The article explores Joseph Mazur’s three kinds of logic—classical, infinite, and plausible reasoning—detailing their historical origins, formal representations, real‑world examples, and how confusing them can lead to faulty judgments.
This article treats life as an optimization problem and breaks it into three core forces—cognition, choice, and growth—showing how Bayesian inference, multi‑objective optimization, and dynamic system theory can model their interactions, guide decision‑making, and illustrate the feedback loops that drive personal development.
This article explores how understanding others' mental states—from basic intentions to recursive mindreading—can be modeled with Bayesian inference and applied to robots for predicting human behavior in scenarios like pedestrian crossing, shopping assistance, and multi‑agent games.
The article offers a thorough examination of Facebook’s Prophet forecasting model, detailing its additive decomposition of trend, seasonality, holidays and regressors, the underlying Bayesian inference via Stan, the full training‑and‑prediction pipeline, data‑normalization tricks, uncertainty estimation, and practical source‑code insights for e‑commerce applications.
This article explores the Beta distribution’s role in Bayesian statistics, detailing its definition, properties, conjugate prior relationship, and practical examples such as coin flips and bus arrivals, illustrating how it simplifies probability updates and supports intuitive belief revision.
This article explains Bayesian methods—its core theorem, historical and everyday applications, a detailed medical testing model, and provides a step‑by‑step Python calculation illustrating how prior probabilities and new evidence combine to produce posterior probabilities.
This article explains the principles of probabilistic programming languages and walks through a step‑by‑step implementation of a minimal PPL in Python, covering model definition, variable representation, DAG traversal, log‑density computation, and a posterior grid illustration.
This article explains the principles of probabilistic programming languages and walks through constructing a basic PPL in Python, covering model definition with latent and observed variables, distribution handling, DAG traversal for log‑density computation, and demonstrates evaluation with example code and visualizations.
Markov Chain Monte Carlo (MCMC) extends classic Monte Carlo by generating dependent samples via a Markov chain, enabling Bayesian inference through concepts like the plug‑in principle, burn‑in, asymptotic independence, and algorithms such as Metropolis‑Hastings and Gibbs sampling, while addressing convergence and effective sample size.
This review outlines modern Bayesian phylogenetic methods for reconstructing the origins, timing, and population dynamics of rapidly evolving RNA viruses such as HIV, HCV, and influenza, highlighting coalescent theory, relaxed molecular clocks, and the integration of epidemiological models with genetic data.
This article explains the principles behind Markov Chain Monte Carlo methods, including Monte Carlo sampling, the Metropolis‑Hastings algorithm, and the Hamiltonian Monte Carlo (HMC) approach, illustrating how they efficiently approximate posterior distributions in Bayesian analysis.
This article explains Bayesian statistics as a probabilistic framework, describes how modern numerical methods and probabilistic programming languages automate inference, and reviews both Markov and non‑Markov techniques such as MCMC, grid computation, Laplace approximation, and variational inference for building complex models.
This article introduces Bayesian inference through the classic coin‑toss example, explaining how to model bias with a beta prior and binomial likelihood, derive the posterior distribution, and understand convergence of different priors as data accumulates.
This article explains the concept of probability distributions, describes the Gaussian (normal) distribution with its parameters, demonstrates how to visualize it using Python code, and discusses random variables, independence, and real‑world examples such as atmospheric CO₂ time‑series data.
This article explains Bayesian linear regression, describing its probabilistic treatment of weights, prior and posterior computation, MAP and numerical solutions, and how it enables uncertainty quantification, online learning, and model comparison through Bayes factors.
The article explains how normal (Gaussian) distributions underpin many machine‑learning algorithms, reviewing the central limit theorem, multivariate Gaussian sampling, and key properties such as products, sums, conditional and marginal distributions, linear transformations, and Gaussian‑based Bayesian inference.
This article explains how probabilistic programming languages work and walks through building a minimal PPL in Python, covering model definition, latent and observed variables, DAG traversal, log‑density computation, and extensions such as posterior grid approximation.
This article describes how a Chinese securities firm applied big‑data‑driven clustering and Bayesian methods to automate root‑cause analysis of trading‑system anomalies, detailing the challenges, algorithmic designs, practical implementations, and evaluation results that demonstrate significant reductions in false alarms and faster recovery.
This article details the challenges of root‑cause identification in high‑availability securities trading platforms and presents two intelligent‑operations solutions—DBSCAN‑based clustering and Bayesian inference—to quickly locate anomalies and improve recovery efficiency.
The article reports on Ant Financial’s participation in ICML 2019, highlighting a finance‑focused AI workshop and summarizing three of its cutting‑edge research papers on adversarial reinforcement‑learning recommendation, distributional gradient temporal‑difference learning, and particle‑flow Bayesian inference.
This NSF‑funded project aims to develop algorithms that incrementally process partially observed data, integrating generative models with reinforcement‑learning policies to decide when to act, applied to simultaneous machine translation and quiz‑bowl style question answering.
