Roberto Fernandez

 


Description
Stochastic description of signals
Many natural phenomena are characterized by a large level of variability. Repeated experiments lead different answers, even under tightly controlled experimental conditions. Examples include biological phenomena (e.g. neuron spike trains), social phenomena (market behavior, language acquisition) and, of course, many well known physical phenomena involving noise. These phenomena require the use of a stochastic framework in which signals are characterized by a distribution law which must be determined through samples of the signal.

There exist, however, competing forms of determining the law of a signal. Customarily, signals are studied in terms of transition probabilities, which determine the probability of the next bit given the history. Nothing prevents, however, to characterize the distribution of this bit by studying past *and future*. The former approach is related to the theory of stochastic processes, while the latter corresponds to the theory of Gibbs measures in statistical mechanics.

The project involves a comparative study of these approaches. Depending on the interest of the student, the study can be done at the foundational level, with emphasis on rigorous results, or at a more applied level, with emphasis in empirical (numerical) comparisons. A mixed approach, and even the work of two students as a team, is also possible.


Prerequisite

Advanced probability


Preferred Time of Research

1 semester or all year


Weekly Commitment

Minimum 6 hours


Location

NYUSH


Paid?
No

Contact
rf87@nyu.edu