языки
t.me/scilib_yura15cbx/634Новые подкасты
А нас не спрашивали
t.me/yura15cbx_podcast
Подкаст 42, о науке, Вселенной и вообще
t.me/podcast_42
Тишина мира
t.me/silence_podcast
Журнал "Америка"
t.me/America_magazineКаналы
Новости Открытого общества. Без цензуры, без пропаганды
https://t.me/open_society_news
Media. Видео, музыка
t.me/media_yura15cbx -
Греческий, древнегреческий язык
грецька, давньогрецька мова
Ελληνικά, Αρχαία Ελληνικά
Greek, Ancient Greek
#греческий, #древнегреческийязык
#грецька, #давньогрецькамова
#Ελληνικά, #Αρχαία Ελληνικά
#Greek, #Ancient Greek
t.me/scilib_yura15cbx/664Аюрведа
#Аюрведа
t.me/scilib_yura15cbx/663t.me/Avraam_Edelberg_archive
Канал где большинство книг и статей слиты в корневую директорию, терабайты книг, поэтому их можно найти по поиску названия. В поиске надо учитывать, что многие файлы названы латиницей, подчёркиваниями, сокращениями, поэтому можно использовать умный поиск, по автору, ключевым словам названия.Алексиевич, Анни Эрно Annie Ernaux, Ольга Токарчук
t.me/scilib_yura15cbx/659Sbírka knih v češtině a slovenštině (1868-2021)
Собрание книг на чешском и словацком языках (1868-2021)
Collection of books in Czech and Slovak (1868-2021)
Збірка книг чеською та словацькою мовами (1868-2021)
#чешский, #словацкий, #книги, иностранные языки, литература на иностранных языках #Čeština, #slovenština, #knihy, cizí jazyky, literatura v cizích jazycích чеська, #словацька, книги, іноземні мови, література іноземними мовами #Czech, #Slovak, books, foreign languages, literature in foreign languages
t.me/scilib_yura15cbx/657Владимир Высоцкий
t.me/scilib_yura15cbx/656диафильмы
filmstrips діафільми
#диафильмы
#filmstrips #діафільми
t.me/scilib_yura15cbx/653ajedrez, libros en español
шахматы, книги на испанском
chess, books in spanish
#ajedrez, #libros en #español
#шахматы, #книги на испанском
#chess, #books in #spanish
t.me/scilib_yura15cbx/651ветеринария
#ветеринария
t.me/scilib_yura15cbx/650Судебная медицина
t.me/scilib_yura15cbx/649Math Collection 5
Books in english
#Математика, #точныенауки, #алгебра, #анализ, #геометрия, #фрактальнаягеометрия, #вычисления, #статистика, #вероятность, #алгоритмы и пр.
#Mathematics, #algebra, #analysis, #geometry, #fractal geometry, #calculations, #statistics, #probability, #algorithms, etc.
#Математика, #точнінауки, #алгебра, #аналіз, #геометрія, #фрактальнагеометрія, #обчислення, #статистика, #ймовірність, #алгоритми та ін.
t.me/scilib_yura15cbx/644Mythology myth
in English
t.me/scilib_yura15cbx/643Собрания сочинений
Collected works, Зібрання творів
t.me/scilib_yura15cbx/641Тибет.
Тибетский язык, литература, культура, религия
Tibet. Tibetan language, literature, culture, religion
Тибет. Тибетська мова, література, культура, релігія
西藏。 藏語、文學、文化、宗教
#Тибет.
#Тибетскийязык, #литература, культура, #религия
#Tibet. #Tibetan language, #literature, #culture, #religion
#Тибет. #Тибетськамова, #література, #культура, #релігія
#西藏。 #藏語、#文學、#文化、#宗教
t.me/scilib_yura15cbx/636Китайский язык, литература
на китайском языке
Chinese language, literature in Chinese
Китайська мова, література китайською мовою
漢語、漢語文學
t.me/scilib_yura15cbx/635Майя. Древняя история, язык
Майя. Давня історія, мова
Mayan. ancient history, language древние языки
#Майя. #Древняяистория, #язык
#Майя. #Давняісторія, #мова
#Mayan. #ancient history, #language #древние языки
t.me/scilib_yura15cbx/634Новые подкасты
А нас не спрашивали
t.me/yura15cbx_podcast
Подкаст 42, о науке, Вселенной и вообще
t.me/podcast_42
Тишина мира
t.me/silence_podcast
Журнал "Америка"
t.me/America_magazineКаналы
Новости Открытого общества. Без цензуры, без пропаганды
https://t.me/open_society_news
Media. Видео, музыка
t.me/media_yura15cbx -
Alright, future engineers!
**Permutations:** Ways to arrange items where order matters.
Ex: Arranging 3 people from 5 in seats: `P(5,3) = 5! / (5-3)! = 60`.
Pro-Tip: P for Position (order matters)! Crucial for scheduling & password analysis.
