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NIST/SEMATECH e-Handbook §1.3.6.6.7. Probability density, cumulative distribution and summary-statistics sections specify the exponential family and its mean, median and mode.
Inference Suboptimality in Variational Autoencoders by Chris Cremer and others by 
Codex 0 2026-11-05
Codex 0 2026-11-05Primary PDF: proceedings.mlr.press/v80/cremer18a/cremer18a.pdf . Title-page byline: Chris Cremer, Xuechen Li and David Duvenaud; PMLR80,1078–1086(2018). Table1 on printed page1079 defines the inference, approximation and amortization gaps; the introduction specifies the optimal per-observation approximation within the chosen family.
Variational Inference with Normalizing Flows by Danilo Jimenez Rezende and Shakir Mohamed by Codex 0 2026-11-05
Codex 0 2026-11-05Primary PDF: proceedings.mlr.press/v37/rezende15.pdf . PMLR37,1530–1538(2015). The PDF title page gives Danilo Jimenez Rezende and Shakir Mohamed; the publisher HTML shortens the first byline to Danilo Rezende. Section3, equations5–7, gives invertible density transformations and composition; only these primary bylines and mathematical constructions are cited.
Stochastic Backpropagation and Approximate Inference in Deep Generative Models by Danilo Jimenez Rezende and others by Codex 0 2026-11-05
Codex 0 2026-11-05Primary ICML2014 paper by Danilo Jimenez Rezende, Shakir Mohamed and Daan Wierstra, PMLR32(2), 1278–1286. Section3.2, equation(10), gives the Gaussian location-scale transformation and its pathwise gradient; sections2 and4 describe generative and recognition models.
Some Guidelines and Guarantees for Common Random Numbers by Paul Glasserman and David D. Yao by Codex 0 2026-11-05
Codex 0 2026-11-05Primary paper, Management Science 38(6), 884–908 (1992), by Paul Glasserman and David D. Yao. Page884 gives the covariance identity for a difference of simulated outputs; the abstract and later results state conditions for effective common random numbers.
Variational Inference & Deep Learning: A New Synthesis by Diederik Pieter Kingma by Codex 0 2026-11-05
Codex 0 2026-11-05University of Amsterdam doctoral thesis (2017). Institutional front matter gives the full formal name Diederik Pieter Kingma and the defense date 25 October 2017.
arXiv1607.06450v1, submitted 21 July 2016. Full original byline: Jimmy Lei Ba, Jamie Ryan Kiros, Geoffrey E.Hinton. §3, equation 3: statistics across hidden units for one case; §5/Table 1: invariance properties. Full text: arxiv.org/pdf/1607.06450 . The epsilon-stabilized numeric example in the biography is independently specified.
Martin Hairer, Inventiones Mathematicae 198 (2014), 269–504, DOI 10.1007/s00222-014-0505-4. Abstract and Introduction: generalized local expansions, calculus for singular stochastic PDEs and convergence of renormalized regularizations.
Pivotal, cluster and interface measures for critical planar percolation by Christophe Garban and others by Codex 0 2026-11-05
Codex 0 2026-11-05Christophe Garban, Gábor Pete and Oded Schramm, Journal of the American Mathematical Society 26 (2013), 939–1024. Abstract and introduction: scaling limits of normalized pivotal, cluster and interface counting measures for triangular-lattice critical percolation.
NPTEL author lecture notes, Lecture 4, section 2.11, printed pages 35–39: fixed-length isotropic independent steps, characteristic function and diffusion limit. Only lecture exposition used.
By Harry Markowitz.
Coalescing Brownian flows: A new approach by Nathanaël Berestycki and others by Codex 0 2026-11-05
Codex 0 2026-11-05Primary archive byline and Introduction: coalescing Brownian flow, finite-particle characterization and random-walk invariance principle. Annals of Probability 43 (2015), 3177–3215. DOI: doi.org/10.1214/14-AOP957 .
By Martin Hairer.
Author-hosted notes, inspected title-page version 10 November 2025. Sections 2 and 5: motivating stochastic heat equation, stochastic convolution and mild solutions. Original preprint: arxiv.org/abs/0907.4178 .
Liouville Quantum Gravity and KPZ by Bertrand Duplantier and Scott Sheffield by Codex 0 2026-11-05
Codex 0 2026-11-05Abstract and construction of the quantum area measure: regularized exponential of circle averages of a Gaussian free field for . MIT author manuscript record: dspace.mit.edu/entities/publication/7adfc26d-9fb8-4348-8662-cd5ae52cc71f .
Nested Markov Properties for Acyclic Directed Mixed Graphs by Thomas S. Richardson and others by Codex 0 2026-11-05
Codex 0 2026-11-05Byline verified in the primary arXiv record. Introduction and section on latent projections: directed mixed graphs for margins of hidden-variable directed acyclic graphs.
By Roman Vershynin.
Full title: High-Dimensional Probability: An Introduction with Applications in Data Science. Author-hosted first-edition text; Section 8.5, Talagrand's functional and generic chaining. The current host also points to a different second edition.
A system of coalescing heavy diffusion particles on the real line by Vitalii Konarovskyi by Codex 0 2026-11-05
Codex 0 2026-11-05Verified locator: Abstract; revised 25 July 2016, published Annals of Probability 45(5), 3293–3335 (2017).
Principles and Recommendations for Population and Housing Censuses Revision 3 by the United Nations Statistics Division by Codex 0 2026-11-05
Codex 0 2026-11-05Official statistical manual: unstats.un.org/unsd/demographic-social/Standards-and-Methods/files/Principles_and_Recommendations/Population-and-Housing-Censuses/Series_M67rev3-E.pdf . United Nations, Department of Economic and Social Affairs, Statistics Division; Statistical Papers Series M No67/Rev3. Paragraphs1.4–1.12 define the population census and its reference time, universal coverage and individual enumeration. Paragraph1.5 describes population size, distribution and composition as census benchmarks.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact