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Aneesh SatheMy Road to Bayesian StatsBy 2015, I had heard of Bayesian Stats but didn’t bother to go deeper into it. After all, significance stars, and p-values worked fine. I started to explore Bayesian Statistics when considering small sample sizes in biological experiments. How much can you say when you are comparing means of 6 or even 60 observations? This is the nature work at the edge of knowledge. Not knowing what to expect is normal. Multiple possible routes to a seen a result is normal. Not knowing how to pick the route to the observed result is also normal. Yet, our statistics fails to capture this reality and the associated uncertainties. There must be a way I thought. <a href="https://aneeshsathe.com/wp-content/uploads/2025/07/image-from-rawpixel-id-2968487-jpeg.jpg" rel="nofollow noopener" target="_blank"></a>Free Curve to the Point: Accompanying Sound of Geometric Curves (1925) print in high resolution by Wassily Kandinsky. Original from The MET Museum. Digitally enhanced by rawpixel.I started by searching for ways to overcome small sample sizes. There are minimum sample sizes recommended for t-tests. Thirty is an often quoted number with qualifiers. Bayesian stats does not have a minimum sample size. This had me intrigued. Surely, this can’t be a thing. But it is. Bayesian stats creates a mathematical model using your observations and then samples from that model to make comparisons. If you have any exposure to AI, you can think of this a bit like training an AI model. Of course the more data you have the better the model can be. But even with a little data we can make progress. How do you say, there is something happening and it’s interesting, but we are only x% sure. Frequentist stats have no way through. All I knew was to apply the t-test and if there are “***” in the plot, I’m golden. That isn’t accurate though. Low p-values indicate the strength of evidence against the null hypothesis. Let’s take a minute to unpack that. The null hypothesis is that nothing is happening. If you have a control set and do a treatment on the other set, the null hypothesis says that there is no difference. So, a low p-value says that it is unlikely that the null hypothesis is true. But that does not imply that the alternative hypothesis is true. What’s worse is that there is no way for us to say that the control and experiment have no difference. We can’t accept the null hypothesis using p-values either. Guess what? Bayes stats can do all those things. It can measure differences, accept and reject both  null and alternative hypotheses, even communicate how uncertain we are (more on this later). All without making assumptions about our data.It’s often overlooked, but frequentist analysis also requires the data to have certain properties like normality and equal variance. Biological processes have complex behavior and, unless observed, assuming normality and equal variance is perilous. The danger only goes up with small sample sizes. Again, Bayes requires you to make no assumptions about your data. Whatever shape the distribution is, so called outliers and all, it all goes into the model. Small sample sets do produce weaker fits, but this is kept transparent. Transparency is one of the key strengths of Bayesian stats. It requires you to work a little bit harder on two fronts though. First you have to think about your data generating process (DGP). This means how do the data points you observe came to be. As we said, the process is often unknown. We have at best some guesses of how this could happen. Thankfully, we have a nice way to represent this. DAGs, directed acyclic graphs, are a fancy name for a simple diagram showing what affects what. Most of the time we are trying to discover the DAG, ie the pathway of a biological outcome. Even if you don’t do Bayesian stats, using DAGs to lay out your thoughts is a great. In Bayesian stats the DAGs can be used to test if your model fits the data we observe. If the DAG captures the data generating process the fit is good, and not if it doesn’t. The other hard bit is doing analysis and communicating the results. Bayesian stats forces you to be verbose about your assumptions in your model. This part is almost magicked away in t-tests. Frequentist stats also makes assumptions about the model that your data is assumed to follow. It all happens so quickly that there isn’t even a second to think about it. You put in your data, click t-test and woosh! You see stars. In Bayesian stats stating the assumptions you make in your model (using DAGs and hypothesis about DGPs) communicates to the world what and why you think this phenomenon occurs. Discovering causality is the whole reason for doing science. Knowing the causality allows us to intervene in the forms of treatments and drugs. But if my tools don’t allow me to be transparent and worse if they block people from correcting me, why bother?Richard McElreath says it best:<blockquote>There is no method for making causal models other than science. There is no method to science other than honest anarchy.</blockquote><a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/ai/" target="_blank">#AI</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/bayesian-statistics/" target="_blank">#BayesianStatistics</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/biological-data-analysis/" target="_blank">#BiologicalDataAnalysis</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/business/" target="_blank">#Business</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/causal-inference-2/" target="_blank">#CausalInference</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/dags/" target="_blank">#DAGs</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/data-generating-process/" target="_blank">#DataGeneratingProcess</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/data-science/" target="_blank">#dataScience</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/experimental-design/" target="_blank">#ExperimentalDesign</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/frequentist-vs-bayesian/" target="_blank">#FrequentistVsBayesian</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/leadership/" target="_blank">#Leadership</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/machine-learning/" target="_blank">#machineLearning</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/philosophy/" target="_blank">#philosophy</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/science/" target="_blank">#science</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/scientific-method/" target="_blank">#ScientificMethod</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/small-sample-size/" target="_blank">#SmallSampleSize</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/statistical-modeling/" target="_blank">#StatisticalModeling</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/statistical-philosophy/" target="_blank">#StatisticalPhilosophy</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/statistics/" target="_blank">#statistics</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/transparent-science/" target="_blank">#TransparentScience</a> <a rel="nofollow noopener" class="hashtag u-tag u-category" href="https://aneeshsathe.com/tag/uncertainty-quantification/" target="_blank">#UncertaintyQuantification</a>

