Specialty › Bayesian

Informative hypotheses

Informative-hypothesis Bayes factors test competing order and equality constraints on group means — 'A < B < C' against 'A = B = C' — reporting fractional Bayes factors and posterior hypothesis probabilities.

What is Informative hypotheses?

Classical ANOVA answers 'are the means equal?'; researchers usually believe something more specific — a direction or an ordering. Informative-hypothesis testing evaluates those theories directly: each constraint set gets a Bayes factor against the unconstrained model (adjusted fractional BF, O'Hagan/Mulder), and the competing hypotheses plus an automatic complement are ranked by posterior probability.

Coefficients are the group means (dummy coding without intercept), named by group level so hypotheses read naturally. The exploratory table additionally tests each mean for = 0 / < 0 / > 0.

When should I use Informative hypotheses?

  • Theories that predict an ordering (dose ordering, severity gradient) rather than mere inequality.
  • Comparing several competing structural predictions in one analysis.

What data does it need?

Response (numeric) + group column + optional numeric covariates + semicolon-separated hypotheses on level names (empty = exploratory only).

What does it report?

Per-hypothesis BF vs unconstrained + posterior probabilities (best in bold), exploratory =0/<0/>0 table per coefficient.

What does it assume?

  • Normal homoscedastic residuals (lm).
  • Posterior probabilities assume equal prior weights over the stated hypotheses + complement.
  • Level names are R-normalized — spaces become dots.

How do I interpret the result?

PHP 0.95 for 'A < B < C' means: among your stated theories (plus 'anything else'), the ordering has 95% posterior support. It is relative evidence — a poorly specified competitor set inflates it.

See also

References

  • Mulder et al. (2021). Flexible Bayes factor testing of scientific theories. JSS 100.
  • Hoijtink (2012). Informative Hypotheses: Theory and Practice.