kolektiva.social

36 posts9 participants12 posts today

AvaSuppose I have a random event with k possible outcomes of equal probability. What distribution (if any) describes the probability of obtaining a specific sequence of length m after n events?<a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://mathstodon.xyz/tags/probabilitydistribution" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilitydistribution</a> <a href="https://mathstodon.xyz/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a>

pglpmHappy Birthday, Laplace! 🎂 🪐 🎓 One of the first to use Bayesian probability theory in the modern way!"One sees in this essay that the theory of probabilities is basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it. It leaves nothing arbitrary in the choice of opinions and of making up one's mind, every time one is able, by this means, to determine the most advantageous choice. Thereby, it becomes the most happy supplement to ignorance and to the weakness of the human mind. If one considers the analytical methods to which this theory has given rise, the truth of the principles that serve as the groundwork, the subtle and delicate logic needed to use them in the solution of the problems, the public-benefit businesses that depend on it, and the extension that it has received and may still receive from its application to the most important questions of natural philosophy and the moral sciences; if one observes also that even in matters which cannot be handled by the calculus, it gives the best rough estimates to guide us in our judgements, and that it teaches us to guard ourselves from the illusions which often mislead us, one will see that there is no science at all more worthy of our consideration, and that it would be a most useful part of the system of public education." *Philosophical Essay on Probabilities*, 1814 <<a href="https://doi.org/10.1007/978-1-4612-4184-3" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://doi.org/10.1007/978-1-4612-4184-3</a>><a href="https://c.im/tags/science" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#science</a> <a href="https://c.im/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://c.im/tags/bayesian" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bayesian</a> <a href="https://c.im/tags/physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#physics</a>

CubeRootOfTrueChatGPT's thought processes:I'm tying together the rich tapestry of philosophical insights and category theory, exploring how enriched categories, with their hom-sets as objects in a monoidal category, aid in managing complexity, partial orders, or metrics, moving beyond conventional morphism sets.I'm starting to see how enriched categories with hom-sets as partially ordered sets can capture complexity, cost, or transformation intricacies through preorders, partial orders, metrics, or probabilities.I’m piecing together how enriched categories can reveal more about morphisms by incorporating structures like complexity, cost, or probability, allowing short and long morphisms to be systematically compared.... and then it crashed, without producing a response. This is very similar to my experience with this material, yes, quite human-like<a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#categorytheory</a> <a href="https://mathstodon.xyz/tags/enriched" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#enriched</a> <a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a>

Christian TestaOver the past couple of years, I've really fallen in love with <a href="https://fediscience.org/tags/tikz" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tikz</a> and all of its quirks. TikZ is a plotting/graphics package for LaTeX that is especially useful for creating mathematical diagrams. The support for mathematical notation is unbeatable and the flexibility of the language is extremely high. Also, graphics rendered to pdf/svg in this way are extremely lightweight and reproducible. I do find it very challenging syntax to remember though, so I put together this GitHub repository to keep track of tikz code I've written. <a href="https://github.com/ctesta01/tikz-examples/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://github.com/ctesta01/tikz-examples/</a>Each graphic shown in the README is linked to its underlying .tex code. Also the README has several links to documentation / tutorials that I've found helpful along with some tips I've learned from experience. <a href="https://fediscience.org/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://fediscience.org/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a> <a href="https://fediscience.org/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://fediscience.org/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://fediscience.org/tags/graphics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#graphics</a> <a href="https://fediscience.org/tags/TeXLaTeX" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TeXLaTeX</a>

kazéDear LazyWeb: is there a C/C++, <a href="https://mastodon.social/tags/RustLang" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RustLang</a> or <a href="https://mastodon.social/tags/Zig" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Zig</a> equivalent of <a href="https://mastodon.social/tags/SciPy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SciPy</a>’s `stats` module for statistical analysis? Namely: • a collection of common PDFs (probability density functions); • MLE (maximum likelihood estimation) for these common distributions; • KDE (kernel density estimation).SciPy’s API is a pleasure to work with. Anything that comes close but usable from C/C++/Rust/Zig would make my life so much easier. Boosts appreciated for visibility.<a href="https://mastodon.social/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a> <a href="https://mastodon.social/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://mastodon.social/tags/DataScience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DataScience</a>

