Abstract
We show that many ideal observer models used to decode neural activity can be generalized to a conceptually and analytically simple form. This enables us to study the statistical properties of this class of ideal observer models in a unified manner. We consider in detail the problem of estimating the performance of this class of models. We formulate the problem de novo by deriving two equivalent expressions for the performance and introducing the corresponding estimators. We obtain a lower bound on the number of observations (N) required for the estimate of the model performance to lie within a specified confidence interval at a specified confidence level. We show that these estimators are unbiased and consistent, with variance approaching zero at the rate of 1/N. We find that the maximum likelihood estimator for the model performance is not guaranteed to be the minimum variance estimator even for some simple parametric forms (e.g., exponential) of the underlying probability distributions. We discuss the application of these results for designing and interpreting neurophysiological experiments that employ specific instances of this ideal observer model.
Highlights
We address the following questions: 1) How does the performance of the generalized ideal observer compare to the area under the receiver operating characteristic (ROC) curve? 2) Is it possible to determine a priori the number of input samples required so that the estimated value of the observer’s performance will lie within a specified confidence interval at a specified confidence level? 3) Are these estimates unbiased and consistent, i.e., does estimation error decrease with increasing number of observations and at what rate? 4) Do efficient estimators exist for the performance of these ideal observers? 5) Is the standard method of estimating performance efficient? Answers to these questions will facilitate a more efficient design of neurophysiological experiments for ideal observer analysis
We proposed a general form of an ideal observer for decoding stimulus information and perceptual decisions from neural responses
We have provided a lower bound on the number of observations required for the estimate to lie within a pre-specified range of its true value (“confidence interval”), within a specified confidence level
Summary
Ideal observer models are an important tool in the effort to understand the neural bases of perception and behavior (FitzHugh, 1957; Ratliff, 1962; De Valois et al, 1967; Ratliff et al, 1968; Talbot et al, 1968; Barlow and Levick, 1969; Barlow et al, 1971; Mountcastle et al, 1972; Johansson and Vallbo, 1979; Bradley et al, 1987; Newsome et al, 1989; Vogels and Orban, 1990; Geisler, 2001). Barlow et al (1971) used an ideal detector model to compute detection probability from the number of photons absorbed by photoreceptors and related the results to retinal ganglion cell responses In this manner, they were able to estimate the average number of impulses emitted by a retinal ganglion cell per quantum of light absorbed by photoreceptors. In the intermediate stages of sensorimotor transformation, ideal observer models are often used to optimally decode behavioral choice related information from the responses of a single sensory neuron (Celebrini and Newsome, 1994; Britten et al, 1996). Such analyses associate neural responses with perceptual decisions Ideal observer analysis can be applied to optically imaged cortical signals to assess neural population sensitivity for detection or discrimination (Chen et al, 2006, 2008; Purushothaman et al, 2009; see rev: Cohen et al, 2011)
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