Serial dependence in a superposition of renewal processes

Abstract

Superposition of point processes has often been suggested [I. Gath, Math. Biosci. 22, 211–222 (1974); C. E. Molnar and R. R. Pfeiffer, Proc. IEEE 56, 993–1004 (1968)] as a model for neural discharge patterns due to its intuitive appeal (input spike trains are simply merged and then retransmitted), and the tendency for successive interspike intervals in the superposition to be negatively correlated. Discharge patterns in the lateral superior olive (LSO) of the cat often display such negative serial dependence. The properties of the superposition of two identical renewal processes are examined in relation to the properties of its components. Components with increasing intensity functions are proven to yield a superposition process having negative serial dependence. However, the imposition of a dead time on a superposition process is shown to remove much of the serial dependence. For this reason, it is suggested that superposition of renewal processes is not a good model for discharge patterns having both a dead time and significant serial dependence, such as LSO discharge patterns.