Stimulus Sampling Theory (SST), introduced by William K. Estes in 1950, was one of the earliest mathematically rigorous models of learning. It represents the stimulus situation as a population of elements, a random sample of which is active on any trial. Learning occurs as sampled elements become conditioned to (associated with) reinforced responses.
The Model
θ = probability that any one element is sampled on a trial
On each trial, sampled elements become conditioned to the reinforced response
P(correct, trial n+1) = P(correct, trial n) + θ·[1 − P(correct, trial n)]
This produces negatively accelerated learning curves approaching asymptote — the same general shape predicted by the Rescorla-Wagner model, but derived from a fundamentally different mechanism (random sampling rather than prediction error).
All-or-None vs. Incremental Learning
SST naturally accommodates both incremental learning (when many elements are sampled with small probability, producing gradual changes) and all-or-none learning (when one element dominates, producing sudden transitions). Estes' development of SST demonstrated that mathematical models could make precise, testable predictions about learning phenomena and laid the groundwork for the entire field of mathematical learning theory.