Philip L. Smith, working at the University of Melbourne, has made fundamental contributions to the mathematical modeling of visual attention, psychophysical discrimination, and speeded decision making. His work is distinguished by its integration of signal detection theory, visual attention models, and diffusion models of response time into unified quantitative frameworks that span from sensory encoding to motor response.
The Integrated Diffusion Model
x = evidence state
A(t) = time-varying attention gain
mu = stimulus-driven drift
s = noise coefficient
Decision at boundaries +/- a
Smith's integrated approach connects the sensory front end (how stimuli are encoded and filtered by attention) to the decision back end (how noisy evidence is accumulated to a criterion). Unlike standard diffusion models that treat drift rate as a fixed input, Smith's models derive drift rate from explicit models of sensory processing, allowing the same framework to explain both psychophysical discrimination and response time distributions. This integration shows how changes in attention, stimulus quality, and masking affect not just accuracy but the entire shape of the RT distribution.
Smith and colleagues have developed detailed models of how spatial attention filters visual input before evidence accumulation begins. Their work shows that attention modulates the quality of sensory evidence (the signal-to-noise ratio driving the diffusion process) rather than simply biasing the starting point or threshold. This provides a principled account of how attention affects both speed and accuracy of perceptual decisions.
Psychophysical Models
Smith has contributed to understanding the relationship between classical psychophysics and modern decision models. His work shows how Weber's law, the psychometric function, and signal detection measures emerge naturally from the properties of the evidence accumulation process, unifying traditionally separate areas of quantitative psychology within a common mathematical framework.
Legacy and Impact
Smith's work demonstrates that the most productive mathematical models are those that integrate across levels of analysis -- from sensory encoding through attention to decision and response. His approach has influenced how researchers think about the relationship between signal detection theory and sequential sampling models, and his models have been applied to understanding attentional deficits in clinical populations, the effects of aging on perceptual decisions, and the neural basis of evidence accumulation.