Victoria Stuart 🇨🇦 🏳️‍⚧️[2502.05244] Probabilistic Artificial Intelligence <a href="https://arxiv.org/abs/2502.05244" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://arxiv.org/abs/2502.05244</a> <a href="https://news.ycombinator.com/item?id=43318624" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://news.ycombinator.com/item?id=43318624</a>Manuscript 418pp ...<a href="https://mastodon.social/tags/ML" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ML</a> <a href="https://mastodon.social/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://mastodon.social/tags/MLbooks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MLbooks</a> <a href="https://mastodon.social/tags/MLtheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MLtheory</a>

Eric Maugendre<a href="https://a.gup.pe/u/data" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@data</a> <a href="https://a.gup.pe/u/datadon" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@datadon</a> 🧵Accuracy! To counter regression dilution, a method is to add a constraint on the statistical modeling. Regression Redress restrains bias by segregating the residual values. My article: <a href="http://data.yt/kit/regression-redress.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">http://data.yt/kit/regression-redress.html</a><a href="https://hachyderm.io/tags/bias" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bias</a> <a href="https://hachyderm.io/tags/modeling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modeling</a> <a href="https://hachyderm.io/tags/dataDev" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#dataDev</a> <a href="https://hachyderm.io/tags/AIDev" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AIDev</a> <a href="https://hachyderm.io/tags/modelEvaluation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modelEvaluation</a> <a href="https://hachyderm.io/tags/regression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#regression</a> <a href="https://hachyderm.io/tags/modelling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modelling</a> <a href="https://hachyderm.io/tags/dataLearning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#dataLearning</a> <a href="https://hachyderm.io/tags/linearRegression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#linearRegression</a> <a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://hachyderm.io/tags/probabilities" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilities</a> <a href="https://hachyderm.io/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a> <a href="https://hachyderm.io/tags/stats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#stats</a> <a href="https://hachyderm.io/tags/correctionRatio" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#correctionRatio</a> <a href="https://hachyderm.io/tags/ML" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ML</a> <a href="https://hachyderm.io/tags/distributions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#distributions</a> <a href="https://hachyderm.io/tags/accuracy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#accuracy</a> <a href="https://hachyderm.io/tags/RegressionRedress" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RegressionRedress</a> <a href="https://hachyderm.io/tags/Python" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Python</a> <a href="https://hachyderm.io/tags/RStats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RStats</a>

Eric Maugendre<a href="https://a.gup.pe/u/data" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@data</a> <a href="https://a.gup.pe/u/datadon" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@datadon</a> 🧵How to assess a statistical model? How to choose between variables?Pearson's <a href="https://hachyderm.io/tags/correlation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#correlation</a> is irrelevant if you suspect that the relationship is not a straight line.If monotonic relationship: "<a href="https://hachyderm.io/tags/Spearman" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Spearman</a>’s rho is particularly useful for small samples where weak correlations are expected, as it can detect subtle monotonic trends." It is "widespread across disciplines where the measurement precision is not guaranteed". "<a href="https://hachyderm.io/tags/Kendall" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Kendall</a>’s Tau-b is less affected [than Spearman’s rho] by outliers in the data, making it a robust option for datasets with extreme values." Ref: <a href="https://statisticseasily.com/kendall-tau-b-vs-spearman/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://statisticseasily.com/kendall-tau-b-vs-spearman/</a><a href="https://hachyderm.io/tags/normality" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#normality</a> <a href="https://hachyderm.io/tags/normalDistribution" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#normalDistribution</a> <a href="https://hachyderm.io/tags/modeling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modeling</a> <a href="https://hachyderm.io/tags/dataDev" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#dataDev</a> <a href="https://hachyderm.io/tags/AIDev" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AIDev</a> <a href="https://hachyderm.io/tags/ML" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ML</a> <a href="https://hachyderm.io/tags/modelEvaluation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modelEvaluation</a> <a href="https://hachyderm.io/tags/regression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#regression</a> <a href="https://hachyderm.io/tags/modelling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modelling</a> <a href="https://hachyderm.io/tags/dataLearning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#dataLearning</a> <a href="https://hachyderm.io/tags/featureEngineering" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#featureEngineering</a> <a href="https://hachyderm.io/tags/linearRegression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#linearRegression</a> <a href="https://hachyderm.io/tags/modeling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modeling</a> <a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://hachyderm.io/tags/probabilities" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilities</a> <a href="https://hachyderm.io/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a> <a href="https://hachyderm.io/tags/stats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#stats</a> <a href="https://hachyderm.io/tags/correctionRatio" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#correctionRatio</a> <a href="https://hachyderm.io/tags/ML" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ML</a> <a href="https://hachyderm.io/tags/Pearson" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Pearson</a> <a href="https://hachyderm.io/tags/bias" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bias</a> <a href="https://hachyderm.io/tags/regressionRedress" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#regressionRedress</a> <a href="https://hachyderm.io/tags/distributions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#distributions</a>

Eric Maugendre"In real life, we weigh the anticipated consequences of the decisions that we are about to make. That approach is much more rational than limiting the percentage of making the error of one kind in an artificial (null hypothesis) setting or using a measure of evidence for each model as the weight." Longford (2005) <a href="http://www.stat.columbia.edu/~gelman/stuff_for_blog/longford.pdf" rel="nofollow noopener noreferrer" translate="no" target="_blank">http://www.stat.columbia.edu/~gelman/stuff_for_blog/longford.pdf</a><a href="https://hachyderm.io/tags/modeling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modeling</a> <a href="https://hachyderm.io/tags/nullHypothesis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nullHypothesis</a> <a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://hachyderm.io/tags/probabilities" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilities</a> <a href="https://hachyderm.io/tags/pValues" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pValues</a> <a href="https://hachyderm.io/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a> <a href="https://hachyderm.io/tags/stats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#stats</a> <a href="https://hachyderm.io/tags/statisticalLiteracy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statisticalLiteracy</a> <a href="https://hachyderm.io/tags/bias" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bias</a> <a href="https://hachyderm.io/tags/inference" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#inference</a> <a href="https://hachyderm.io/tags/modelling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modelling</a> <a href="https://hachyderm.io/tags/regression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#regression</a> <a href="https://hachyderm.io/tags/linearRegression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#linearRegression</a>

Eric MaugendreFeature Selection in Python; a script ready to use: <a href="https://johfischer.com/2021/08/06/correlation-based-feature-selection-in-python-from-scratch/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://johfischer.com/2021/08/06/correlation-based-feature-selection-in-python-from-scratch/</a><a href="https://hachyderm.io/tags/interpretability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#interpretability</a> <a href="https://hachyderm.io/tags/featureSelection" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#featureSelection</a> <a href="https://hachyderm.io/tags/python" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#python</a> <a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://hachyderm.io/tags/probabilities" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilities</a> <a href="https://hachyderm.io/tags/bigData" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bigData</a> <a href="https://hachyderm.io/tags/classification" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#classification</a> <a href="https://hachyderm.io/tags/linearRegression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#linearRegression</a> <a href="https://hachyderm.io/tags/regression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#regression</a> <a href="https://hachyderm.io/tags/Schusterbauer" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Schusterbauer</a> <a href="https://hachyderm.io/tags/inference" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#inference</a> <a href="https://hachyderm.io/tags/AIDev" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AIDev</a>

Eric MaugendreSurveys, coincidences, statistical significance 🧵"What Educated Citizens Should Know About Statistics and Probability" By Jessica Utts, in 2003: <a href="https://ics.uci.edu/~jutts/AmerStat2003.pdf" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://ics.uci.edu/~jutts/AmerStat2003.pdf</a> via <a href="https://hachyderm.io/@hrefna" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@hrefna</a> <a href="https://a.gup.pe/u/edutooters" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@edutooters</a><a href="https://hachyderm.io/tags/nullHypothesis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nullHypothesis</a> <a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://hachyderm.io/tags/probabilities" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilities</a> <a href="https://hachyderm.io/tags/pValues" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pValues</a> <a href="https://hachyderm.io/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a> <a href="https://hachyderm.io/tags/stats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#stats</a> <a href="https://hachyderm.io/tags/education" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#education</a> <a href="https://hachyderm.io/tags/higherEd" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#higherEd</a> <a href="https://hachyderm.io/tags/statisticalLiteracy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statisticalLiteracy</a> <a href="https://hachyderm.io/tags/bias" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bias</a> <a href="https://hachyderm.io/tags/media" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#media</a> <a href="https://hachyderm.io/tags/causalInference" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#causalInference</a>

