Assessing risk through composite FMEA with pairwise matrix and Markov chains

Pairwise Markov Chains

We propose a new model called a Pairwise Markov Chain (PMC), which generalizes the classical Hidden Markov Chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like Maximum A Posteriori (MAP), or ...

Pairwise Choice Markov Chains

As datasets capturing human choices grow in richness and scale—particularly in online domains—there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce’s choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not ...

Pairwise Markov Chains and Bayesian Unsupervised Fusion

Particle Filtering in Pairwise and Triplet Markov Chains

The estimation of an unobservable process x from an observed process y is often performed in the framework of Hidden Markov Models (HMM). In the linear Gaussian case, the classical recursive solution is given by the Kalman filter. On the other hand, particle filters provide approximate solutions in more complex situations. In this paper, we propose two successive generalizations of the classica...

Unsupervised Signal Restoration Using Copulas and Pairwise Markov Chains

This work deals with the statistical restoration of hidden discrete signals. The problem we deal with is how to take into account, in recent pairwise and triplet Markov chain context, complex noises that can be non-Gaussian, correlated, and of class-varying nature. We propose to solve this modeling problem using Copulas. The interest of the new modeling is validated by experiments performed in ...