EuroSciPyAdvancing probabilistic programming for scientific applications?<a href="https://fosstodon.org/tags/EuroSciPy2025" class="mention hashtag" rel="nofollow noopener" target="_blank">#EuroSciPy2025</a> welcomes original research on Bayesian methods, MCMC algorithms, and statistical modeling in <a href="https://fosstodon.org/tags/Python" class="mention hashtag" rel="nofollow noopener" target="_blank">#Python</a>.Submit your work as tutorials, talks, or posters!<a href="https://fosstodon.org/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a> <a href="https://fosstodon.org/tags/ScientificPython" class="mention hashtag" rel="nofollow noopener" target="_blank">#ScientificPython</a> <a href="https://fosstodon.org/tags/PyMC" class="mention hashtag" rel="nofollow noopener" target="_blank">#PyMC</a> <a href="https://fosstodon.org/tags/PyStan" class="mention hashtag" rel="nofollow noopener" target="_blank">#PyStan</a> <a href="https://fosstodon.org/tags/EuroSciPy" class="mention hashtag" rel="nofollow noopener" target="_blank">#EuroSciPy</a>

EuroSciPyDeveloping Bayesian inference methods for complex scientific problems?<a href="https://fosstodon.org/tags/EuroSciPy2025" class="mention hashtag" rel="nofollow noopener" target="_blank">#EuroSciPy2025</a> is seeking original work on Hamiltonian Monte Carlo, variational inference, and statistical modeling in <a href="https://fosstodon.org/tags/Python" class="mention hashtag" rel="nofollow noopener" target="_blank">#Python</a>.Submit your innovations: <a href="https://pretalx.com/euroscipy-2025/cfp" rel="nofollow noopener" translate="no" target="_blank">https://pretalx.com/euroscipy-2025/cfp</a> <a href="https://fosstodon.org/tags/CfP" class="mention hashtag" rel="nofollow noopener" target="_blank">#CfP</a><a href="https://fosstodon.org/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a> <a href="https://fosstodon.org/tags/ScientificPython" class="mention hashtag" rel="nofollow noopener" target="_blank">#ScientificPython</a> <a href="https://fosstodon.org/tags/BayesianInference" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianInference</a> <a href="https://fosstodon.org/tags/PyMC" class="mention hashtag" rel="nofollow noopener" target="_blank">#PyMC</a> <a href="https://fosstodon.org/tags/PyStan" class="mention hashtag" rel="nofollow noopener" target="_blank">#PyStan</a> <a href="https://fosstodon.org/tags/EuroSciPy" class="mention hashtag" rel="nofollow noopener" target="_blank">#EuroSciPy</a>

Pierre-Simon Laplace⚽ Football is more than tactics and talent—it's driven by 𝐝𝐚𝐭𝐚. From 𝐩𝐥𝐚𝐲𝐞𝐫 𝐫𝐞𝐜𝐫𝐮𝐢𝐭𝐦𝐞𝐧𝐭 to 𝐦𝐚𝐭𝐜𝐡 𝐚𝐧𝐚𝐥𝐲𝐬𝐢𝐬, data science gives clubs a winning edge.🎧 In the latest episode, Alex Andorra sits down with Matthew Penn to break it all down:👉<a href="https://learnbayesstats.com/episode/128-building-winning-data-team-football-matt-penn" rel="nofollow noopener" translate="no" target="_blank">https://learnbayesstats.com/episode/128-building-winning-data-team-football-matt-penn</a><a href="https://mstdn.science/tags/FootballAnalytics" class="mention hashtag" rel="nofollow noopener" target="_blank">#FootballAnalytics</a> <a href="https://mstdn.science/tags/DataScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#DataScience</a> <a href="https://mstdn.science/tags/SportsTech" class="mention hashtag" rel="nofollow noopener" target="_blank">#SportsTech</a> <a href="https://mstdn.science/tags/Recruitment" class="mention hashtag" rel="nofollow noopener" target="_blank">#Recruitment</a> <a href="https://mstdn.science/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a> <a href="https://mstdn.science/tags/FootballData" class="mention hashtag" rel="nofollow noopener" target="_blank">#FootballData</a>