Eric Maugendre"In <a href="https://mas.to/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> theory, a log-normal (or <a href="https://mas.to/tags/lognormal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#lognormal</a>) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution.""It is a convenient and useful model for measurements in exact and engineering sciences, as well as medicine, economics […], energies, concentrations, lengths, prices".<a href="https://en.wikipedia.org/wiki/Log-normal_distribution" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Log-normal_distribution</a><a href="https://mas.to/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a> <a href="https://mas.to/tags/finance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#finance</a> <a href="https://mas.to/tags/modeling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modeling</a>

Eric Maugendre<a href="https://mastodon.social/@level98" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@level98</a> 😀 There even wikipedia on the "Misuse of p-values": <a href="https://en.wikipedia.org/wiki/Misuse_of_p-values" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://en.wikipedia.org/wiki/Misuse_of_p-values</a>I therefore am adding to my guidelines: "Instead of telling researchers what they want to know, statisticians should teach researchers which questions they can ask. […] Before we can improve our statistical inferences, we need to improve our statistical questions."Excerpt from Daniël Lakens (2021) <a href="https://journals.sagepub.com/doi/10.1177/1745691620958012" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://journals.sagepub.com/doi/10.1177/1745691620958012</a><a href="https://hachyderm.io/tags/quotes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quotes</a> <a href="https://hachyderm.io/tags/nullHypothesis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nullHypothesis</a> <a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://hachyderm.io/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://hachyderm.io/tags/pValues" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pValues</a> <a href="https://hachyderm.io/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://hachyderm.io/tags/AIEthics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AIEthics</a> <a href="https://hachyderm.io/tags/ML" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ML</a> <a href="https://hachyderm.io/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a>

Eric MaugendreIn 2016, the American Statistical Association <a href="https://hachyderm.io/tags/ASA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ASA</a> made a formal statement that "a p-value, or statistical significance, does not measure the size of an effect or the importance of a result".It also stated that "p-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone".<a href="https://hachyderm.io/tags/nullHypothesis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nullHypothesis</a> <a href="https://hachyderm.io/tags/probabilities" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probabilities</a> <a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://hachyderm.io/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://hachyderm.io/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://hachyderm.io/tags/vectors" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#vectors</a> <a href="https://hachyderm.io/tags/data" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#data</a> <a href="https://hachyderm.io/tags/bigData" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bigData</a> <a href="https://hachyderm.io/tags/matrices" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#matrices</a> <a href="https://hachyderm.io/tags/ML" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ML</a> <a href="https://hachyderm.io/tags/distributions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#distributions</a> <a href="https://hachyderm.io/tags/stats" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#stats</a> <a href="https://hachyderm.io/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#statistics</a>

Adrian Riskin 🇵🇸🍉NYT crosswords are usually so precise, but this one has a mistake, which I think is the first one I ever found after doing thousands of them over the years. The clue is "36:1, for snake-eyes" and the correct answer is "ODDS". But the odds for snake-eyes are 1:35. Argh!<a href="https://kolektiva.social/tags/NYTCrossword" class="mention hashtag" rel="tag">#NYTCrossword</a> <a href="https://kolektiva.social/tags/Math" class="mention hashtag" rel="tag">#Math</a> <a href="https://kolektiva.social/tags/Probability" class="mention hashtag" rel="tag">#Probability</a>

Eric Maugendre"Majorizing measures provide bounds for the supremum of stochastic processes. They represent the most general possible form of the chaining argument".Michel Talagrand, 1996, <a href="https://projecteuclid.org/journals/annals-of-probability/volume-24/issue-3/Majorizing-measures-the-generic-chaining/10.1214/aop/1065725175.full" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://projecteuclid.org/journals/annals-of-probability/volume-24/issue-3/Majorizing-measures-the-generic-chaining/10.1214/aop/1065725175.full</a><a href="https://hachyderm.io/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://hachyderm.io/tags/theorem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theorem</a> <a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://hachyderm.io/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://hachyderm.io/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://hachyderm.io/tags/Talagrand" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Talagrand</a> <a href="https://hachyderm.io/tags/data" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#data</a> <a href="https://hachyderm.io/tags/bigData" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#bigData</a> <a href="https://hachyderm.io/tags/chaining" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#chaining</a> <a href="https://hachyderm.io/tags/ML" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ML</a> <a href="https://hachyderm.io/tags/AbelPrize" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AbelPrize</a> <a href="https://hachyderm.io/tags/Abel" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Abel</a>

