Experience matters 1 Experience matters : Information acquisition optimizes probability gain

Deciding which piece of information to acquire or attend to is fundamental to perception, categorization, medical diagnosis, and scientific inference. Four statistical theories of the value of information—information gain, Kullback-Liebler distance, probability gain (error minimization), and impact—are equally consistent with extant data on human information acquisition (Nelson, 2005; 2008). Three experiments, designed via computer optimization to be maximally informative, tested which of these theories best describes human information search. Experiment 1, which used natural sampling and experience-based learning to convey environmental probabilities, found that probability gain explained participants’ information search better than the other statistical theories or the probability of certainty heuristic. Experiments 1 and 2 found that participants behaved differently when the standard method of verbally-presented summary statistics was used to convey environmental probabilities. Experiment 3 found that participants’ preference for probability gain is robust, suggesting that other models contribute little to participants’ search behavior. Experience matters 3 Many situations require careful selection of information. Appropriate medical tests can improve diagnosis and treatment. Carefully designed experiments can facilitate choosing between competing scientific theories. Visual perception also requires careful selection of eye movements to informative parts of a visual scene. Intuitively, useful experiments are those for which plausible competing theories make the most contradictory predictions. A Bayesian optimal experimental design (OED) framework provides a mathematical scheme for calculating which query (experiment, medical test, or eye movement) is expected to be most useful. Mathematically, it is a special case of Bayesian decision theory (Savage, 1954). Note that a single theory is not tested in this framework, but rather multiple theories. The usefulness of an experiment is a function of the probabilities of the hypotheses under consideration, the explicit (and perhaps probabilistic) predictions that those hypotheses entail, and which utility function is being used. In situations where different queries cost different amounts, and different kinds of mistakes have different costs, those constraints should be used to determine the best queries to make, rather than general purpose criteria for the value of information. This article, however, deals with situations where information gathering is the only goal. Specifically, we focus on situations in which the goal is to categorize an object by selecting useful features to view. Querying a feature, to obtain information about the probability of a stimulus belonging to a particular category, corresponds to an “experiment” in the OED framework, and will generally change one’s belief about the probability the stimulus belongs to each of several categories. For instance, in environments where a higher proportion of men than women have beards, learning that a particular individual has a beard increases the probability that they are male. The various OED models differ in terms of how they calculate the usefulness of looking at particular features. All of the models Experience matters 4 use Bayes’s theorem to update beliefs about the probability of each category ci when a particular feature value f is observed: