Using Hazard and Surrogate Functions for Understanding Memory and Forgetting

• Published in: AppliedMath 2022-12, Vol.2 (4), p.518-546
• Main Author: Chechile, Richard A.
• Format: Article
• Language: English
• Subjects: hazard functions; mathematical psychology; mathematics of human forgetting; memory hazard functions; memory modeling; modeling forgetting
• ISSN: 2673-9909; 2673-9909
• DOI: 10.3390/appliedmath2040031

The retention of human memory is a process that can be understood from a hazard-function perspective. Hazard is the conditional probability of a state change at time t given that the state change did not yet occur. After reviewing the underlying mathematical results of hazard functions in general, there is an analysis of the hazard properties associated with nine theories of memory that emerged from psychological science. Five theories predict strictly monotonically decreasing hazard whereas the other four theories predict a peaked-shaped hazard function that rises initially to a peak and then decreases for longer time periods. Thus, the behavior of hazard shortly after the initial encoding is the critical difference among the theories. Several theorems provide a basis to explore hazard for the initial time period after encoding in terms of a more practical surrogate function that is linked to the behavior of the hazard function. Evidence for a peak-shaped hazard function is provided and a case is made for one particular psychological theory of memory that posits that memory encoding produces two redundant representations that have different hazard properties. One memory representation has increasing hazard while the other representation has decreasing hazard.