Inference of dominant modes for linear stochastic processes

Tractable Inference for Complex Stochastic Processes

The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state—a probability distribution over the state of the process at a given point in time. Unfortunately, the state spaces of complex processes are very large, making an...

A Useful Family of Stochastic Processes for Modeling Shape Diffusions

 One of the new area of research emerging in the field of statistics is the shape analysis. Shape is defined as all the geometrical information of an object whose location, scale and orientation is not of interest. Diffusion in shape analysis can be studied via either perturbation of the key coordinates identifying the initial object or random evolution of the shape itself. Reviewing the f...

Some Inference Theorems in Stochastic Processes

Exact Statistical Inference for Some Parametric Nonhomogeneous Poisson Processes

Nonhomogeneous Poisson processes (NHPPs) are often used to model recurrent events, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness-of-fit tests for certain parametric NHPPs, using a method based on Monte Carlo simulation conditional on sufficient statistics. A closely related way of obtaining exact confidence intervals in parametri...

Deterministic Anytime Inference for Stochastic Continuous-Time Markov Processes

We describe a deterministic anytime method for calculating filtered and smoothed distributions in large variable-based continuous time Markov processes. Prior non-random algorithms do not converge to the true distribution in the limit of infinite computation time. Sampling algorithms give different results each time run, which can lead to instability when used inside expectationmaximization or ...