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.
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- 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.
Forecast Combination: Why Averaging Usually Wins
Choosing the best model is the obvious strategy. Averaging several is usually better, and the reason is not that the average is smarter but that it is less wrong in a specific way.
Regime-Switching Models for Time Series
A single model fitted across a recession and an expansion describes neither. Regime-switching models allow the dynamics themselves to change, with the regime inferred rather than assumed.
Nowcasting with Mixed-Frequency Data
The quantity you care about arrives quarterly and two months late. Related indicators arrive daily. Nowcasting is the problem of estimating the present from what has already been published.
Interrupted Time Series and Causal Impact
A intervention happened at a known date and you need its effect. There is no control group, only the series itself before and after, and the counterfactual has to be constructed.
Temporal Hierarchies: Reconciling Across Time Granularities
A hierarchy does not have to be geographic. Aggregating a series over time produces the same coherence problem, and the same machinery solves it.
Modelling Count Time Series
Daily incident counts are integers, non-negative, often small, and correlated with yesterday. ARIMA assumes none of that and Poisson regression assumes independence.
Uncertainty and decision-making
Calibration, confidence intervals, prediction intervals, Bayesian decision theory and operational risk.
Modelling Count Time Series
Daily incident counts are integers, non-negative, often small, and correlated with yesterday. ARIMA assumes none of that and Poisson regression assumes independence.
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.