Eric MaugendreConcentration of measures: Talagrand's "work illustrates the idea that the interplay of many random events can, counter-intuitively, lead to outcomes that are more predictable, and gives estimates for the extent to which the uncertainty is reigned in."Marianne Freiberger: <a href="https://plus.maths.org/content/abel-prize-2024" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://plus.maths.org/content/abel-prize-2024</a> <a href="https://a.gup.pe/u/data" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@data</a> <a href="https://a.gup.pe/u/mathematics" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@mathematics</a><a href="https://hachyderm.io/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://hachyderm.io/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://hachyderm.io/tags/Talagrand" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Talagrand</a> <a href="https://hachyderm.io/tags/data" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#data</a> <a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#probability</a> <a href="https://hachyderm.io/tags/magnets" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#magnets</a> <a href="https://hachyderm.io/tags/spinGlasses" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#spinGlasses</a> <a href="https://hachyderm.io/tags/physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#physics</a>

Ariadne“Climate change is now reaching the end-game, where very soon humanity must choose between taking unprecedented action, or accepting that it has been left too late and bear the consequences. Therefore, it is all the more important to listen to non-mainstream voices who do understand the issues and are less hesitant to cry wolf. Unfortunately for us, the wolf may already be in the house.” - Hans-Joachim Schnellhuber, founding director of the Potsdam Institute for Climate Impact Research [1]There is a 10% chance, according to <a href="https://kolektiva.social/tags/ClimateModels" class="mention hashtag" rel="tag">#ClimateModels</a>, that we are on course for a total collapse of <a href="https://kolektiva.social/tags/Earth" class="mention hashtag" rel="tag">#Earth</a>'s <a href="https://kolektiva.social/tags/climate" class="mention hashtag" rel="tag">#climate</a> (the <a href="https://kolektiva.social/tags/atmosphere" class="mention hashtag" rel="tag">#atmosphere</a> - <a href="https://kolektiva.social/tags/ocean" class="mention hashtag" rel="tag">#ocean</a> <a href="https://kolektiva.social/tags/ClimateSystem" class="mention hashtag" rel="tag">#ClimateSystem</a>) - 6°C of <a href="https://kolektiva.social/tags/GlobalWarming" class="mention hashtag" rel="tag">#GlobalWarming</a> above <a href="https://kolektiva.social/tags/PreIndustrial" class="mention hashtag" rel="tag">#PreIndustrial</a> (pre-1750) levels [1]. Which is what 700 ppm atmospheric <a href="https://kolektiva.social/tags/CO2" class="mention hashtag" rel="tag">#CO2</a> would bring. We are projected to reach 700 ppm CO2 in 2075 (and 950 ppm by 2100) [2]. This would mean not only <a href="https://kolektiva.social/tags/EconomicCollapse" class="mention hashtag" rel="tag">#EconomicCollapse</a> and complete breakdown of <a href="https://kolektiva.social/tags/human" class="mention hashtag" rel="tag">#human</a> <a href="https://kolektiva.social/tags/society" class="mention hashtag" rel="tag">#society</a>, but a 6th <a href="https://kolektiva.social/tags/MassExtinction" class="mention hashtag" rel="tag">#MassExtinction</a> of nearly all <a href="https://kolektiva.social/tags/species" class="mention hashtag" rel="tag">#species</a>. And very likely near extinction of humans. Would you board an aircraft that you knew had a 10% <a href="https://kolektiva.social/tags/probability" class="mention hashtag" rel="tag">#probability</a> of crashing? Well, the <a href="https://kolektiva.social/tags/IPCC" class="mention hashtag" rel="tag">#IPCC</a> and most mainstream scientists apparently would. 