Bayesian methods
Methods and validation
Why a Favorite Still Loses Most of the Time: A Bracket Forecast Under UncertaintyA single-elimination bracket does not ask a team to be good once. It asks a team to be good repeatedly, against opponents decided by other matches it does not control.
Methods and validation
Bayesian Modeling for Marketing Attribution: Interpreting UncertaintyMissing tracking data can make channel attribution harder to trust.
Methods and validation
Bayesian Spatial Modeling for Evaluating Hockey Goaltending PerformanceA goalie's save percentage answers a narrow question: what share of shots did they stop?
Methods and validation
When a Fixed Forecasting Rule Should Become a DistributionA fixed shrinkage rule can be a useful forecasting baseline. A hierarchical alternative estimates pooling parameters and represents uncertainty, but it still needs to outperform…
Comparisons
AI-Generated Models That Run vs. Models You Can TrustAn AI-generated model deserves a closer look only after it clears a viability gate checking convergence and usable posteriors, and then scores well on a documented quality rubric…
Methods and validation
Simulating Data with PyMCThis walkthrough draws on Ricardo Vieira and Tomás Capretto’s PyMC Labs simulation tutorial.
Methods and validation
Prediction and Intervention Answer Different Business QuestionsA pricing team may forecast next month’s sales accurately and still lack an estimate of what changing the price would do.
Methods and validation
Why a Bayesian Marketing Mix Model Still Needs Calibration Before You Reallocate BudgetA Bayesian Marketing Mix Model (MMM) can tell you which channel looks most effective.
Methods and validation
Bayesian A/B Testing at Scale: Why Millions of Observations Slow MCMC DownA head of experimentation with a large A/B dataset needs posterior estimates that finish in time to inform the decision.
Methods and validation
Why a 20% Retention Rate Means Different Things for a 10-User Cohort and a Million-User CohortA marketing analytics lead sees 20 percent retention. Two active users out of ten and 200,000 out of a million have the same observed ratio, but different sampling uncertainty…
Methods and validation
Likelihood Approximations Through Neural Networks: A Validation Checklist Before You Trust the OutputA behavioral model that reports a choice probability or a causal effect is only as trustworthy as the likelihood behind it.
Industries
Why a Single Forecast Number Hides the Risk You're Actually TakingA point forecast leaves out the uncertainty and assumptions that determine a decision's downside.
Methods and validation
Marketing Mix Modeling: A Complete GuideMarketing mix modeling relates historical outcomes to transformed media inputs and other drivers. Adstock represents carryover; saturation represents diminishing returns.
Methods and validation
Bayesian Marketing Measurement When Individual Tracking WeakensWhen individual-level attribution loses coverage, marketing teams should not treat the remaining tracked journeys as the whole market.
Methods and validation
Predicting Swinging Strikes with Bayesian Additive Regression TreesBayesian additive regression trees predict swinging strikes by summing many shallow trees fit through MCMC sampling over pitch-tracking features like velocity and spin rate…
Methods and validation
Bayesian Media Mix Modeling for Marketing OptimizationA marketing analytics team allocating budget across TV, paid social, and direct mail usually starts from last-touch attribution or a spend-to-revenue heuristic.
Methods and validation
How Partial Pooling Supports Decisions from Sparse Survey DataA sparse survey can support a segment decision when the model shares information across related groups and the result carries its uncertainty.
Methods and validation
From Uncertainty to Insight: What Bayesian Reasoning Means for a Business DecisionA marketing or analytics leader deciding how much stock to buy, how to price a product, or when to worry about churn usually has a forecast in hand.
Methods and validation
Is Your Marketing Model's Answer Data-Driven, or Just Your Priors Talking Back?A statistical model hands a marketing team a channel-attribution number, and the team has to decide: act on it now, or check it first.
Methods and validation
Quantify the Uncertainty Before You Pick a Risk PolicyA planner committing capacity against a point forecast needs an explicit policy for forecast errors. A single expected value does not describe shortage probability or severity.
Methods and validation
Why Causal Effects Come With a Spread, Not a Single NumberA vendor hands you a causal effect with a confidence interval attached.
