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Bayesian Particle Tracking of Traffic Flows
Nicholas Polson, Vadim Sokolov
We develop a Bayesian particle filter for tracking traffic flows that is capable of capturing non-linearities and discontinuities present in flow dynamics. Our model includes a hid…
Bayesian analysis of traffic flow on interstate I-55: The LWR model
Nicholas Polson, Vadim Sokolov
Transportation departments take actions to manage traffic flow and reduce travel times based on estimated current and projected traffic conditions. Travel time estimates and foreca…
Vertical-likelihood Monte Carlo
Nicholas G. Polson, James G. Scott
In this review, we address the use of Monte Carlo methods for approximating definite integrals of the form , where is a target function (often a likelihoo…
Mixtures, envelopes, and hierarchical duality
Nicholas G. Polson, James G. Scott
We develop a connection between mixture and envelope representations of objective functions that arise frequently in statistics. We refer to this connection using the term "hierarc…
Sampling Polya-Gamma random variates: alternate and approximate techniques
Jesse Windle, Nicholas G. Polson, James G. Scott
Efficiently sampling from the Pólya-Gamma distribution, , is an essential element of Pólya-Gamma data augmentation. Polson et. al (2013) show how to efficiently sample f…