38% of the denizens of <a href="https://kolektiva.social/tags/Mastodon" class="mention hashtag" rel="tag">#Mastodon</a> who responded to a poll I did the other day would at least consider boarding an aircraft with a 1% chance of crashing. If 1% of aircraft flights ended in a crash, that would mean over 1,000 crashes per day. At 10% probability of a crash it would be 10,000 per day. Unthinkable, right? Apparently not. Not when it comes to playing with the earth's <a href="https://kolektiva.social/tags/climate" class="mention hashtag" rel="tag">#climate</a>. There's still a 90% chance of this not happening, after all, the IPCC reasons. So it is not “very likely”, not even “likely”. This represents ignorance of <a href="https://kolektiva.social/tags/risk" class="mention hashtag" rel="tag">#risk</a> and <a href="https://kolektiva.social/tags/RiskAnalysis" class="mention hashtag" rel="tag">#RiskAnalysis</a>, ignorance of the way <a href="https://kolektiva.social/tags/probability" class="mention hashtag" rel="tag">#probability</a> and <a href="https://kolektiva.social/tags/statistics" class="mention hashtag" rel="tag">#statistics</a> works in <a href="https://kolektiva.social/tags/ComplexSystems" class="mention hashtag" rel="tag">#ComplexSystems</a>, ignorance of <a href="https://kolektiva.social/tags/FatTail" class="mention hashtag" rel="tag">#FatTail</a> probability distributions, ignorance of the fact that all <a href="https://kolektiva.social/tags/NaturalSystems" class="mention hashtag" rel="tag">#NaturalSystems</a> are complex systems, which by their nature are subject to <a href="https://kolektiva.social/tags/TippingPoints" class="mention hashtag" rel="tag">#TippingPoints</a> – and a bizarre belief that the <a href="https://kolektiva.social/tags/NormalDistribution" class="mention hashtag" rel="tag">#NormalDistribution</a> (the so-called <a href="https://kolektiva.social/tags/BellCurve" class="mention hashtag" rel="tag">#BellCurve</a>) applies to natural systems, which it decidedly does not. Allow me to elaborate.A couple of days ago, I ran a <a href="https://kolektiva.social/tags/ClimateCrisis" class="mention hashtag" rel="tag">#ClimateCrisis</a> <a href="https://kolektiva.social/tags/poll" class="mention hashtag" rel="tag">#poll</a> masquerading as a poll asking if you would board an aircraft which you knew had a 1% chance of crashing. The hints that this poll was allegorical were the <a href="https://kolektiva.social/tags/Climate" class="mention hashtag" rel="tag">#Climate</a> hashtags and the link to the straightforward climate poll I ran in parallel with it.) As to the latter, which asked “Can we ignore unlikely but high risk <a href="https://kolektiva.social/tags/GlobalWarming" class="mention hashtag" rel="tag">#GlobalWarming</a> scenarios?”, 80% of respondents to both the German and English versions said “Absolutely Not! We risk annihilation of <a href="https://kolektiva.social/tags/Earth" class="mention hashtag" rel="tag">#Earth</a>!” Only 7% picked “the <a href="https://kolektiva.social/tags/IPCC" class="mention hashtag" rel="tag">#IPCC</a> ignores these [scenarios]. Me too.” This closely mirrors a statistically valid poll of 14,000 adult German citizens published in August 2021 in which 74% of people responded that humanity is about to face an <a href="https://kolektiva.social/tags/ecological" class="mention hashtag" rel="tag">#ecological</a> <a href="https://kolektiva.social/tags/catastrophe" class="mention hashtag" rel="tag">#catastrophe</a> [3]. But surprisingly (shockingly?) 20% of respondents to the “aircraft crash” poll said they would board the aircraft even if they knew there was a 1% chance of it crashing, and 18% said they weren't sure and “would have to think about it” (94 people responded to the “aircraft” poll, 45 to the “climate” poll). Which means 38% of people would at least consider boarding such a plane. Very bad idea.Now <a href="https://kolektiva.social/tags/Mastodon" class="mention hashtag" rel="tag">#Mastodon</a> polls are in no way statistically valid (but then neither are many commercial polls that get touted by news organizations). Nonetheless, the results are very illuminating when it comes to how the IPCC, <a href="https://kolektiva.social/tags/governments" class="mention hashtag" rel="tag">#governments</a>, <a href="https://kolektiva.social/tags/business" class="mention hashtag" rel="tag">#business</a>, and indeed the <a href="https://kolektiva.social/tags/ScientificCommunity" class="mention hashtag" rel="tag">#ScientificCommunity</a> are dealing, or rather not dealing, with the fact that there is not a 1% probability but a 10% chance that <a href="https://kolektiva.social/tags/humans" class="mention hashtag" rel="tag">#humans</a> have put our planet on a trajectory in which <a href="https://kolektiva.social/tags/humans" class="mention hashtag" rel="tag">#humans</a> and most <a href="https://kolektiva.social/tags/species" class="mention hashtag" rel="tag">#species</a> may well become <a href="https://kolektiva.social/tags/extinct" class="mention hashtag" rel="tag">#extinct</a> sometime