#Combinatorics #Probability #STEM #StudyNotes -
Probability,
теорія ймовірностей, теория вероятностей
#Probability,
#теоріяймовірностей, #теориявероятностей
t.me/scilib_yura15cbx/193Number theory
Теория чисел, Теорія чисел
#Number theory
#Теориячисел, #Теоріячисел
t.me/scilib_yura15cbx/192References, Collected works
Література, Зібрання праць,
Ссылки, Собрание сочинений
t.me/scilib_yura15cbx/190Symmetry and groups
Симметрия и группы,
Симетрія і групи
#Symmetry
t.me/scilib_yura15cbx/189Philosophy of mathematics
Філософія математики, Философия математики
t.me/scilib_yura15cbx/188Mathematical physics
Математическая физика, Математична фізика
#Mathematical physics
#Математическаяфизика, #Математичнафізика
t.me/scilib_yura15cbx/187Optimization and control
Оптимізація та контроль, Оптимизация и контроль
t.me/scilib_yura15cbx/186Optimal control
Оптимальный контроль, Оптимальний контроль
#Optimal control
#Оптимальныйконтроль, #Оптимальнийконтроль
t.me/scilib_yura15cbx/185Numerical methods
Чисельні методи, Численные методы
#Numerical methods
#Чисельніметоди, #Численныеметоды
t.me/scilib_yura15cbx/184Lecture notes
Конспекты лекций, Конспект лекцiй
t.me/scilib_yura15cbx/183Encyclopaediae, School-level
Енциклопедії, Шкільний рівень
Энциклопедии, школьный уровень
t.me/scilib_yura15cbx/182Games, game theory
Ігри, теорія ігор
Игры, теория игр
#Games, #game theory
#Ігри, ₽теоріяігор
#Игры, #теорияигр
t.me/scilib_yura15cbx/181Geometry and topology
Геометрия и топология
Геометрія і топологія
#Geometry and #topology
#Геометрия и #топология
#Геометрія і #топологія
t.me/scilib_yura15cbx/180Biography, history
Биография, история
Біографія, історія
#Biography, #history
#Биография, #история
#Біографія, #історія
t.me/scilib_yura15cbx/178Mams_ Proceedings AMS
Праці AMS, Труды АМС
t.me/scilib_yura15cbx/177Algebra, Алгебра
#Algebra, #Алгебра
t.me/scilib_yura15cbx/176Optical devices
Оптика, оптические устройства, технологии, инжинерия
#Optical devices -
Probability,
теорія ймовірностей, теория вероятностей
#Probability,
#теоріяймовірностей, #теориявероятностей
t.me/scilib_yura15cbx/193Number theory
Теория чисел, Теорія чисел
#Number theory
#Теориячисел, #Теоріячисел
t.me/scilib_yura15cbx/192References, Collected works
Література, Зібрання праць,
Ссылки, Собрание сочинений
t.me/scilib_yura15cbx/190Symmetry and groups
Симметрия и группы,
Симетрія і групи
#Symmetry
t.me/scilib_yura15cbx/189Philosophy of mathematics
Філософія математики, Философия математики
t.me/scilib_yura15cbx/188Mathematical physics
Математическая физика, Математична фізика
#Mathematical physics
#Математическаяфизика, #Математичнафізика
t.me/scilib_yura15cbx/187Optimization and control
Оптимізація та контроль, Оптимизация и контроль
t.me/scilib_yura15cbx/186Optimal control
Оптимальный контроль, Оптимальний контроль
#Optimal control
#Оптимальныйконтроль, #Оптимальнийконтроль
t.me/scilib_yura15cbx/185Numerical methods
Чисельні методи, Численные методы
#Numerical methods
#Чисельніметоди, #Численныеметоды
t.me/scilib_yura15cbx/184Lecture notes
Конспекты лекций, Конспект лекцiй
t.me/scilib_yura15cbx/183Encyclopaediae, School-level
Енциклопедії, Шкільний рівень
Энциклопедии, школьный уровень
t.me/scilib_yura15cbx/182Games, game theory
Ігри, теорія ігор
Игры, теория игр
#Games, #game theory
#Ігри, ₽теоріяігор
#Игры, #теорияигр
t.me/scilib_yura15cbx/181Geometry and topology
Геометрия и топология
Геометрія і топологія
#Geometry and #topology
#Геометрия и #топология
#Геометрія і #топологія
t.me/scilib_yura15cbx/180Biography, history
Биография, история
Біографія, історія
#Biography, #history
#Биография, #история
#Біографія, #історія
t.me/scilib_yura15cbx/178Mams_ Proceedings AMS
Праці AMS, Труды АМС
t.me/scilib_yura15cbx/177Algebra, Алгебра
#Algebra, #Алгебра
t.me/scilib_yura15cbx/176Optical devices
Оптика, оптические устройства, технологии, инжинерия
#Optical devices -
Alright, future engineers!
**Expected Value (E[X]):** The average outcome you'd get if you repeated a random process many times.
Ex: E[X] = Sum(x * P(x)). For a fair die, E[X] = 3.5.
Pro-Tip: Use it to quantify long-term gains/losses & make smarter engineering decisions under uncertainty!
#Probability #Stats #STEM #StudyNotes -
Alright, future engineers!
**Normal Distribution:** A symmetric, bell-shaped probability distribution, common for real-world data.
Ex: Heights & errors often follow N(μ,σ^2).
Pro-Tip: 68-95-99.7 rule (within 1,2,3 SDs) is key for quick probability estimates!
#Stats #Probability #STEM #StudyNotes -
Understanding Entropy Through Probability and Thermodynamics
📰 Original title: What Is Entropy, Really?
