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A primer on information theory, with applications to neuroscience

Given the constant rise in quantity and quality of data obtained from neural systems on many scales ranging from molecular to systems', information-theoretic analyses became increasingly necessary during the past few decades in the neurosciences. Such analyses can provide deep insights into the functionality of such systems, as well as a rigid mathematical theory and quantitative measures of information processing in both healthy and diseased states of neural systems. This chapter will present a short introduction to the fundamentals of information theory, especially suited for people having a less firm background in mathematics and probability theory. To begin, the fundamentals of probability theory such as the notion of probability, probability distributions, and random variables will be reviewed. Then, the concepts of information and entropy (in the sense of Shannon), mutual information, and transfer entropy (sometimes also referred to as conditional mutual information) will be outlined. As these quantities cannot be computed exactly from measured data in practice, estimation techniques for information-theoretic quantities will be presented. The chapter will conclude with the applications of information theory in the field of neuroscience, including questions of possible medical applications and a short review of software packages that can be used for information-theoretic analyses of neural data.