Wald Sequential Likelihood Ratio
Follow binary observations until the likelihood ratio first reaches an evidence boundary.
Free theory articleFollow binary observations until the likelihood ratio first reaches an evidence boundary.
Concept & interpretation
Consider comparing two simple Bernoulli hypotheses: H0 where p = 1/3 and H1 where p = 2/3. The likelihood ratio (LR) updates sequentially with each observation in a sequence. Let's trace the sequence "11" with an evidence exponent of 2 (meaning boundaries are 22 = 4 and 2-2 = 1/4).
Experiment
You can interact with the Wald Sequential Likelihood Ratio module to visualize this process:
- Set the Sequence to
00. - Observe that the LR halves at each step: it drops from 1 to 1/2, then to 1/4.
- With the default Evidence exponent set to
2, the sequence hits the lower boundary (1/4), and the Decision updates toSupport H0. - Now, change the Sequence to
1010. The LR alternates between 2 and 1, never reaching either boundary. The status remainsContinue.