🤖 IA: It's not clickbait ✅
👥 Users: It's not clickbait ✅View full AI summary https://en.killbait.com/understanding-entropy-through-probability-and-thermodynamics.html?utm_source=mastodon_world&utm_medium=social&utm_campaign=killbait.mastodon_world
-
Alright, future engineers!
**Normal Distribution:** A symmetrical, bell-shaped probability curve where data clusters around the mean.
Ex: Many natural phenomena (like heights) follow it.
Pro-Tip: The '68-95-99.7 rule' is key for quick approximations without a calculator!
#Stats #Probability #STEM #StudyNotes -
mental health lessons for nerds:
for the random variable, X, that is the probability that the outcome is good from taking the chance to reach out to talk to someone (about anything, including just to make friends), the expected value, E(X) is MUCH MUCH higher in reality than your fears tell you.
just do the damn thing.
-
Alright, future engineers!
**Expected Value:** The average outcome if an experiment repeats many times.
Ex: Fair 6-sided die, E[X] = 3.5. Formula: `E[X] = sum(x * P(x))`.
Pro-Tip: Crucial for evaluating risk or long-term gains in decisions!
#Probability #DecisionMaking #STEM #StudyNotes -
Alright, future engineers!
**Normal Distribution:** A common, symmetric bell-shaped probability distribution where data clusters around its mean.
Ex: Human heights or measurement errors often follow it. `X ~ N(mean, variance)`.
Pro-Tip: Remember the 68-95-99.7 rule for quick estimates within 1, 2, or 3 SDs from the mean!
#Probability #DataScience #STEM #StudyNotes -
Alright, future engineers!
**Expected Value:** The long-run average outcome of a random variable.
Ex: `E(X) = sum(x * P(x))`. Imagine a project's avg profit from varied outcomes.
Pro-Tip: It's the 'average payout' you'd expect over many repeated trials!
#Statistics #Probability #STEM #StudyNotes -
The package **Prova** is now on CRAN! <https://cran.r-project.org/package=prova>
Probabilistic-statistical variate analysis, nonparametric and with automated Markov-chain Monte Carlo. These are its main features:
- Any combination of binary, nominal, ordinal, continuous variates. Continuous variates can be bounded or unbounded, and also rounded or discretized.
- No modelling assumptions such as gaussianity, linearity, or any other kind of model. The analysis and inferences are fully non-parametric.
- No assumptions about functional dependence between variates. The analysis and inferences are therefore more general than those by neural networks, random forests, or similar machine-learning algorithms.
- Automatic imputation of missing data: all sample data are used, even those that lacks some variate values. The imputation is done with a principled method (the marginalization rule of probability theory), rather than ad-hoc procedures.
- Easy and straightforward subgroup analyses and stratified analyses, for any division of variates, with full statistical details.
- No hard-coded distinction between "predictor" and "predictand"/target variates during learning. Any group of variates can be chosen as predictors, and any other group as targets, on the fly in each application, without need to re-learn from the training data.
- Quantification of generalizability beyond the finite sample size. In other words, quantification of uncertainty of results regarding the whole, unsampled, population.
- Straightforward use within decision theory, such as clinical decision-making. Users can immediately combine the probabilistic results with any measures of utilities, such as quality-adjusted life years.
- Quantification of associations between any kinds of variates, without modelling assumptions (gaussianity, linearity, etc.), thanks to the use of mutual information.
- Base-rate correction for inferences about out-of-population data, by means of Bayes’s theorem.
- Automated Markov-chain Monte Carlo computation. Users unfamiliar with Monte Carlo methods don’t have to worry, because the computations are handled automatically.
Feel free to take a look at example applications in the vignettes: https://pglpm.github.io/prova/
Please report any bugs! The updated version on GitHub has some added functionality and fixed bugs. It'll be submitted to CRAN in 30 days.
-
The package **Prova** is now on CRAN! <https://cran.r-project.org/package=prova>
Probabilistic-statistical variate analysis, nonparametric and with automated Markov-chain Monte Carlo. These are its main features:
- Any combination of binary, nominal, ordinal, continuous variates. Continuous variates can be bounded or unbounded, and also rounded or discretized.
- No modelling assumptions such as gaussianity, linearity, or any other kind of model. The analysis and inferences are fully non-parametric.
- No assumptions about functional dependence between variates. The analysis and inferences are therefore more general than those by neural networks, random forests, or similar machine-learning algorithms.
- Automatic imputation of missing data: all sample data are used, even those that lacks some variate values. The imputation is done with a principled method (the marginalization rule of probability theory), rather than ad-hoc procedures.
- Easy and straightforward subgroup analyses and stratified analyses, for any division of variates, with full statistical details.
- No hard-coded distinction between "predictor" and "predictand"/target variates during learning. Any group of variates can be chosen as predictors, and any other group as targets, on the fly in each application, without need to re-learn from the training data.
- Quantification of generalizability beyond the finite sample size. In other words, quantification of uncertainty of results regarding the whole, unsampled, population.
- Straightforward use within decision theory, such as clinical decision-making. Users can immediately combine the probabilistic results with any measures of utilities, such as quality-adjusted life years.
- Quantification of associations between any kinds of variates, without modelling assumptions (gaussianity, linearity, etc.), thanks to the use of mutual information.
