Ideal observer analysis is a method for investigating how information is processed in a

perceptual system A perceptual system is a computational system (biological or artificial) designed to make inferences about properties of a physical environment based on senses. Other definitions may exist. In this context, a scene is defined as information that ...

. It is also a basic principle that guides modern research in

perception Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous system ...

. The ''ideal observer'' is a theoretical system that performs a specific task in an optimal way. If there is uncertainty in the task, then perfect performance is impossible and the ideal observer will make errors. ''Ideal performance'' is the theoretical upper limit of performance. It is theoretically impossible for a real system to perform better than ideal. Typically, real systems are only capable of sub-ideal performance. This technique is useful for analyzing psychophysical data (see

psychophysics Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, m ...

Definition

Many definitions of this term have been offered. Geisler (2003) (slightly reworded): The central concept in ideal observer analysis is the ''ideal observer'', a theoretical device that performs a given task in an optimal fashion given the available information and some specified constraints. This is not to say that ideal observers perform without error, but rather that they perform at the physical limit of what is possible in the situation. The fundamental role of uncertainty and noise implies that ideal observers must be defined in probabilistic (statistical) terms. ''Ideal observer analysis'' involves determining the performance of the ideal observer in a given task and then comparing its performance to that of a real

, which (depending on the application) might be the system as a whole, a subsystem, or an elementary component of the system (e.g. a neuron).

Sequential ideal observer analysis

In sequential ideal observer analysis, the goal is to measure a real system's performance deficit (relative to ideal) at different processing stages. Such an approach is useful when studying systems that process information in discrete (or semi-discrete) stages or modules.

Natural and pseudo-natural tasks

To facilitate experimental design in the laboratory, an artificial task may be designed so that the system's performance in the task may be studied. If the task is too artificial, the system may be pushed away from a natural mode of operation. Depending on the goals of the experiment, this may diminish its

external validity External validity is the validity of applying the conclusions of a scientific study outside the context of that study. In other words, it is the extent to which the results of a study can be generalized to and across other situations, people, stim ...

. In such cases, it may be important to keep the system operating naturally (or almost naturally) by designing a pseudo-natural task. Such tasks are still artificial, but they attempt to mimic the natural demands placed on a system. For example, the task might employ stimuli that resemble natural scenes and might test the system's ability to make potentially useful judgments about these stimuli. Natural scene statistics are the basis for calculating ideal performance in natural and pseudo-natural tasks. This calculation tends to incorporate elements of

signal detection theory Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (ca ...

information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...

, or

estimation theory Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their valu ...

Normally distributed stimuli

Das and Geisler {{cite arXiv , last1=Das, first1=Abhranil, last2=Geisler, first2=Wilson, eprint=2012.14331, title=A method to integrate and classify normal distributions, date=2020, class=stat.ML described and computed the detection and classification performance of ideal observers when the stimuli are normally distributed. These include the error rate and

confusion matrix In the field of machine learning and specifically the problem of statistical classification, a confusion matrix, also known as an error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a su ...

for ideal observers when the stimuli come from two or more univariate or multivariate normal distributions (i.e. yes/no, two-interval, multi-interval tasks and general multi-category classification tasks), the discriminability index of the ideal observer ( Bayes discriminability index) and its relation to the

receiver operating characteristic A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied. The method was originally developed for operators of ...

Notes

Perception Neuroscience