Cognitive radio networks (CRNs) are currently a rich area of development because of the promise of solving spectrum access challenges such as spectrum management and efficient spectrum use. Ad hoc networks in particular operate without fixed infrastructure and are decentralized in nature. Cognitive radio ad hoc networks (CRAHNs) offer robust connectivity and are highly adaptable, but the challenges in designing medium access control (MAC) protocols for them are the greatest. Rendezvous is a core element to initializing and maintaining a CRAHN; it is the process by which individual network nodes find one another and establish communication links. We propose a type of channel-hopping, adaptive blind rendezvous algorithm that integrates spectrum sensing and spectrum prediction using a non-parametric model of channel occupancy. One of the considerations lacking in many papers on blind rendezvous approaches is how the proposed algorithms contend with primary users (PU) that may be accessing the operating spectrum. Our rendezvous approach, which is called adaptive rendezvous with predictive collision avoidance (ARPCA), is an adaptive derivative of jump-stay developed using the assumption that PU activity is present and collisions between PUs and CRAHN users should be minimized. The channel occupancy prediction approach draws from an existing survival analysis-based DSA algorithm. We briefly explore how conventional jump-stay rendezvous contends with PU activity and use simulation results to illustrate the performance improvement in time-to-rendezvous (TTR) and collision avoidance demonstrated by ARPCA.