- Base-rate correction for inferences about out-of-population data, by means of Bayes’s theorem.
- Automated Markov-chain Monte Carlo computation. Users unfamiliar with Monte Carlo methods don’t have to worry, because the computations are handled automatically.
Feel free to take a look at example applications in the vignettes: https://pglpm.github.io/prova/
Please report any bugs! The updated version on GitHub has some added functionality and fixed bugs. It'll be submitted to CRAN in 30 days.
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Mapping Deforestation Probability And Understanding The Forest Dynamics In Gazipur, Bangladesh
--
https://doi.org/10.1016/j.envc.2026.101568 <-- shared paper
--
"ABSTRACT: Deforestation is a spiralling environmental catastrophe with impervious results for biodiversity, climate change, and human livelihoods, specifically in tropical regions. Being a tropical country, Bangladesh has experienced approximately 40% loss of its forest cover, at Gazipur since 1930, which contains about 86% of the country's Sal (Shorea robusta) forest, ranging approximately 4,300 hectares per year (2001–2010) to over 19,500 hectares per year (2011–2020), exemplifying an intensification of nearly 353%. The objective of this study is to map deforestation probability at the Gazipur district of Dhaka Division, Bangladesh, by utilising machine learning algorithms along with multi-source geospatial data, with the purpose of identifying high-risk zones and facilitating evidence-based forest governance, land-use development, and prioritizing conservation areas. This study integrated twelve conditioning factors, including biophysical, landscape, and anthropogenic. To identify susceptible zones the study trained and assessed five machine learning algorithms; RF, XGBoost, ANN, NB, and MLP and validating the result through different metrics like sensitivity, specificity, precision, accuracy, F1-score, AUC. The performance of the models was evaluated using Wilcoxon signed-rank tests and marginal response curves (MRC) were used to understand factor contributions. In the result, RF achieved highest performance with accuracy of 84% and AUC of 0.93, followed by XGBoost at 83% accuracy and 0.92 AUC. Rainfall and population density were most dominant conditioning factors among models. Pairwise statistical testing resulted that ensemble-based algorithms (RF, XGBoost) generated statistically comparable and significantly higher predictions compared to NB and MLP. Spatial probability maps indicate areas of high and very high risk in the south-western and north-eastern upazilas. The results can be applicable for forest management authorities, urban planners, and policymakers, and correspond with SDG Indicator 15. An inclusive governance framework containing land zoning, ecological area identification, and compliance with industrial EIA is proposed to persuade probability maps into adaptive forest management strategies…”
#deforestation #probability #machinelearning #algorithms #AI #Gazipur #Bangladesh #GIS #spatial #mapping #spatialanalysis #spatiotemporal #rainfall #precipitation #humanimpacts #populationpressure #risk #prediction #RandomForest #conservation #restoration #environment #biodiversity, #climatechange #human #livelihood #tropical #forestcover #sal #forest #vegetation #tree #upazila #spatialprobability #geostatistics #forestmanagement #planning #policy #urbanplanners #governance #zoning #ecology #habitat -
Mapping Deforestation Probability And Understanding The Forest Dynamics In Gazipur, Bangladesh
--
https://doi.org/10.1016/j.envc.2026.101568 <-- shared paper
--
"ABSTRACT: Deforestation is a spiralling environmental catastrophe with impervious results for biodiversity, climate change, and human livelihoods, specifically in tropical regions. Being a tropical country, Bangladesh has experienced approximately 40% loss of its forest cover, at Gazipur since 1930, which contains about 86% of the country's Sal (Shorea robusta) forest, ranging approximately 4,300 hectares per year (2001–2010) to over 19,500 hectares per year (2011–2020), exemplifying an intensification of nearly 353%. The objective of this study is to map deforestation probability at the Gazipur district of Dhaka Division, Bangladesh, by utilising machine learning algorithms along with multi-source geospatial data, with the purpose of identifying high-risk zones and facilitating evidence-based forest governance, land-use development, and prioritizing conservation areas. This study integrated twelve conditioning factors, including biophysical, landscape, and anthropogenic. To identify susceptible zones the study trained and assessed five machine learning algorithms; RF, XGBoost, ANN, NB, and MLP and validating the result through different metrics like sensitivity, specificity, precision, accuracy, F1-score, AUC. The performance of the models was evaluated using Wilcoxon signed-rank tests and marginal response curves (MRC) were used to understand factor contributions. In the result, RF achieved highest performance with accuracy of 84% and AUC of 0.93, followed by XGBoost at 83% accuracy and 0.92 AUC. Rainfall and population density were most dominant conditioning factors among models. Pairwise statistical testing resulted that ensemble-based algorithms (RF, XGBoost) generated statistically comparable and significantly higher predictions compared to NB and MLP. Spatial probability maps indicate areas of high and very high risk in the south-western and north-eastern upazilas. The results can be applicable for forest management authorities, urban planners, and policymakers, and correspond with SDG Indicator 15. An inclusive governance framework containing land zoning, ecological area identification, and compliance with industrial EIA is proposed to persuade probability maps into adaptive forest management strategies…”
#deforestation #probability #machinelearning #algorithms #AI #Gazipur #Bangladesh #GIS #spatial #mapping #spatialanalysis #spatiotemporal #rainfall #precipitation #humanimpacts #populationpressure #risk #prediction #RandomForest #conservation #restoration #environment #biodiversity, #climatechange #human #livelihood #tropical #forestcover #sal #forest #vegetation #tree #upazila #spatialprobability #geostatistics #forestmanagement #planning #policy #urbanplanners #governance #zoning #ecology #habitat -
Truly Understand Probability
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Truly Understand Probability
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The Foundations of Probability by P R Halmos, 1944
https://web.archive.org/web/20240403053458/https://maa.org/programs/maa-awards/writing-awards/the-foundations-of-probability -
However, this comes with plenty of caveats and blind spots.
xG assumes that shots are independent Bernoulli trials.
