Estimating ensemble flows on a hidden Markov chain

We propose a new framework to estimate the evolution of an ensemble of indistinguishable agents on a hidden Markov chain using only aggregate output data. This work can be viewed as an extension of the recent developments in optimal mass transport and Schr\"odinger bridges to the finite state space hidden Markov chain setting. The flow of the ensemble is estimated by solving a maximum likelihood problem, which has a convex formulation at the infinite-particle limit, and we develop a fast numerical algorithm for it. We illustrate in two numerical examples how this framework can be used to track the flow of identical and indistinguishable dynamical systems.Comment: 8 pages, 4 figure

Extreme Quantum Advantage for Rare-Event Sampling

We introduce a quantum algorithm for efficient biased sampling of the rare events generated by classical memoryful stochastic processes. We show that this quantum algorithm gives an extreme advantage over known classical biased sampling algorithms in terms of the memory resources required. The quantum memory advantage ranges from polynomial to exponential and when sampling the rare equilibrium configurations of spin systems the quantum advantage diverges.Comment: 11 pages, 9 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/eqafbs.ht

Default Estimation, Correlated Defaults, and Expert Information

Capital allocation decisions are made on the basis of an assessment of creditworthiness. Default is a rare event for most segments of a bank's portfolio and data information can be minimal. Inference about default rates is essential for efficient capital allocation, for risk management and for compliance with the requirements of the Basel II rules on capital standards for banks. Expert information is crucial in inference about defaults. A Bayesian approach is proposed and illustrated using prior distributions assessed from industry experts. A maximum entropy approach is used to represent expert information. The binomial model, most common in applications, is extended to allow correlated defaults yet remain consistent with Basel II. The application shows that probabilistic information can be elicited from experts and econometric methods can be useful even when data information is sparse.