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The functional relationship between an input and a sensory neuron's responsecan be described by the neuron's stimulus-response mapping function. A generalapproach for characterizing the stimulus-response mapping function is calledsystem identification. Many different names have been used for thestimulus-response mapping function: kernel or transfer function, transducer,spatiotemporal receptive field. Many algorithms have been developed to estimatea neuron's mapping function from an ensemble of stimulus-response pairs. Theseinclude the spike-triggered average, normalized reverse correlation, linearizedreverse correlation, ridge regression, local spectral reverse correlation,spike-triggered covariance, artificial neural networks, maximally informativedimensions, kernel regression, boosting, and models based on leakyintegrate-and-fire neurons. Because many of these system identificationalgorithms were developed in other disciplines, they seem very differentsuperficially and bear little relationship with each other. Each algorithmmakes different assumptions about the neuron and how the data is generated.Without a unified framework it is difficult to select the most suitablealgorithm for estimating the neuron's mapping function. In this review, wepresent a unified framework for describing these algorithms called maximum aposteriori estimation (MAP). In the MAP framework, the implicit assumptionsbuilt into any system identification algorithm are made explicit in three MAPconstituents: model class, noise distributions, and priors. Understanding theinterplay between these three MAP constituents will simplify the task ofselecting the most appropriate algorithms for a given data set. The MAPframework can also facilitate the development of novel system identificationalgorithms by incorporating biophysically plausible assumptions and mechanismsinto the MAP constituents.

The unified maximum a posteriori (MAP) framework for neuronal system identification