Posted in 2026
Hidden Markov Models in PyMC: marginalize and recover a DiscreteMarkovChain
- 09 July 2026
A hidden Markov model (HMM) describes a system that moves through a sequence of hidden discrete states, where each state emits a noisy observation. We never see the states directly; we only see the emissions, and we want to reason backward to the states that most likely produced them.
Sensitivity Analysis for Unmeasured Confounding
- 09 May 2026
All applied inference is argument. Against every experiment you can set the contention that the working conditions were imperfect. Some aspect of the evaluation was flawed. Maybe treatment assignment introduced a subtle kind of bias, or the subjects didn’t comply fully with the design. Against every experiment you can contrast the scientific ideal of perfect randomisation and clear adherence. Holding an experiment against that ideal is due diligence. Sensitivity analysis does it systematically, by varying how far the working conditions fall short of perfect randomisation.
Multiple Experiments and Bayesian Meta-analysis
- 09 May 2026
Eight quarterly A/B tests of the same checkout-flow redesign, run across eight markets, return eight different point estimates. Two cross the conventional significance threshold; the other six do not. The product manager asks the natural question, “did it work?”, and gets two incompatible defaults depending on which colleague answers: vote-counting (“four out of eight worked, so it’s a wash”), or pool-everything (“the combined estimate is positive, so it works”). Both are mistakes. The vote-count discards the magnitude information in each estimate; the pool-everything pretends the markets are exchangeable in a way the evidence does not support. The honest answer requires a model that estimates between-market differences rather than assuming them away.
Assurance Planning via Simulation
- 09 May 2026
Experimental questions are seeded in the science that preceded them. Answers are stress-tested and refined. New experiments spawn further questions again. This is the cycle.
Heteroscedastic Bayesian Robust Regression
- 30 April 2026
The PyMC gallery has two robust regression notebooks: one with a Student-t likelihood (pymc-examples:GLM-robust) and one with the Hogg (2010) signal-vs-noise mixture (pymc-examples:GLM-robust-with-outlier-detection). Both protect against vertical outliers (points with unusual response values), but neither defends against leverage points: observations far from the bulk of the predictor space, which can drag the regression line even under a heavy-tailed likelihood.
Estimating species distributions with occupancy models
- 09 January 2026
Estimating where species live is one of the most common tasks in ecology. Recreational birders know that every field guide includes a range map showing where a species can be found, as well as habitat information to help locate the animals. For example, a field guide for Swiss birds might tell you that Red Crossbills (Loxia curvirostra) are most likely found in forests at intermediate elevations. Both of these tasks–mapping ranges and estimating habitat relationships–fall under the umbrella of species distribution modeling.