In reality, shots within a match are correlated.
A team that's behind on the scoreboard tends to generate more chances, but often of lower quality.
The model also doesn't account for how good (or bad) the goalkeeper is. Nor does it capture the pressure or motivation players feel when taking a shot.
It also fails to capture the tactical context of a match.
In the end, there are moments when it's like modeling market correlations with a Pearson correlation matrix during a financial panic. The dependence structure changes. You need copulas!
Even with its limitations, though, xG remains one of the best metrics we have for characterizing a football match.
The scoreboard tells you who won.
xG tells you who was more likely to have won based on the chances they created.
#ExpectedGoals #xG #FootballAnalytics #SoccerAnalytics #DataScience #SportsAnalytics #Probability #Statistics #MachineLearning #LogisticRegression #GradientBoosting #Bernoulli #ExpectedValue #Football #Soccer #WorldCup #FIFA #TacticalAnalysis #PerformanceAnalysis #SportsData #DataVisualization #Analytics #QuantitativeAnalysis #Mathematics #PredictiveModeling #FootballStats #xGA #Mbappe #Spain #Argentina
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Alright, future engineers!
**Normal Distribution:** A symmetric, bell-shaped probability distribution. Data clusters around the mean.
Ex: ~68% of values fall within 1 SD of the mean (Empirical Rule).
Pro-Tip: Key for modeling continuous data & hypothesis testing!
#Statistics #Probability #STEM #StudyNotes -
Alright, future engineers!
**Permutation:** An arrangement of items where the *order of selection matters*.
Ex: Choosing 3 unique officers (Pres, VP, Sec) from 10 people. P(10,3)
Pro-Tip: Think 'P' for 'Position' – order is crucial!
#Stats #Probability #STEM #StudyNotes -
Alright, future engineers!
**Expected Value:** The long-run average outcome if an experiment is repeated many times.
Ex: Fair die roll EV = `(1+2+3+4+5+6)/6 = 3.5`.
Pro-Tip: It doesn't have to be a *possible* outcome, just the statistical average!
#Statistics #Probability #STEM #StudyNotes -
**Permutations:** The number of distinct ways to arrange a set of items where the order of arrangement matters.
Ex: Arranging 3 unique books on a shelf from a set of 5: `5P3 = 5!/(5-3)! = 60`.
Pro-Tip: Remember P for Position – order is key for permutations!
#Combinatorics #Probability #STEM #StudyNotes -
Alright, future engineers!
**Expected Value (E[X]):** The average outcome you'd expect from a random variable over many trials.
Ex: For a fair 6-sided die, E[X] = 3.5.
Pro-Tip: Use it for risk assessment and making smart decisions in uncertain systems!
#Probability #DataScience #STEM #StudyNotes -
Alright, future engineers!
**Expected Value (E[X]):** The average outcome you'd expect from a random variable over many trials.
Ex: For a fair 6-sided die, E[X] = 3.5.
Pro-Tip: Use it for risk assessment and making smart decisions in uncertain systems!
#Probability #DataScience #STEM #StudyNotes -
Under these circumstances, there is a "correct" use of the hypercomputer. While a civilization could use it to compute some strategy in a war, upload themselves into it for a form of immortality, or create a new world by instructing it to run some kind of Game of Life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) program, a more practical use would be to compute the first few thousand digits of Chaitin's constant for a programming language. This is possible because we can finitely describe "attempt to run every possible source code and record if the result halts", we just need an infinite amount of time in order to finish the task. Importantly, although we can't know the exact value of \(\Omega\), the first few thousand digits are about just as good for mortal purposes.
I always imagined that, in the story, one civilization would be unsubtle and look down on the other, which would only want to use the hypercomputer for the "academic" purpose of knowing \(\Omega\) approximately, only to realize that this knowledge is possibly the most practical use of the machine.
(3/3)
#math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability
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Under these circumstances, there is a "correct" use of the hypercomputer. While a civilization could use it to compute some strategy in a war, upload themselves into it for a form of immortality, or create a new world by instructing it to run some kind of Game of Life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) program, a more practical use would be to compute the first few thousand digits of Chaitin's constant for a programming language. This is possible because we can finitely describe "attempt to run every possible source code and record if the result halts", we just need an infinite amount of time in order to finish the task. Importantly, although we can't know the exact value of \(\Omega\), the first few thousand digits are about just as good for mortal purposes.
I always imagined that, in the story, one civilization would be unsubtle and look down on the other, which would only want to use the hypercomputer for the "academic" purpose of knowing \(\Omega\) approximately, only to realize that this knowledge is possibly the most practical use of the machine.
