Climate-smart agriculture in Zambia
Bayesian Double Machine Learning
The same logic, returning a distribution instead of a single number.
This runs the same logic as double machine learning and returns a distribution instead of a single number.
A confidence interval answers a narrow technical question about what would happen if you repeated the study many times. A distribution lets you ask how likely it is that the effect is positive at all, and how wide a range you should be willing to defend. That is much closer to how anybody actually makes a decision.
Running the two versions side by side is a check in its own right. Two estimators resting on different philosophies of inference, arriving at the same magnitude, are harder to dismiss than either one alone.
What it cannot do
A distribution is a function of what you assumed before you looked. If the starting assumption is doing the work, a confident-looking result is telling you about your own beliefs rather than about farmers, and the way to find out is to re-run it across a range of starting assumptions and see whether the conclusion moves.
The equation
p(θ | data) ∝ p(data | θ) × p(θ), with θ ~ Normal(0, 1)
- p(θ)
- what you were willing to believe before looking
- p(data | θ)
- how well each candidate effect explains what was observed
- p(θ | data)
- the posterior: the full range of effects still standing afterwards, with their weights
The frequentist version hands back one number and an interval. This hands back the whole distribution, which is what lets you say how much of it sits above zero rather than only whether a threshold was cleared.
Further reading
- Chernozhukov, V. and others (2018). "Double/Debiased Machine Learning for Treatment and Structural Parameters", The Econometrics Journal. free Read it.For the orthogonalisation, which the Bayesian version keeps unchanged.
- McElreath, R. Statistical Rethinking.The clearest explanation of what a posterior actually is, for anyone who has never met one.
From the Zambia climate-smart agriculture research, built on the Water and Soil Accelerator household survey, which was funded by USAID. The thesis is under examination and the three papers drawn from it are under anonymous peer review, so there is nothing to link to yet.