Methods and validation
When Partial Pooling Helps a Thin Segment EstimateA segment-level causal estimate can look strong for a reason that has nothing to do with the segment.
Methods and validation
Why a Confounder Can Make a Marketing Channel Look Effective When It Isn'tA marketing team sees sales rise whenever Google Ads run. Coordinated TV spending may explain that pattern.
Methods and validation
Why Per-Test Bayesian Model Loops Stop ScalingMany modest Bayesian A/B, ABC and ABCD datasets can spend substantial time in repeated compilation, warmup and adaptation.
Methods and validation
When a Fixed CAC Assumption Misleads a Budget ReallocationThe decision this affects
Methods and validation
When a Forecasted-Control MMM Can (and Can't) Answer a Budget QuestionA forecasted-control MMM combines a fitted sales model with predictions of future external conditions.
Methods and validation
What Should Transfer to a New Context? A PyMC Walkthrough for Evaluating Causal Simulation PredictionsA causal simulation predicts a segment, product, or time period it never observed directly.
Methods and validation
A Regime-Aware Risk Model: What to Validate Before You Trust the ProbabilityA single distribution can obscure changing return behavior. A regime-aware model is one possible representation, with probabilities conditional on its assumed states and…
Methods and validation
Hierarchical Bayesian Models for Customer Lifetime Value Across CohortsA marketing analytics team comparing customer cohorts must decide whether to fit separate transaction models, one global model or a hierarchy that partially shares information.
Methods and validation
Hierarchical Bayesian Latent-Trait Estimation, ExplainedA number published without its limits reads as marketing. Trusting a model's output for a pricing or positioning decision means trusting how it handles uncertainty.
Methods and validation
A Faster MMM Pipeline Doesn't Answer Whether the Numbers Are CausalA marketing mix modeling (MMM) team needs aligned spend and outcome data before it can fit a model.
Methods and validation
Funnel-Aware MMM: A Bayesian Architecture for Full-Funnel Marketing OptimizationAn additive, funnel-blind marketing mix model (MMM) can omit a path that matters for budget decisions: upper-funnel activity creates demand that lower-funnel channels later…
Methods and validation
Counterfactual Causal Inference in PyMCPrediction forecasts the outcome under current conditions. Causal inference instead estimates the outcome that a different action would have produced.
Methods and validation
Estimating a Private-Market Benchmark When There Is No Public PriceA public equity index is built from transaction prices that happen constantly: every trade updates the number.
Methods and validation
Gaussian Process Geospatial Modeling: Beyond Hierarchical ModelsA geospatial model should use a justified relationship between locations.
Industries
Bayesian Computation in Finance: Modeling Risk as a Distribution, Not a GuessA financial-model buyer needs more than a point estimate of beta, loss, or option value: ask which uncertainty is quantified and which assumptions remain outside the calculation.
Industries
Where Should the Next Wegmans Open? 7 Checks for a Bayesian Site-Selection ForecastA new-store forecast should separate observed evidence from assumptions before a retail real estate team commits build-out and lease capital or accepts the risk that a new…
Industries
8 Questions to Ask Before You Trust a Segment EstimateA quant researcher who owns a firm-characteristic return model has to choose every time a new segment shows up in the data: report one pooled coefficient for every sector, split…
Implementation
When Metrics Predict One Another: A Buyer's Guide to Vector AutoregressionAn analytics leader forecasting several business metrics should ask whether their histories improve prediction of one another.
Implementation
PyMC in the Browser: Why Deployment Architecture Isn't a Causal Validity SignalThomas Wiecki's PyMC Labs demonstration, dated May 16, 2022, describes Bayesian modeling in a browser using PyScript and Pyodide.
Comparisons
Hire a Bayesian Expert or Buy On-Demand Access? A Buyer's Decision FrameworkA head of analytics who needs Bayesian or causal-modeling depth for marketing mix modeling, customer lifetime value, or causal inference is choosing between two paths: put a…
Comparisons
GPU Sampling vs. CPU Sampling for Bayesian MCMC: When Is the Switch Worth It?A data science team running MCMC-based causal inference in PyMC or Stan eventually hits the same question: move sampling to GPU, or stay on CPU? Getting it wrong either way costs.