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We consider the problem of predicting the spin states in a kinetic Isingmodel when spin trajectories are observed for only a finite fraction of sites.In a Bayesian setting, where the probabilistic model of the spin dynamics isassumed to be known, the optimal prediction can be computed from theconditional (posterior) distribution of unobserved spins given the observedones. Using the replica method, we compute the error of the Bayes optimalpredictor for parallel discrete time dynamics in a fully connected spin systemwith non symmetric random couplings. The results, exact in the thermodynamiclimit, agree very well with simulations of finite spin systems.

Inferring hidden states in a random kinetic Ising model: replica analysis