Oliver D. ReithmaierAny academics know of <a href="https://infosec.exchange/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a> or <a href="https://infosec.exchange/tags/datascience" class="mention hashtag" rel="nofollow noopener" target="_blank">#datascience</a> winter schools in Europe? <a href="https://infosec.exchange/tags/academicchatter" class="mention hashtag" rel="nofollow noopener" target="_blank">#academicchatter</a> <a href="https://infosec.exchange/tags/WinterSchool" class="mention hashtag" rel="nofollow noopener" target="_blank">#WinterSchool</a>

Oliver D. ReithmaierQuestion for all the <a href="https://infosec.exchange/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a> and <a href="https://infosec.exchange/tags/epistemology" class="mention hashtag" rel="nofollow noopener" target="_blank">#epistemology</a> folks: can a Bayesian falsify things? Or is falsification just a different updating function for knowledge? Reason for saying this: falsification to me is kind of a Schumpeterian version of epistemology. You tear down a building (theory) to get a new, better one. Bayesianism on the other hand is more akin to a formative evaluation.

C.Suthorn :prn:Der "britische Tech Milliardär", der vermisst wird, heißt Mike Lynch. Die gesunkene Jacht gehört ihm Und hieß "Bayesian". Reich geworden ist er mit der Firma "Autonomy" die Pattern Matching mit "Bayesian Inference" betrieb. 2011 wurde Autonomy an HP verkauft und ging ein. Lynch wurde des Betrugs beschuldigt, an die USA ausgeliefert, im März 2024 vor gericht gestellt und im juni 2024 freigesprochen. Seit 2013 betreibt er die CyberSecurity firma DarkTrace.<a href="https://en.wikipedia.org/wiki/Mike_Lynch_%28businessman%29" rel="nofollow noopener" translate="no" target="_blank">https://en.wikipedia.org/wiki/Mike_Lynch_%28businessman%29</a><a href="https://chaos.social/@HonkHase" class="u-url mention" rel="nofollow noopener" target="_blank">@HonkHase</a> <a href="https://troet.cafe/@geist" class="u-url mention" rel="nofollow noopener" target="_blank">@geist</a> <a href="https://infosec.space/@kkarhan" class="u-url mention" rel="nofollow noopener" target="_blank">@kkarhan</a> <a href="https://no-pony.farm/tags/datenschutz" class="mention hashtag" rel="nofollow noopener" target="_blank">#datenschutz</a> <a href="https://no-pony.farm/tags/MikeLynch" class="mention hashtag" rel="nofollow noopener" target="_blank">#MikeLynch</a> <a href="https://no-pony.farm/tags/IT" class="mention hashtag" rel="nofollow noopener" target="_blank">#IT</a> <a href="https://no-pony.farm/tags/Bayesian" class="mention hashtag" rel="nofollow noopener" target="_blank">#Bayesian</a> <a href="https://no-pony.farm/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a> <a href="https://no-pony.farm/tags/cybersecurity" class="mention hashtag" rel="nofollow noopener" target="_blank">#cybersecurity</a>

earthlingEverything Is Predictable: How Bayesian Statistics Explain Our World by Tom Chivers, 2024A captivating and user-friendly tour of Bayes's theorem and its global impact on modern life from the acclaimed science writer and author of The Rationalist's Guide to the Galaxy.<a href="https://a.gup.pe/u/bookstodon" class="u-url mention" rel="nofollow noopener" target="_blank">@bookstodon</a> <a href="https://mastodon.social/tags/books" class="mention hashtag" rel="nofollow noopener" target="_blank">#books</a> <a href="https://mastodon.social/tags/nonfiction" class="mention hashtag" rel="nofollow noopener" target="_blank">#nonfiction</a> <a href="https://mastodon.social/tags/probability" class="mention hashtag" rel="nofollow noopener" target="_blank">#probability</a> <a href="https://mastodon.social/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a> <a href="https://mastodon.social/tags/BayesTheorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesTheorem</a>

