Stochastic Modeling of Deterioration Processes through Dynamic Bayesian Networks

Dynamic Bayesian Networks as Formal Abstractions of Structured Stochastic Processes

We study the problem of finite-horizon probabilistic invariance for discrete-time Markov processes over general (uncountable) state spaces. We compute discrete-time, finite-state Markov chains as formal abstractions of general Markov processes. Our abstraction differs from existing approaches in two ways. First, we exploit the structure of the underlying Markov process to compute the abstractio...

Combinatorial stochastic processes and nonparametric Bayesian modeling

An Empirical Study of Dynamic Bayesian User Modeling with Stochastic Processes

Six topologies of dynamic Bayesian Networks are evaluated for predicting the future user events: (1) Markov Chain of order 1, (2) Hidden Markov Model, (3) autoregressive Hidden Markov Model, (4) factorial Hidden Markov Model, (5) simple hierarchical Hidden Markov Model and (6) tree structured Hidden Markov Model. Goal of the investigation is to evaluate, which of these models has the best fit f...

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...

The modeling of body's immune system using Bayesian Networks

In this paper, the urinary infection, that is a common symptom of the decline of the immune system, is discussed based on the well-known algorithms in machine learning, such as Bayesian networks in both Markov and tree structures. A large scale sampling has been executed to evaluate the performance of Bayesian network algorithm. A number of 4052 samples wereobtained from the database of the Tak...