  In this work we introduce an approach for modeling and analyzing collective
behavior of a group of agents using moments. We represent the group of agents
via their distribution and derive a method to estimate the dynamics of the
moments. We use this to predict the evolution of the distribution of agents by
first computing the moment trajectories and then use this to reconstruct the
distribution of the agents. In the latter an inverse problem is solved in order
to reconstruct a nominal distribution and to recover the macro-scale properties
of the group of agents. The proposed method is applicable for several types of
multi-agent systems, e.g., leader-follower systems. We derive error bounds for
the moment trajectories and describe how to take these error bounds into
account for computing the moment dynamics. The convergence of the moment
dynamics is also analyzed for cases with monomial moments. To illustrate the
theory, two numerical examples are given. In the first we consider a
multi-agent system with interactions and compare the proposed methods for
several types of moments. In the second example we apply the framework to a
leader-follower problem for modeling pedestrian crowd dynamics.
