## Bayesian models applied to perceptual behavior

### Friday, May 9, 2008, 3:30 – 5:30 pm Royal Palm 4

**Organizer:** Peter Battaglia (University of Minnesota)

**Presenters:** Alan Yuille (University of California Los Angeles), David Knill (University of Rochester), Paul Schrater (University of Minnesota), Tom Griffiths (University of California, Berkeley), Konrad Koerding (Northwestern University), Peter Battaglia (University of Minnesota)

### Symposium Description

This symposium will provide information and methodological tools for researchers who are interested in modeling perception as probabilistic inference, but are unfamiliar with the practice of such techniques. In the last 20 years, scientists characterizing perception as Bayesian inference have produced a number of robust models that explain observed perceptual behaviors and predict new, unobserved behaviors. Such successes are due to the formal, universal language of Bayesian models and the powerful hypothesis-evaluation tools they allow. Yet many researchers who attempt to build and test Bayesian models feel overwhelmed by the potentially steep learning curve and abandon their attempts after stumbling over unintuitive obstacles. It is important that those scientists who recognize the explanatory power of Bayesian methods and wish to implement the framework in their own research have the tools, and know-how to use them, at their disposal. This symposium will provide a gentle introduction to the most important elements of Bayesian models of perception, while avoiding the nuances and subtleties that are not critical. The symposium will be geared toward senior faculty and students alike, and will require no technical prerequisites to understand the major concepts, and only knowledge of basic probability theory and experimental statistics to apply the methods. Those comfortable with Bayesian modeling may find the symposium interesting, but the target audience will be the uninitiated.

The formalism of Bayesian models allows a principled description of the processes that allow organisms to recover scene properties from sensory measurements, thereby enabling a clear statement of experimental hypotheses and their connections with related theories. Many people believe Bayesian modeling is primarily for fitting unpleasant data using a prior: this is a misconception that will be dealt with! In previous attempts to correct such notions, most instruction about probabilistic models of perception falls into one of two categories: qualitative, abstract description, or quantitative, technical application. This symposium constitutes a hybrid of these categories by phrasing qualitative descriptions in quantitative formalism. Intuitive and familiar examples will be used so the connection between abstract and practical issues remains clear.

The goals of this symposium are two-fold: to present the most current and important ideas involving probabilistic perceptual models, and provide hands-on experience working with them. To accomplish these goals, our speakers will address topics such as the history and motivation for probabilistic models of perception, the relation between sensory uncertainty and probability-theoretic representations of variability, the brain�s assumptions about how the world causes sensory measurements, how to investigate the brain�s internal knowledge of probability, framing psychophysical tasks as perceptually-guided decisions, and hands-on modeling tutorials presented as Matlab scripts that will be made available for download beforehand so those with laptops can follow along. Each talk will link the conceptual material to the scientific interests of the audience by presenting primary research and suggesting perceptual problems that are ripe for the application of Bayesian methods.

## Abstracts

### Modeling Vision as Bayesian Inference: Is it Worth the Effort?

Alan Yuille

The idea of perception as statistical inference grew out of work in the 1950s in the context of a general theory of auditory and visual signal detectability. Signal detection theory from the start used concepts and tools from Bayesian Statistical Decision theory that are with us today: 1) a generative model that specifies the probability of sensory data conditioned on signal states; 2) prior probabilities of those states; 3) the utility of decisions or actions as they depend on those states. By the 1990s, statistical inference models were being extended to an increasingly wider set of problems, including object and motion perception, perceptual organization, attention, reading, learning, and motor control. These applications have relied in part on the development of new concepts and computational methods to analyze and model more realistic visual tasks. I will provide an overview of current work, describing some of the success stories. I will try to identify future challenges for testing and modeling theories of visual behavior–research that will require learning, and computing probabilities on more complex, structured representations.

### Bayesian modeling in the context of robust cue integration

David Knill

Building Bayesian models of visual perception is becoming increasingly popular in our field. Those of us who make a living constructing and testing Bayesian models are often asked the question, “What good are models that can be fit to almost any behavioral data?” I will address this question in two ways: first by acknowledging the ways in which Bayesian modeling can be misused, and second by outlining how Bayesian modeling, when properly applied, can enhance our understanding of perceptual processing. I will use robust cue integration as an example to illustrate some ways in which Bayesian modeling helps organize our understanding of the factors that determine perceptual performance, makes predictions about performance, and generates new and interesting questions about perceptual processes. Robust cue integration characterizes the problem of how the brain integrates information from different sensory cues that have unnaturally large conflicts. To build a Bayesian model of cue integration, one must explicitly model the world processes that give rise to such conflicting cues. When combined with models of internal sensory noise, such models predict behaviors that are consistent with human performance. While we can “retro-fit” the models to the data, the real test of our models is whether they agree with what we know about sensory processing and the structure of the environment (though mismatches may invite questions ripe for future research). At their best, such models help explain how perceptual behavior relates to the computational structure of the problems observers face and the constraints imposed by sensory mechanisms.