Martin ModrákNew on the blog: showcasing the immense hackability of <a href="https://fediscience.org/tags/brms" class="mention hashtag" rel="nofollow noopener" target="_blank">#brms</a> by extending a random intercept model with linear predictors on the standard deviation of the random intercept. Should you do it? Most likely not, but if you really really want, there is a way. Also the techniques shown are general and let you do a lot of other crazy stuff with brms. Happy for any feedback! <a href="https://www.martinmodrak.cz/2024/02/17/brms-hacking-linear-predictors-for-random-effect-standard-deviations/" rel="nofollow noopener" translate="no" target="_blank">https://www.martinmodrak.cz/2024/02/17/brms-hacking-linear-predictors-for-random-effect-standard-deviations/</a><a href="https://fediscience.org/tags/bayesian" class="mention hashtag" rel="nofollow noopener" target="_blank">#bayesian</a> <a href="https://fediscience.org/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a> <a href="https://fediscience.org/tags/BayesianInference" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianInference</a> <a href="https://fediscience.org/tags/MixedModels" class="mention hashtag" rel="nofollow noopener" target="_blank">#MixedModels</a>

Jón GrétarBeen looking forward to this <a href="https://fosstodon.org/tags/ElixirConf" class="mention hashtag" rel="nofollow noopener" target="_blank">#ElixirConf</a> talk(“<a href="https://fosstodon.org/tags/ExStan" class="mention hashtag" rel="nofollow noopener" target="_blank">#ExStan</a>: Elixir 🤝 Stan for Probabilistic Modeling”) by young master Shubham Gupta. Mostly because I want this package to be released to Hex so I can play with <a href="https://fosstodon.org/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a> in <a href="https://fosstodon.org/tags/ElixirLang" class="mention hashtag" rel="nofollow noopener" target="_blank">#ElixirLang</a>. Also it is a big stepping stone to porting the Prophet time-series prediction library to Elixir by someone. Hopefully someone smarter than me though. <a href="https://www.elixirconf.eu/talks/exstan-elixir-stan-for-probabilistic-modeling/" rel="nofollow noopener" translate="no" target="_blank">https://www.elixirconf.eu/talks/exstan-elixir-stan-for-probabilistic-modeling/</a>

doctorambientI will take Bayesians' criticisms of frequentist approaches more seriously when I finally hear a Bayesian statistician actually present a reasonable approximation to a frequentist analysis, rather than engaging in low parody.Note that this is a criticism of people, not of any particular statistical method or theory. Also, every statistician I work with uses multiple frameworks for their analyses so 乁⁠(⁠ ⁠•⁠_⁠•⁠ ⁠)⁠ㄏ.<a href="https://mastodon.social/tags/statistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#statistics</a> <a href="https://mastodon.social/tags/stats" class="mention hashtag" rel="nofollow noopener" target="_blank">#stats</a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mastodon.social/tags/computationalscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#computationalscience</a> <a href="https://mastodon.social/tags/bayesian" class="mention hashtag" rel="nofollow noopener" target="_blank">#bayesian</a> <a href="https://mastodon.social/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a>

Jim DownieReposting my <a href="https://mstdn.science/tags/introduction" class="mention hashtag" rel="nofollow noopener" target="_blank">#introduction</a> so I can pin it - I'm a postdoctoral researcher doing <a href="https://mstdn.science/tags/MicrobialEcology" class="mention hashtag" rel="nofollow noopener" target="_blank">#MicrobialEcology</a> at Bangor University.I'm interested in the interactions between <a href="https://mstdn.science/tags/plants" class="mention hashtag" rel="nofollow noopener" target="_blank">#plants</a> and their associated <a href="https://mstdn.science/tags/microorganisms" class="mention hashtag" rel="nofollow noopener" target="_blank">#microorganisms</a>, particularly how they affect health outcomes in host plants, and how microbial communities differ on hosts across landscapes. I'm also interested in the question of how to accurately quantify and model microbial communities.Keen on <a href="https://mstdn.science/tags/rstats" class="mention hashtag" rel="nofollow noopener" target="_blank">#rstats</a>, <a href="https://mstdn.science/tags/OpenScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#OpenScience</a>, <a href="https://mstdn.science/tags/BayesianStatistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#BayesianStatistics</a>, <a href="https://mstdn.science/tags/Stan" class="mention hashtag" rel="nofollow noopener" target="_blank">#Stan</a>

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