We present a fast and simple tree model to price simple and exotic options in Markov Regime Switching Model (MRSM) with multi-regime. We modify the trinomial tree model of Boyle (1986) by controlling the risk neutral probability measure in different regime states to ensure that the tree model can accommodate the data of all different regimes at the same time preserve its combining tree structur...

Given a general critical or sub-critical branching mechanism, we define a pruning procedure of the associated Lévy continuum random tree. This pruning procedure is defined by adding some marks on the tree, using Lévy snake techniques. We then prove that the resulting sub-tree after pruning is still a Lévy continuum random tree. This last result is proved using the exploration process that codes...

We consider streaming prediction model for tree Markov Random fields. Given the random field, at any point in time we may perform one of three actions: i) predict a label at a vertex on the tree ii) update by associating a label with a vertex or iii) delete the label at a vertex. Using the standard methodology of belief propagation each such action requires time linear in the size of the tree. ...

We consider the problem of inferring an ancestral state from observations at the leaves of a tree, assuming the state evolves along the tree according to a two-state symmetric Markov process. We establish a general branching rate condition under which maximum parsimony, a common reconstruction method requiring only the knowledge of the tree, succeeds better than random guessing uniformly in the...

We describe a simple transformation that allows for the fast recovery of a tree from the probabilities such a tree induces on the colourations of its leaves under a simple Markov process (with unknown parameters). This generalizes earlier results by not requiring the transition matrices associated with the edges of the tree to be of a particular form, or to be related by some fixed rate matrix,...

We consider Gibbs distributions on finite random plane trees with bounded branching. We show that as the order of the tree grows to infinity, the distribution of any finite neighborhood of the root of the tree converges to a limit. We compute the limiting distribution explicitly and study its properties. We introduce an infinite random tree consistent with these limiting distributions and show ...

We investigate a simple model that generates random partitions of the leaf set of a tree. Of particular interest is the reconstruction question: what number k of independent samples (partitions) are required to correctly reconstruct the underlying tree (with high probability)? We demonstrate a phase transition for k as a function of the mutation rate, from logarithmic to polynomial dependence o...

We present a simple, effective generalisation of variable order Markov models to full online Bayesian estimation. The mechanism used is close to that employed in context tree weighting. The main contribution is the addition of a prior, conditioned on context, on the Markov order. The resulting construction uses a simple recursion and can be updated efficiently. This allows the model to make pre...

In this paper the abstraction-refinement paradigm based on 3-valued logics is extended to the setting of probabilistic systems. We define a notion of abstraction for Markov chains. To be able to relate the behavior of abstract and concrete systems, we equip the notion of abstraction with the concept of simulation. Furthermore, we present model checking for abstract probabilistic systems (abstra...

In this paper, we employed Naïve Bayes, Augmented Naïve Bayes, Tree Augmented Naïve Bayes, Sons & Spouses, Markov Blanket, Augmented Markov Blanket, Semi Supervised and Bayesian network techniques to rank web services. The Bayesian Network is demonstrated on a dataset taken from literature. The dataset consists of 364 web services whose quality is described by 9 attributes. Here, the attributes...