### Bayesian models for sequential decisions

Paul Schrater

Performing common perceptually-guided actions, like saccades and reaches, requires our brains to overcome uncertainty about the objects and geometry relevant to our actions (world state), potential consequences of our actions, and individual rewards attached to these consequences. A principled approach to such problems is termed “stochastic-optimal control”, and uses Bayesian inference to simultaneously update beliefs about the world state, action consequences, and individual rewards. Rational agents seek rewards, and since rewards depend on the consequences of actions, and those consequences depend on the world state, updating beliefs about all three is necessary to acquire the most reward possible.

Consider the example of reaching to grasp your computer mouse while viewing your monitor. Some strategies and outcomes for guiding your reach include: 1.) keeping your eyes fixed, moving quickly, and probably missing the mouse, 2.) keeping your eyes fixed, moving slowly, and wasting time reaching, 3.) turning your head, staring at the mouse, wasting time moving your head, or 4.) quickly saccading toward the mouse, giving you enough positional information to make a fast reach without wasting much time. This example highlights the kind of balance perceptually-guided actions strike thousands of times a day: scheduling information-gathering and action-execution when there are costs (i.e. time, missing the target) attached. Using the language of stochastic-optimal control, tradeoffs like these can be formally characterized and explain otherwise opaque behavioral decisions. My presentation will introduce stochastic-optimal control theory, and show how applying the basic principles offer a powerful framework for describing and evaluating perceptually-guided action.

### Exploring subjective probability distributions using Bayesian statistics

Tom Griffiths

Bayesian models of cognition and perception express the expectations of learners and observers in terms of subjective probability distributions – priors and likelihoods. This raises an interesting psychological question: if human inferences adhere to the principles of Bayesian statistics, how can we identify the subjective probability distributions that guide these inferences? I will discuss two methods for exploring subjective probability distributions. The first method is based on evaluating human judgments against distributions provided by the world. The second substitutes people for elements in randomized algorithms that are commonly used to generate samples from probability distributions in Bayesian statistics. I will show how these methods can be used to gather information about the priors and likelihoods that seem to characterize human judgments.

### Causal inference in multisensory perception

Konrad Koerding

Perceptual events derive their significance to an animal from their meaning about the world, that is from the information they carry about their causes. The brain should thus be able to efficiently infer the causes underlying our sensory events. Here we use multisensory cue combination to study causal inference in perception. We formulate an ideal-observer model that infers whether two sensory cues originate from the same location and that also estimates their location(s). This model accurately predicts the nonlinear integration of cues by human subjects in two auditory-visual localization tasks. The results show that indeed humans can efficiently infer the causal structure as well as the location of causes. By combining insights from the study of causal inference with the ideal-observer approach to sensory cue combination, we show that the capacity to infer causal structure is not limited to conscious, high-level cognition; it is also performed continually and effortlessly in perception.

### How to: Applying a Bayesian model to a perceptual question

Peter Battaglia

Bayesian models provide a powerful language for describing and evaluating hypotheses about perceptual behaviors. When implemented properly they allow strong conclusions about the brain�s perceptual solutions in determining what caused incoming sensory information. Unfortunately, constructing a Bayesian model may seem challenging and perhaps �not worth the trouble� to those who are not intimately familiar with the practice. Even with a clear Bayesian model, it is not always obvious how experimental data should be used to evaluate the model�s parameters. This presentation will demystify the process by walking through the modeling and analysis using a simple, relevant example of a perceptual behavior.

First I will introduce a familiar perceptual problem and describe the choices involved in formalizing it as a Bayesian model. Next, I will explain how standard experimental data can be exploited to reveal model parameter values and how the results of multiple experiments may be unified to fully evaluate the model. The presentation will be structured as a tutorial that will use Matlab scripts to simulate the generation of sensory data, the brain�s hypothetical inference procedure, and the quantitative analysis of this hypothesis. The scripts will be made available beforehand so the audience has the option of downloading and following along to enhance the hands-on theme. My goal is that interested audience members will be able to explore the scripts at a later time to familiarize themselves more thoroughly with a tractable modeling and analysis process.