Frequentist to Bayesian Translation

Objective

Translate familiar classical regression instincts into the DSAMbayes workflow so users coming from OLS, GLM, or general frequentist econometrics can adopt Bayesian MMM without losing methodological discipline.

What does not change

Moving to DSAMbayes does not remove the need for:

  • careful data definition
  • sensible controls
  • thinking about omitted variables
  • residual scrutiny
  • skepticism about causal claims

Bayesian MMM is not a shortcut around model design. It is a different way of expressing assumptions and uncertainty.

What changes

1. From one best coefficient to a posterior distribution

In OLS, the default object of interest is a point estimate plus a standard error. In DSAMbayes, the default object is a posterior distribution. That means:

  • coefficients are uncertain objects, not fixed truths
  • decomposition and optimisation should inherit that uncertainty
  • wide intervals are information, not a nuisance to hide

2. From “no prior” to “explicit prior assumptions”

Frequentist workflows often treat themselves as prior-free. In practice, they still encode structure through model choice, variable transformations, and constraints.

DSAMbayes makes that structure explicit:

  • default priors express mild regularisation
  • boundaries express structural sign assumptions
  • overrides should be sparse and justified

3. From significance-thinking to decision-thinking

The key question becomes less “is beta significantly different from zero?” and more:

  • is the posterior sufficiently stable?
  • is the model adequate?
  • is the interval narrow enough for the business decision?
  • what risks remain if we act on this estimate?

Quick translation table

Frequentist instinct DSAMbayes replacement
“Run the regression and inspect coefficients” Specify the model, priors, and boundaries, then inspect the full posterior
“Use p-values to screen variables” Use posterior intervals, sign stability, and workflow diagnostics
“Choose the model with the best fit statistic” Choose among models that first pass diagnostics and then compare predictive evidence
“If the model converged, the answer is credible” Convergence is only the computation gate; adequacy and interpretation are separate gates
“No prior means unbiased starting point” Defaults are still assumptions; make them explicit and inspect whether they are defensible
“A high R-squared validates the model” Fit can be good while causal interpretation remains weak

The priors question in frequentist language

The question “where do priors come from?” is often really one of these:

  1. What assumptions am I already making implicitly?
  2. Which assumptions deserve to be encoded explicitly?
  3. Where do I have stable directional knowledge versus weak intuition?

For DSAMbayes, the practical default is:

  • start with package defaults
  • add boundaries only for structural signs you would defend in writing
  • add sparse prior overrides only for high-conviction terms
  • do not use priors to force a preferred answer out of weak data

See Stage 2: Model and Priors.

The diagnostics question in frequentist language

The question “which diagnostics matter?” is best answered in order:

  1. Are the posterior draws numerically trustworthy?
  2. Does the model fit the data adequately?
  3. Are the business conclusions robust to what remains uncertain?

This translates into:

  • Stage 4: Rhat, ESS, divergences, treedepth, BFMI
  • Stage 5: fit plots, residual behavior, PPC, LOO/Pareto-k

See Stage 4: Computation and Sampler and Stage 5: Model Adequacy.

Common transition mistakes

Mistake 1: treating defaults as magic

Default priors are a sensible starting point, not proof that prior design is solved forever.

Mistake 2: using priors as a repair tool for poor design

If media terms are badly collinear with baseline structure or controls are missing, stronger priors may stabilise numerics without fixing the underlying modelling problem.

Mistake 3: treating warning-level diagnostics as a cosmetic issue

A warned run may still be usable, but only if the warning is understood and disclosed. The right response is not “the model ran, so ship it.”

Mistake 4: confusing predictive success with causal proof

A model can rank well by ELPD and still be causally fragile.

Practical recommendation

If you are used to classical MMM, use DSAMbayes in this order:

  1. run Quickstart to learn the tool surface
  2. read What Principled Means
  3. use Stage 2: Model and Priors before customising priors
  4. use Stage 4: Computation and Sampler and Stage 5: Model Adequacy before interpreting any decision-layer output