Quick Answer: Fisher Information And Its Relationship With Likelihood And Density Functions

The Fisher information serves a crucial role in quantifying the precision of neural codes, primarily when analyzing the collective responses of numerous neurons that encode a lower-dimensional variable, often denoted as θ (such as a stimulus parameter). One notable application of the Fisher information involves establishing bounds on the accuracy of these neural codes. In this context, researchers focus on investigating the impact of correlations within the noise inherent in neural responses, shedding light on how these correlations affect the overall coding accuracy.

To grasp the distinction between a likelihood function and a density function, it’s essential to delve into measure-theoretic probability theory. Here, we encounter the density function, which is formally described as the Radon-Nikodym derivative of a probability distribution concerning a common dominating measure. This density function quantifies the probability distribution’s behavior with respect to this dominating measure. In contrast, the likelihood function takes this density and views it as a function of the parameter, rather than the random variable. Essentially, it represents how likely certain parameter values are, given observed data, making it a crucial tool in statistical inference.