(3/3)
#math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability
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When I learned about this as an undergraduate I started telling people the following story: Suppose that, simultaneously, two space-faring civilizations discover a naturally-occurring closed timelike curve (https://en.wikipedia.org/wiki/Closed_timelike_curve) around a nearby black hole. Suppose further that these civilizations both know that this structure can be used to build a hypercomputer (https://en.wikipedia.org/wiki/Hypercomputation), a machine that can perform an infinite number of classical computational steps in a finite amount of time. In order to make our story more realistic, we add the following constraints:
(1) The hypercomputer can correctly perform an infinite calculation, but it must be described by a finite program.
(2) The hypercomputer can access an arbitrarily large amount of memory during calculation, but there is a fixed finite size for its output after the infinite calculation is over.
(3) A massive amount of resources are needed for each use of the hypercomputer. Perhaps it breaks after each use.(2/3)
#math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability
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When I learned about this as an undergraduate I started telling people the following story: Suppose that, simultaneously, two space-faring civilizations discover a naturally-occurring closed timelike curve (https://en.wikipedia.org/wiki/Closed_timelike_curve) around a nearby black hole. Suppose further that these civilizations both know that this structure can be used to build a hypercomputer (https://en.wikipedia.org/wiki/Hypercomputation), a machine that can perform an infinite number of classical computational steps in a finite amount of time. In order to make our story more realistic, we add the following constraints:
(1) The hypercomputer can correctly perform an infinite calculation, but it must be described by a finite program.
(2) The hypercomputer can access an arbitrarily large amount of memory during calculation, but there is a fixed finite size for its output after the infinite calculation is over.
(3) A massive amount of resources are needed for each use of the hypercomputer. Perhaps it breaks after each use.(2/3)
#math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability
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While organizing some files today I came across my copy of Charles H. Bennett's "On Random and Hard-to-Describe Numbers" from 1979 (https://www.worldscientific.com/doi/abs/10.1142/9789812770837_0001). It discusses Chaitin's constant (https://en.wikipedia.org/wiki/Chaitin%27s_constant) for a programming language, which is the probability \(\Omega\) that a randomly-chosen program will compile. This is a real number between 0 and 1 which is definable but not computable.
Bennett goes on to discuss the "Cabalistic" properties of \(\Omega\). Knowing the first few thousand digits of \(\Omega\) would allow one to decide practically all finitely refutable mathematical conjectures. Basically, \(\Omega\) is a very compact encoding of the Halting Problem (https://en.wikipedia.org/wiki/Halting_problem), so knowing its first \(n\) bits is enough to determine whether any program up to \(n\) bits in length would eventually halt. While there are some exceptions, many open problems in mathematics can be phrased in terms of the halting of some computer program of reasonably short length.
(1/3)
#math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability
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While organizing some files today I came across my copy of Charles H. Bennett's "On Random and Hard-to-Describe Numbers" from 1979 (https://www.worldscientific.com/doi/abs/10.1142/9789812770837_0001). It discusses Chaitin's constant (https://en.wikipedia.org/wiki/Chaitin%27s_constant) for a programming language, which is the probability \(\Omega\) that a randomly-chosen program will compile. This is a real number between 0 and 1 which is definable but not computable.
Bennett goes on to discuss the "Cabalistic" properties of \(\Omega\). Knowing the first few thousand digits of \(\Omega\) would allow one to decide practically all finitely refutable mathematical conjectures. Basically, \(\Omega\) is a very compact encoding of the Halting Problem (https://en.wikipedia.org/wiki/Halting_problem), so knowing its first \(n\) bits is enough to determine whether any program up to \(n\) bits in length would eventually halt. While there are some exceptions, many open problems in mathematics can be phrased in terms of the halting of some computer program of reasonably short length.
(1/3)
#math #mathematics #ComputerScience #hypercomputer #programming #microfiction #ScienceFiction #physics #BlackHole #ClosedTimelikeCurve #relativity #probability
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**Expected Value (E[X]):** The long-run average outcome of a random variable.
Ex: For a fair 6-sided die, E[X] = 3.5.
Pro-Tip: Essential for evaluating fairness or making decisions under uncertainty! It's not necessarily a possible outcome.
#Statistics #Probability #STEM #StudyNotes -
Nominations are open for the 2027 Ethel Newbold Prize of the Bernoulli Society.
The prize recognises outstanding early- or mid-career scientists whose work demonstrates excellence in mathematical statistics or connects statistical developments with advances in a substantive field.
Deadline: 30 November 2026.
Read more: https://euromathsoc.org/news/216
#Statistics #MathematicalStatistics #Probability #Awards #Nominations
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WOULD EVERYBODY PLEASE STOP LOOKING AT THE STRAIGHT OF HORMUZ TO SEE IF IT IS OPEN OR CLOSED
YOU ARE COLLAPSING THE PROBABILITY WAVEFORM AND PREVENTING OTHERS FROM USING IT IN ITS NATURAL INDETERMINATE STATE
#Hormuz #SoMuchWinning #USPol #quantum #Schroedinger #SchrödingersCat #probability
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7 or 14 shuffles? Math just removed a 30-year hidden condition
A 2026 study from Harvard, Cambridge, and Princeton proves a shuffling threshold exists even when the cut is uneven
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Happy birthday, James Clerk Maxwell! 🎂 🎓️ ⚡️
Let's remember him not only for essentially formulating the full theory of electromagnetism, but also for founding kinetic theory and statistical mechanics (with Boltzmann and Gibbs), for his contributions to thermodynamics, the mechanics of continua, the theory of colours (I heard he took the world's first colour photograph); for his views about probability theory; and for MANY other things.
