Developing a consensus on how to model neural and behavioral responses and to quantify important response properties is a challenging signal processing problem because models do not always adequately capture the data and different methods often yield different estimates of the same response property. The threshold, the first stimulus level for which a difference between baseline activity and stimulus-driven activity exists, is an example of such a response property for both neural and behavioral responses.In the first and second sections of this work, we show how the state-space model framework can be used to represent neural and behavioral responses to auditory stimuli with a high degree of model goodness-of-fit. In the first section, we use likelihood methods to develop a state-space generalized linear model and estimate maximum likelihood parameters for neural data. In the second section, we develop the alternative Bayesian state-space model for behavioral data. Based on the estimated joint density, we then illustrate how important response properties, such as the neural and behavioral threshold, can be estimated, leading to lower threshold estimates than current methods by at least 2 dB. Our methods provide greater sensitivity, obviation of the hypothesis testing framework, and a more accurate description of the data.Formulating appropriate models to describe neural data in response to natural sound stimulation is another problem that currently represents a challenge. In the third section of the thesis, we develop a generalized linear model for responses to natural sound stimuli and estimate maximum likelihood parameters. Our methodology has the advantage of describing neural responses as point processes, capturing aspects of the stimulus response such as past spiking history and estimating the contributions of the various response covariates, resulting in a high degree of model goodness-of-fit.
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