Compressed sensingCompressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. There are two conditions under which recovery is possible.
Statistical modelA statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities, the corresponding term is probabilistic model. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
Motion perceptionMotion perception is the process of inferring the speed and direction of elements in a scene based on visual, vestibular and proprioceptive inputs. Although this process appears straightforward to most observers, it has proven to be a difficult problem from a computational perspective, and difficult to explain in terms of neural processing. Motion perception is studied by many disciplines, including psychology (i.e. visual perception), neurology, neurophysiology, engineering, and computer science.
Time perceptionThe study of time perception or chronoception is a field within psychology, cognitive linguistics and neuroscience that refers to the subjective experience, or sense, of time, which is measured by someone's own perception of the duration of the indefinite and unfolding of events. The perceived time interval between two successive events is referred to as perceived duration. Though directly experiencing or understanding another person's perception of time is not possible, perception can be objectively studied and inferred through a number of scientific experiments.
Visual perceptionVisual perception is the ability to interpret the surrounding environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and mesopic vision (twilight vision), using light in the visible spectrum reflected by objects in the environment. This is different from visual acuity, which refers to how clearly a person sees (for example "20/20 vision"). A person can have problems with visual perceptual processing even if they have 20/20 vision.
Multilevel modelMultilevel models (also known as hierarchical linear models, linear mixed-effect model, mixed models, nested data models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parameters that vary at more than one level. An example could be a model of student performance that contains measures for individual students as well as measures for classrooms within which the students are grouped.
StatisticA statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the function and for the value of the function on a given sample. When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose.
Statistical assumptionStatistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions. Here are some examples of statistical assumptions: Independence of observations from each other (this assumption is an especially common error). Independence of observational error from potential confounding effects.
Multivariate statisticsMultivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.
Multistable perceptionMultistable perception (or bistable perception) is a perceptual phenomenon in which an observer experiences an unpredictable sequence of spontaneous subjective changes. While usually associated with visual perception (a form of optical illusion), multistable perception can also be experienced with auditory and olfactory percepts. Perceptual multistability can be evoked by visual patterns that are too ambiguous for the human visual system to definitively and uniquely interpret.
Robust statisticsRobust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution.
Bayesian probabilityBayesian probability (ˈbeɪziən or ˈbeɪʒən ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.
