Collaborative spectrum sensing exploits multiuser diversity by combining spectrum sensing information from multiple secondary users to make joint decisions about spectrum occupancy. In hard fusion schemes, each secondary user makes a hard decision on spectrum occupancy and a fusion center makes a final decision by combining the individual hard decisions according to a fusion rule. In soft fusion schemes, each secondary user provides a signal power measurement to the fusion center, which performs further processing on the collection of all observations to make a final decision. In this paper, we propose hard and soft fusion collaborative spectrum sensing schemes based on online hidden bivariate Markov chain modeling of the signals received by secondary users. Compared to prior collaborative sensing schemes, the proposed model-based schemes do not rely on precomputed thresholds or weights, and achieve superior performance. Online estimation of hidden bivariate Markov models provides predictive information that can be used to improve the performance of dynamic spectrum access. Numerical results are presented to demonstrate the performance and communication overhead tradeoffs of the proposed collaborative spectrum sensing schemes.