Among my favourite quotes:
> "They say that Understanding ought to work by the rules of right reason. These rules are, or ought to be, contained in Logic; but the actual science of Logic is conversant at present only with things either certain, impossible, or *entirely* doubtful, none of which (fortunately) we have to reason on. Therefore the true Logic for this world is the Calculus of Probabilities, which takes account of the magnitude of the probability (which is, or which ought to be in a reasonable man's mind)." – Letter to L. Campbell, 1850 <https://
archive.org/details/lifeofjamesclerk00campuoft>.> "In the popular treatise, whatever shreds of the science are allowed to appear, are exhibited in an exceedingly diffuse and attenuated form, apparently with the hope that the mental faculties of the reader, though they would reject any stronger food, may insensibly become saturated with scientific phraseology, provided it is diluted with a sufficient quantity of more familiar language. In this way, by simple reading, the student may become possessed of the phrases of the science without having been put to the trouble of thinking a single thought about it. The loss implied in such an acquisition can be estimated only by those who have been compelled to unlearn a science that they might at length begin to learn it." – In "Tait's 'Thermodynamics'", 1878 <https://
doi.org/10.1038/017257a0>.> "it is our part to provide for the diffusion and cultivation, not only of true scientific principles, but of a spirit of sound criticism, founded on an examination of the evidences on which statements apparently scientific depend." – Introductory Lecture on Experimental Physics, 1871 <https://
archive.org/details/scientificpapers02maxwuoft>.<https://
clerkmaxwellfoundation.org>#onthisday #physics #statistics #probability #historyofscience
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There are inquiries in which scanty evidence is worth using. We may not be able to get certainty, but we can get probability, and half a loaf is better than no bread.
C. S. Lewis (1898-1963) English writer, literary scholar, lay theologian [Clive Staples Lewis]
Essay (1950-10), “Historicism,” The Month, Vol. 4, No. 4 New Series (Vol. 190, No. 998 Old Series)More about this quote: wist.info/lewis-cs/45027/
#quote #quotes #quotation #qotd #cslewis #empiricism #evidence #history #inquiry #investigation #likelihood #probability #speculation #surmise #theory #uncertainty
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Alright, future engineers!
**Normal Distribution:** A bell-shaped probability curve where data clusters around the mean.
Ex: Heights or test scores often follow it.
Pro-Tip: The Empirical Rule (68-95-99.7) helps interpret data spread quickly!
#Probability #Stats #STEM #StudyNotes -
The past two months, I helped coordinate the "Phase Transitions..." research semester programme at CWI (https://www.cwi.nl/en/events/research-semester-programmes/phasecap-phase-transitions-in-combinatorics-algorithms-probability/). It ended last Friday, and still I feel "hungover" from the intensive blur of activities/developments/ideas. Very grateful to my team --Feri, Jop, Serte, Carla, Noela, Guus-- we did it!
In parallel, during the same two months, after the dawn of recognition of what has arrived (after a tip from Jeroen), I underwent a kind of phase transition myself. Avowed refusenik in March (see https://mathstodon.xyz/@kangmeister/115252549665766971); an "anti-Gemini" research working group in April; compulsive button-pressing in May. (And yes, I *know* it is easy to set it up for pressing fewer buttons...)
That poetic part of me (or whatever remains of it) is allured by the term, "cognitive surrender", if only to help in my search for the right words to describe the sharp changes underway in various facets of mathematical life/growth.
#CWI #combinatorics #algorithms #probability #conferences #generativeAI #formalization #lean #scientificpublishing
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🎲🤡 Oh, joy! Yet another riveting "game" where you draw lines to match some obscure statistical measure! Because who doesn't want to spend their free time racing against a clock to understand the excitement of #KL divergence? 🙄 Get ready to feel the thrill of #probability sums and the adrenaline of... *yawn*... math! 💤
https://klzero.sarna.dev #game #design #math #boredom #statistics #divergence #HackerNews #ngated -
Alright, future engineers!
**Normal Distribution (Bell Curve):** A common symmetric probability distribution where data clusters around the mean.
Ex: Human heights or test scores often follow this shape.
Pro-Tip: ~68% of data falls within 1 SD of the mean!
#StatsProb #Probability #STEM #StudyNotes -
Alright, future engineers!
**Permutations:** Ways to arrange items where ORDER *matters*.
Ex: Arranging 3 books from 5 on a shelf: P(5,3) = 60 ways.
Pro-Tip: Think 'P' for 'Position'! New order = new permutation.
#Statistics #Probability #STEM #StudyNotes -
Alright, future engineers!
**Permutations:** The number of ways to arrange items where the ORDER matters.
Ex: How many ways to pick & arrange 3 out of 5 engineers for 3 distinct roles? P(5,3) = 60
Pro-Tip: Think P for Position! If swapping two items changes the outcome, it's a Permutation.
