Decision making under uncertainty
Biological decisions are often made before the true future state is known. Decision theory combines possible outcomes, their probabilities and the consequences of actions.
If action \(a\) has loss \(L(a,\theta)\) under uncertain state \(\theta\), its expected loss is
\[E[L(a,\theta)]=\int L(a,\theta)p(\theta)\,d\theta.\]An expected-loss rule selects an action minimising this quantity, subject to the assumptions and values encoded in the loss function.
Asymmetric consequences
A false alarm and a missed outbreak may have very different costs. Decision rules should reflect this asymmetry rather than relying only on predictive accuracy.
Robust decisions
When probabilities are themselves uncertain, sensitivity and robust-decision analyses can show whether the preferred action changes across plausible assumptions.
Key idea. Uncertainty does not prevent decision making; it changes the problem from choosing the best predicted outcome to comparing consequences across possible outcomes.