Nonparametric bayesian models for neural data

Many neural data analyses can be cast as latent variable modeling problems. Specific examples include spike sorting and neurological data analysis. Challenges in spike sorting include figuring out how many neurons generated a set of recorded action potentials and, further, which neuron generated each action potential. A challenge in analyzing neurological data is to infer both the number and the characteristics of lesions that may be causal with respect to clinical signs presented by stroke patients. A shared characteristic of both of these problems is that the true underlying generative process is unobservable and potentially quite complex, so care must be taken in not only choosing a family of models but also in selecting a model of appropriate complexity. In such cases it may be preferable to employ a model that allows model complexity to be inferred from the data. Non-parametric Bayesian (NPB) modeling is a type of latent variable modeling in which model complexity can be estimated from data without making restrictive a priori assumptions. Our thesis is that using NPB modeling results in theoretical and practical improvements to neural data analysis. In defense of this thesis we develop a NPB spike sorting approach and show how it allows experimentalists to utilize more data, to make assumptions explicit, and to express spike sorting uncertainty at the level of inference from a novel spike train model. We discuss the theoretical advantages of this approach and demonstrate novel and improved neural data analyses including neural decoding. We also develop a new NPB binary matrix factorization model and accompanying posterior estimation algorithms. We illustrate this NPB binary matrix factorization model by inferring a causal model for signs exhibited by stroke patients. Finally, a sequential posterior estimation algorithm for this model is developed and demonstrated.