Redistribution systems iteratively redistribute mass between groups under the control of rules. PRAM is a framework for building redistribution systems. We discuss the relationships between redistribution systems, agent-based systems, compartmental models and Bayesian models. PRAM puts agent-based models on a sound probabilistic footing by reformulating them as redistribution systems. This provides a basis for integrating agent-based and probabilistic models. \pram/ extends the themes of probabilistic relational models and lifted inference to incorporate dynamical models and simulation. We illustrate PRAM with an epidemiological example.

In agent-based models (ABMs, e.g., [4, 3]) agents probabilistically change state. State can be represented as attribute values such as health status, monthly income, age, political orientation, location and so on. A population of agents has a joint state that is typically a joint distribution; for example, a population has a joint distribution over income levels and political beliefs. ABMs are a popular method for exploring the dynamics of joint states, which can be hard to estimate when attribute values depend on each other, and populations are heterogeneous in the sense that not everyone has the same distribution of attribute values, and the principal mechanism for changing attribute values is interactions between agents. For example, suppose all agents have a flu status attribute that changes conditionally - given other attributes such as age, income, and vaccination status - when agents interact. The dynamics of flu - how it moves through heterogeneous populations - can be difficult or impossible to solve, but ABMs can simulate the interactions of agents, and the flu status of these agents can be tracked over time. ABMs are no doubt engines of probabilistic inference, but it is difficult to say anything about the models that underlie the inference. This paper presents pram - Probabilistic Relational Agentbased Models - a new kind of ABM with design influences from compartmental models (e.g., [1]) and probabilistic relational models (PRMs; e.g., [2]).