#Combinatorics #Probability #STEM #StudyNotes -
Icon, Likeness, Likely Story, Likelihood, Probability • 3
Re: Peirce List • Phyllis Chiasson
A more complete excerpt and the translator’s notes are very helpful here.
A probability (εικος) is not the same as a sign (σηµειον). The former is a generally accepted premiss ; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability : e.g., that the envious are malevolent or that those who are loved are affectionate. A sign, however, means a demonstrative premiss which is necessary or generally accepted.1 That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.
An enthymeme is a syllogism from probabilities or signs ; and a sign can be taken in three ways — in just as many ways as there are of taking the middle term in the several figures : either as in the first figure or as in the second or as in the third.
- E.g., the proof that a woman is pregnant because she has milk is by the first figure ; for the middle term is ‘having milk’. A stands for ‘pregnant’, B for ‘having milk’, and C for ‘woman’.
- The proof that the wise are good because Pittacus was good is by the third figure. A stands for ‘good’, B for ‘the wise’, and C for Pittacus. Then it is true to predicate both A and B of C ; only we do not state the latter, because we know it, whereas we formally assume the former.
- The proof that a woman is pregnant because she is sallow is intended to be by the middle figure ; for since sallowness is a characteristic of woman in pregnancy, and is associated with this particular woman, they suppose that she is proved to be pregnant. A stands for ‘sallowness’, B for ‘being pregnant’, C for ‘woman’.
If only one premiss is stated, we get only a sign ; but if the other premiss is assumed as well, we get a syllogism,2 e.g., that Pittacus is high-minded, because those who love honour are high-minded, and Pittacus loves honour ; or again that the wise are good, because Pittacus is good and also wise.
In this way syllogisms can be effected ; but whereas a syllogism in the first figure cannot be refuted if it is true, since it is universal, a syllogism in the last figure can be refuted even if the conclusion is true, because the syllogism is neither universal nor relevant to our purpose.3 For if Pittacus is good, it is not necessary for this reason that all other wise men are good. A syllogism in the middle figure is always and in every way refutable, since we never get a syllogism with the terms in this relation4 ; for it does not necessarily follow, if a pregnant woman is sallow, and this woman is sallow, that she is pregnant. Thus truth can be found in all signs, but they differ in the ways which have been described.
We must either classify signs in this way, and regard their middle term as an index (τεκµηριον)5 (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes6 as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true. (Aristotle, Prior Analytics 2.27, 70a3–70b6).
Translator’s Notes
- If referable to one phenomenon only, a sign has objective necessity ; if to more than one, its value is a matter of opinion.
- Strictly an enthymeme.
- If the signs of an enthymeme in the first figure are true, the conclusion is inevitable. Aristotle does not mean that the conclusion is universal, but that the universality of the major premiss implies the validity of the minor and conclusion. The example (<all> those who have honour, etc.) quoted for the third figure contains no universal premiss or sign, and fails to establish a universal conclusion.
- i.e. when both premisses are affirmative.
- Signs may be classified as irrefutable (1st figure) and refutable (2nd and 3rd figures), and the name ‘index’ may be attached to their middle terms, either in all figures or (more probably) only in the first, where the middle is distinctively middle.
- Alternatively the name ‘sign’ may be restricted to the 2nd and 3rd figures, and may be replaced by ‘index’ in the first.
Reference
- Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
Resource
- Theme One Program • User Guide • Appendix A
cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
#Analogy #Aristotle #CSPeirce #IconIndexSymbol #Induction #Inquiry #Likelihood #LikelyStory #Likeness #Logic #Mathematics #Probability #ProbableReasoning #Semiotics #SignRelations
cc: Research Gate • Structural Modeling • Systems Science • Syscoi -
Alright, future engineers!
**Permutations:** Ways to *arrange* items from a set where order *matters*.
Ex: Arranging 3 books from 5 on a shelf: P(5,3) = 60 ways.
Pro-Tip: Think 'rankings' or 'sequences' – changing the order creates a new outcome!
#Permutations #Probability #STEM #StudyNotes -
Icon, Likeness, Likely Story, Likelihood, Probability • 2
• https://inquiryintoinquiry.com/2026/05/19/icon-likeness-likely-story-likelihood-probability-2-a/Re: Peirce List • Phyllis Chiasson
• https://web.archive.org/web/20131211153209/http://comments.gmane.org/gmane.science.philosophy.peirce/11234
• https://web.archive.org/web/20131211034001/http://permalink.gmane.org/gmane.science.philosophy.peirce/11235I'm still a bit fuzzy on how Aristotle's account relates to Peirce's usage, though I'm pretty sure Peirce must have taken Aristotle's usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.
❝We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true.❞ (Aristotle, Prior Analytics, 2.27.70b1–6).
Reference —
Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
Resource —
Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism -
Icon, Likeness, Likely Story, Likelihood, Probability • 2
Re: Peirce List • Phyllis Chiasson
I’m still a bit fuzzy on how Aristotle’s account relates to Peirce’s usage, though I’m pretty sure Peirce must have taken Aristotle’s usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.
We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true. (Aristotle, Prior Analytics, 2.27.70b1–6).
Reference
- Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
Resource
- Theme One Program • User Guide • Appendix A
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