Statistics & Probability
Statistics is the core of the site: how to reason from incomplete data without turning assumptions into decoration. This hub collects articles on inference, modelling, diagnostics, uncertainty and probability.
Start here
- Conformal Prediction for Operational Risk Decisions
- Understanding Statistical Significance in Data Analysis
- Why the Mann-Whitney Test Is Not Simply a Test of Medians
- Missing Data Mechanisms in Machine Learning
Foundations
Probability, distributions, estimation, hypothesis testing and common errors.
Conformal Prediction for Operational Risk Decisions
Conformal prediction helps teams express model uncertainty as calibrated intervals or prediction sets that can be used in operational risk decisions.
Multilevel Models for Operational Analytics
Multilevel models help analysts estimate group-level performance without overreacting to small samples or ignoring real differences between sites.
Decision Curve Analysis: Measuring Whether Predictive Models Are Worth Acting On
Decision curve analysis evaluates predictive models by asking whether acting on their predictions produces better decisions than simple alternatives.
Prevalence Shift and Base-Rate Drift in Machine Learning
Prevalence shift occurs when the base rate of the outcome changes, breaking thresholds, workloads, and probability interpretation even when the model ranking still looks good.
Label Noise in Supervised Learning: When the Target Cannot Be Trusted
Label noise is one of the most damaging data quality problems in supervised learning because it corrupts the target the model is trained to imitate.
Competing Risks in Healthcare and Predictive Maintenance
Competing risks occur when more than one event can happen, and one event changes or prevents the chance of observing another.
Paired vs. Independent Samples: The Design Choice Behind the Test
The choice between paired and independent tests is not a software option. It is a statement about the study design and the dependence structure in the data.
Preregistering Structural Equation Modeling (SEM) Studies: A Comprehensive Guide
Learn how to preregister your SEM study by systematically locking down modeling and analytic decisions to improve scientific transparency and reduce bias.
Modelling and diagnostics
Regression, GLMs, Bayesian models, robust methods, survival analysis and model checking.
State Space Models and the Kalman Filter
The Kalman filter is usually introduced as a tracking algorithm for spacecraft. It is more useful understood as the general engine for estimating hidden state from noisy observation.
Hierarchical Forecasting: Making Forecasts Add Up
Forecast every store separately and the total will not match the forecast you made for the company. Reconciliation is how you make a hierarchy of forecasts coherent.
Hyperparameter Tuning Strategies
Hyperparameter tuning can drastically improve model performance. Explore common search strategies and tools.
Understanding Statistical Models: Foundations, Functions, and Applications
Statistical models lie at the heart of modern data science and quantitative research, enabling analysts to infer, predict, and simulate outcomes from structured data.
The Impossible Dream: Why Regression Confidence Bands Can’t Exist Without Assumptions
Why the intuitive idea of regression confidence bands breaks down under mathematical scrutiny.
Chauvenet’s Criterion: A Statistical Approach to Detecting Outliers
Chauvenet’s Criterion is a statistical method used to determine whether a data point is an outlier. This article explains how the criterion works, its assumptions, and its application in real-world data analysis.
Exploring Kernel Density Estimation: A Powerful Tool for Data Analysis
Kernel Density Estimation (KDE) is a non-parametric technique offering flexibility in modeling complex data distributions, aiding in visualization, density estimation, and model selection.
Dixon’s Q Test: A Guide for Detecting Outliers
Dixon’s Q test is a statistical method used to detect and reject outliers in small datasets, assuming normal distribution. This article explains its mechanics, assumptions, and application.
Uncertainty and decision-making
Calibration, confidence intervals, prediction intervals, Bayesian decision theory and operational risk.
Probability Calibration in Machine Learning: From Classical Methods to Modern Approaches and Venn–ABERS Predictors
Explore the evolution of probability calibration methods in machine learning, from histogram binning to Venn–ABERS predictors, with a deep dive into theory, implementation, and applications.
Understanding Statistical Models: Foundations, Functions, and Applications
Statistical models lie at the heart of modern data science and quantitative research, enabling analysts to infer, predict, and simulate outcomes from structured data.
Statistical AI: Probabilistic Foundations of Artificial Intelligence
Statistical AI leverages probabilistic reasoning and data-driven inference to build adaptive and intelligent systems.
Outliers: A Detailed Explanation
Outliers, or extreme observations in datasets, can have a significant impact on statistical analysis. Learn how to detect, analyze, and manage outliers effectively to ensure robust data analysis.
The Rich Get Richer: The Physics of Wealth Distribution and Inequality
The rich are getting richer while the poor remain poor. This article dives into the physics-based models that explain the inherent inequality in wealth distribution.
A Critical Examination of Bayesian Posteriors as Test Statistics
This article critically examines the use of Bayesian posterior distributions as test statistics, highlighting the challenges and implications.
Understanding Coverage Probability in Statistical Estimation
Learn about coverage probability, a crucial concept in statistical estimation and prediction. Understand how confidence intervals are constructed and evaluated through nominal and actual coverage probability.
Entropy in Data Science and Machine Learning: A Deep Dive
Explore the deep connection between entropy, data science, and machine learning. Understand how entropy drives decision trees, uncertainty measures, feature selection, and information theory in modern AI.