How does Bayesian reverse-engineering work?

How does Bayesian reverse-engineering work? Carlos Zednik (czednik@uos.de) and Frank Jakel (fjaekel@uos.de) Institute of Cognitive Science, University of Osnabruck 49069 Osnabruck, Germany articulate and test possible algorithms and implementations of that phenomenon. What role do Bayesian models play in reverse- engineering explanations? It is widely agreed that Bayesian models figure at the computational level of analysis. They help researchers understand what a cognitive system actually does, because they describe and predict its behavior. Moreover, these models allow researchers to understand why a system does what it does, because they show that the system’s behavior is an optimal solution to a particular statistical inference task. But how can Bayesian models at the computational level of analysis be used to identify algorithms and implementations at lower levels? In what follows, we review three different answers to this question. The first two answers—Bayesian Realism and Instrumentalist Bayesianism—are well-represented in the literature, but are ultimately unsatisfactory. Thus, we propose a third answer—Pragmatic Bayesianism— according to which Bayesian models are tools for hypothesis generation: they facilitate the development of novel algorithmic-level and implementation-level analyses. Abstract Bayesian models of cognition and behavior are particularly promising when they are used in reverse-engineering explanations: explanations that descend from the computational level of analysis to the algorithmic and implementation levels. Unfortunately, it remains unclear exactly how Bayesian models constrain and influence these lower levels of analysis. In this paper, we review and reject two widespread views of Bayesian reverse-engineering, and propose an alternative view according to which Bayesian models at the computational level impose pragmatic constraints that facilitate the generation of testable hypotheses at the algorithmic and implementation levels. Keywords: Bayesian modeling; rational analysis; reverse- engineering; Marr’s levels; mechanistic explanation Introduction Bayesian models describe cognitive and behavioral phenomena as a form of optimal statistical inference. Using the methodology of rational analysis (Anderson, 1990), researchers attempt to specify the statistical inference task to which a particular phenomenon is adapted. This task is defined formally, in terms of a cognitive system’s prior knowledge about its environment, recent evidence collected within that environment, hypotheses being compared, and the relative cost or benefit of particular actions. Once the task has been defined in this way, the mathematical framework of Bayesian decision theory can be used to derive an optimal solution to the task: how to ideally adjudicate between hypotheses using Bayes’ rule to combine prior knowledge with recent evidence, and how to select actions so as to minimize cost or maximize benefit. If the task has been specified correctly, such optimal solutions often provide descriptively adequate and predictively powerful models of the phenomenon being investigated. Many researchers regard the methodology of Bayesian modeling as a way to reverse-engineer the mind. In cognitive science, reverse-engineering is often associated with David Marr (1982), who proposed that cognitive systems ought to be studied at three distinct levels of analysis. At the computational level, researchers seek to understand what a system is doing and why. At the algorithmic level, they describe how the system does what it does. Finally, at the implementation level, they identify where in a particular physical system that algorithm is realized. Reverse-engineering explanations involve descending “a triumphant cascade” of these three levels (Dennett, 1987, p. 227). That is, they begin with a computational-level analysis of a particular cognitive or behavioral phenomenon, and invoke that analysis to Bayesian Realism According to Bayesian Realism, Bayesian models at the computational level of analysis contribute to reverse- engineering explanations because their mathematical structure is reflected in the functional and physical structure of the mechanisms described at the algorithmic and implementation levels. Insofar as a particular cognitive or behavioral phenomenon can be modeled as a (nearly-) optimal solution to a statistical inference task, Bayesian Realism implies that the mechanisms responsible for this phenomenon themselves perform Bayesian inference. That is, they execute algorithms that invoke (or closely approximate) Bayes’ rule to combine prior knowledge with new evidence, and are implemented by neural structures that represent prior and posterior probability distributions, as well as likelihood and loss functions. Two arguments speak in favor of Bayesian Realism. The first argument is inspired by the classic “no-miracles” argument for scientific realism in philosophy of science. The no-miracles argument seeks to explain the observation that many well-confirmed scientific theories are exceedingly accurate descriptive and predictive devices. Barring miracles, the best explanation seems to be that these theories are true: their theoretical posits successfully refer, and the structures they describe accurately reflect the structure of the world. In much the same way, Bayesian Realism is motivated by the desire to explain the descriptive and predictive successes of Bayesian models at the computational level of analysis. Barring miracles, the best