Comparing Global and Limited sampling Strategies in Size-averaging a Set of Items

Comparing Global and Limited sampling Strategies in Size-averaging a Set of Items Midori Tokita (Tokita.Midori@ocha.ac.jp) Department of Letters and Education, Ochanomizu University, Otsuka, Tokyo 112-8610 Japan Akira Ishiguchi (Ishiguchi.Akira@ocha.ac.jp) Department of Human Developmental Sciences, Ochanomizu University, Otsuka, Tokyo 112-8610 Japan Abstract Many studies have shown that our visual system may construct a “statistical summary representation” over groups of visual objects. Although there is a general understanding that human observers can accurately represent sets of a variety of features, many questions on how the statistical summary is computed still remain unanswered. This study investigated sampling properties of visual information used by human observers in deriving an average representation of a set of items. We presented three models of ideal observers to perform a size averaging task: a global averaging model without item noise (GAM1), a global averaging model with item noise (GAM2), and a limited sampling model (LSM). We compared the performance of the ideal observer of each model to the performance of human observers using statistical efficiency analysis. Our results suggest that average size of items in a set may be computed without representing individual items, discarding the limited sampling model. Keywords: statistical summary representation; Ideal observer analysis; size averaging; attention Introduction Many studies have shown that people accurately perceive and estimate the statistical properties of a set of items or events. For example, the visual system may construct a “statistical summary representation” over groups of visual objects (e.g., Alvarez, 2011; Ariely, 2001, 2008; Chong & Treisman, 2003). It has been shown that observers are able to quickly and accurately extract average values over a range of visual properties, including size (Chong & Treisman, 2005；Oriet & Brand, 2013), brightness (Bauer, 2009), orientation (Parkes, Liend, Angelucci, Solomon & Morgan, 2001), emotional expression (Haberman & Whitney, 2009, 2011), and others. Moreover, this ability is not limited to static and simultaneous events; it is observed in sequentially presented events （Oriet & Corbett, 2008; Whiting & Oriet, 2011）and dynamic objects, such as expanding and contracting circles (Albrecht & Scholl, 2010). In recent studies, it has been shown that the ability of representing statistical properties is not limited to visual properties but is also observed in auditory mechanisms such as extracting frequency information from sequences of sounds (Piazza, Sweeny, Wessel, Silver, & Whitney, 2013). Although there is a general understanding that human observers can accurately represent sets of features, many questions on how the statistical summary is computed still remain unanswered. Three possibilities have been proposed: 1) representations of individual items are computed first and then combined to form a summary representation, 2) summary representations are computed without computing individual items, or 3) Only a couple of items in a set are sampled and included in the calculation of the average size. The first and second proposals predict that there are specialized statistical summary representation mechanisms that are separate from the mechanisms mediated to represent individual objects. Conforming to this argument, many studies have provided evidence that, when attention is distributed across a set of similar items, people can extract the average size of all the items without relying on focused attention to the individual items in the set (e.g., Chong & Treisman, 2003, 2005; Im & Halberda, 2013; Treisman, 2006). The third proposal claims that it is possible to accurately estimate the average size by sampling a couple of items in a set using focused attention. Modeling research has shown that a sampling strategy reasonably predicts the approximate levels of performance exhibited by observers in studies of average size perception (Myczek & Simons, 2008; Marchant, Simons & Fockert, 2013). Neither the proponents of the summary representation mechanisms nor those of the limited sampling strategy have excluded or refuted the opposing argument. Rather, they prompt the necessity for further investigation on the processes of human performance of statistical summary mechanisms (Ariely, 2008; Simons & Myczek, 2008). Overall, it is necessary to examine if people estimate the average size by using the global information of all items in a set or of the limited number of items in a set. The present study investigated sampling properties of visual information used by human observers in deriving an average representation of items in a set using the ideal observer (IO) analysis. We measured performance on a size averaging task for each ideal observer model and for human observers. Next, we compared the performance of the ideal observer of each model to the performance of human observers to evaluate which model could predict how human observers derive the average size of items in a set. While comparing, we used a statistical efficiency analysis that allows direct comparison of efficiencies among different models that represent different uses of information. Statistical efficiency is a relative index for the sampling rate of information in a given task. Many studies have utilized the efficiency to investigate how the visual system uses available information and revealed the characteristics of