in the 22nd Century. And <a href="https://kolektiva.social/tags/SocietalCollapse" class="mention hashtag" rel="tag">#SocietalCollapse</a> will likely happen later in our present century. The level of ignorance of <a href="https://kolektiva.social/tags/probability" class="mention hashtag" rel="tag">#probability</a> and <a href="https://kolektiva.social/tags/statistics" class="mention hashtag" rel="tag">#statistics</a> in <a href="https://kolektiva.social/tags/NaturalSystems" class="mention hashtag" rel="tag">#NaturalSystems</a>, specifically the <a href="https://kolektiva.social/tags/ocean" class="mention hashtag" rel="tag">#ocean</a> - <a href="https://kolektiva.social/tags/atmosphere" class="mention hashtag" rel="tag">#atmosphere</a> system – demonstrated by the IPCC and many mainstream scientists shockingly parallels the ignorance of these same subjects by 38% of the respondents to the “aircraft poll”. (For one thing, there are projected to be about 40,000,000 aircraft flights in 2023 [4]. If there were a 1% chance of a crash, that would mean 400,000 crashes this year, or over 1000 crashes per day. And yet, when we look dispassionately at the <a href="https://kolektiva.social/tags/ClimateScience" class="mention hashtag" rel="tag">#ClimateScience</a>, we are treating the very real models of human-caused global-warming (Anthropogenic Global Warming, or <a href="https://kolektiva.social/tags/AGW" class="mention hashtag" rel="tag">#AGW</a>) as if we've intentionally boarded an aircraft that has a 10% chance of crashing. Which would mean 10,000 aircraft crashes every day. Unthinkable, right? Surely no one would ever board an aircraft if this were the case.In the case of Earth's climate, what would constitute a “crash”, the complete collapse of human society, nearly complete <a href="https://kolektiva.social/tags/MassExtinction" class="mention hashtag" rel="tag">#MassExtinction</a> of most terrestrial species, a broad band (± 20° latitude north and south of the equator) of our <a href="https://kolektiva.social/tags/oceans" class="mention hashtag" rel="tag">#oceans</a> at hot tub temperatures, and an even broader band (± 30° N/S of the equator) which would be uninhabitable for humans, and large regions even further north and south (the <a href="https://kolektiva.social/tags/American" class="mention hashtag" rel="tag">#American</a> <a href="https://kolektiva.social/tags/Southwest" class="mention hashtag" rel="tag">#Southwest</a>, the interior of <a href="https://kolektiva.social/tags/Australia" class="mention hashtag" rel="tag">#Australia</a>, most of the <a href="https://kolektiva.social/tags/Mediterranean" class="mention hashtag" rel="tag">#Mediterranean</a>, <a href="https://kolektiva.social/tags/Arabia" class="mention hashtag" rel="tag">#Arabia</a>, <a href="https://kolektiva.social/tags/Spain" class="mention hashtag" rel="tag">#Spain</a>, <a href="https://kolektiva.social/tags/Portugal" class="mention hashtag" rel="tag">#Portugal</a>, <a href="https://kolektiva.social/tags/India" class="mention hashtag" rel="tag">#India</a>, <a href="https://kolektiva.social/tags/Pakistan" class="mention hashtag" rel="tag">#Pakistan</a>, the south of <a href="https://kolektiva.social/tags/France" class="mention hashtag" rel="tag">#France</a>, to name a few) which would be uninhabitable during the summer months? Scientists agree that 6°C of global warming above <a href="https://kolektiva.social/tags/PreIndustrial" class="mention hashtag" rel="tag">#PreIndustrial</a> (before 1750 CE) would certainly do it; quite possibly less than that, due to positive <a href="https://kolektiva.social/tags/FeedbackLoops" class="mention hashtag" rel="tag">#FeedbackLoops</a>, but let's be conservative, like most scientists, and go with 6°C. What are the chances of that? Well, the chance of 6°C of warming within the next 100 years is 10%! Here is an excellent graphic (see attached screenshot) from the economists Gernot Wagner's and Martin Weitzman's 2015 book “Climate shock: the economic consequences of a hotter planet” [5] (well worth a read, by the way). That doesn't quite look like a Normal distribution, does it? A pretty wonky looking “bell curve”. That's because the statistics that underlie the curve are not Normally distributed. It is not a bell curve. A Normal distribution is based upon the statistical concept known as the Central Limit Theorem <a href="https://kolektiva.social/tags/CentralLimitTheorem" class="mention hashtag" rel="tag">#CentralLimitTheorem</a>, and the Law of [Statistical] Universality which arises from it. And that law works great – when it is applied to data whose variables do not interact with each other or with other systems, when there are no higher order interactions of variables, when there are no <a href="https://kolektiva.social/tags/FeedbackLoops" class="mention hashtag" rel="tag">#FeedbackLoops</a>, etc. If you're looking at a distribution of the heights or weights of 1000 randomly selected <a href="https://kolektiva.social/tags/penguins" class="mention hashtag" rel="tag">#penguins</a>, or people, the data will be Normally distributed, it will follow a “bell curve”, because the Central Limit Theorem tells us it will be so, and the Law of Universality must apply. But none of this is true for natural systems, whether a <a href="https://kolektiva.social/tags/biome" class="mention hashtag" rel="tag">#biome</a>, an <a href="https://kolektiva.social/tags/ecosystem" class="mention hashtag" rel="tag">#ecosystem</a>, or the ocean-atmosphere system that is (primarily) responsible for Earth's climate. There is another kind of statistical universality, indeed a statistical law of universality, that applies to all complex systems, and thus all natural systems, called Tracy-Widom Universality (first elaborated in 1992 by the mathematicians Craig Tracy and Harold Widom) [6]. The statistical distributions that arise from Tracy-Widom Universality are not symmetrical “bell curves” but skewed distributions with “fat tails”. Exactly that of the statistical likelihood of reaching or exceeding 6°C of global warming as shown in Wagner's and Weitzman's figure.Are we totally screwed? Or rather, have we totally screwed ourselves and the planet? As of now, it certainly looks that way. And perhaps we are collectively okay with this. There is after all a 90% chance we won't reach or exceed 6°C of warming. But even the mainstream climate science community acknowledges we are headed for 3°C - 4°C of global warming, and headed there very soon, which will probably be more than enough to set off the collapse of the climate, of the atmospheric and ocean circulation system. And a single species, in about 300 years time, will have managed to destroy the bluest and greenest and most living of planets, 4.5 billion years in the making. It is simply not right.[1] <a href="https://www.breakthroughonline.org.au/whatliesbeneath" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://www.breakthroughonline.org.au/whatliesbeneath</a>[2] <a href="https://yaleclimateconnections.org/2019/06/data-from-earths-past-holds-a-warning-for-our-future-under-climate-change/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://yaleclimateconnections.org/2019/06/data-from-earths-past-holds-a-warning-for-our-future-under-climate-change/</a>[3] <a href="https://www.fom.de/2021/august/deutschlandweite-fom-umfrage-zur-klimakrise.html" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://www.fom.de/2021/august/deutschlandweite-fom-umfrage-zur-klimakrise.html</a>[4] <a href="https://www.statista.com/statistics/564769/airline-industry-number-of-flights/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://www.statista.com/statistics/564769/airline-industry-number-of-flights/</a>[5] <a href="https://archive.org/details/climateshockecon0000wagn/page/53/mode/1up?view=theater" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://archive.org/details/climateshockecon0000wagn/page/53/mode/1up?view=theater</a>[6] <a href="https://www.quantamagazine.org/beyond-the-bell-curve-a-new-universal-law-20141015/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://www.quantamagazine.org/beyond-the-bell-curve-a-new-universal-law-20141015/</a><a href="https://kolektiva.social/tags/Klimakrise" class="mention hashtag" rel="tag">#Klimakrise</a> <a href="https://kolektiva.social/tags/Klimawandel" class="mention hashtag" rel="tag">#Klimawandel</a> <a href="https://kolektiva.social/tags/Klima" class="mention hashtag" rel="tag">#Klima</a> <a href="https://kolektiva.social/tags/Erderw%C3%A4rmung" class="mention hashtag" rel="tag">#Erderwärmung</a> <a href="https://kolektiva.social/tags/Erderhitzung" class="mention hashtag" rel="tag">#Erderhitzung</a> <a href="https://kolektiva.social/tags/Atmosph%C3%A4re" class="mention hashtag" rel="tag">#Atmosphäre</a> <a href="https://kolektiva.social/tags/Ozean" class="mention hashtag" rel="tag">#Ozean</a> <a href="https://kolektiva.social/tags/Klimamodell" class="mention hashtag" rel="tag">#Klimamodell</a>

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