We consider a class of nonlinear estimation problems possessing certain algebraic properties, and we exploit these properties in order to study the computational complexity of nonlinear estimation algorithms. Specifically, we define a class of finite-state Markov processes evolving on finite groups and consider noisy observations of these processes. By introducing some concepts from the theory ...

In this work we propose a Bayesian approach for the parameter estimation problem of stochastic autoregressive models of order p, AR(p), applied to the streamflow forecasting problem. Procedures for model selection, forecasting and robustness evaluation through Monte Carlo Markov Chain (MCMC) simulation techniques are also presented. The proposed approach is compared with the classical one by Bo...

We propose in this report a novel approach to the induction of the structure of Hidden Markov Models (HMMs). The notion of partially observable Markov models (POMMs) is introduced. POMMs form a particular case of HMMs where any state emits a single letter with probability one, but several states can emit the same letter. It is shown that any HMM can be represented by an equivalent POMM. The pro...

in recent years, some statisticians have studied the signal detection problem by using the random field theory. in this paper we have considered point estimation of the gaussian scale space random field parameters in the bayesian approach. since the posterior distribution for the parameters of interest dose not have a closed form, we introduce the markov chain monte carlo (mcmc) algorithm to ap...

In this paper, we describe a new hidden Markov random field model, which we call hierarchical multi-data model, and which is based on a triplet of random fields (two hidden random fields and one observed field) in order to capture inter-scale and within-scale dependencies between various scales of resolution of wavelet-based texture features. We present a variation of the Iterated Conditional M...

We study a networked state estimation problem for a linear system with multiple sensors, each of which transmits its measurements to a central estimator via a lossy communication network for computing the minimum mean-square-error (MMSE) state estimate. Under a general Markov packet loss process, we establish necessary and sufficient conditions for the stability of the estimator for any diagona...

The EM algorithm, e.g. as Baum-Welch reestimation, is an important tool for parameter estimation in discrete-time Hidden Markov Models. We present a direct reestimation of rate constants for applications in which the underlying Markov process is continuous in time. Previous estimation of discrete-time transition probabilities is not necessary.

This paper deals with order identification for Markov chains with Markov regime (MCMR) in the context of finite alphabets. We define the joint order of a MCMR process in terms of the number k of states of the hidden Markov chain and the memory m of the conditional Markov chain. We study the properties of penalized maximum likelihood estimators for the unknown order (k, m) of an observed MCMR pr...

In gene mapping, after an initial genome-wide linkage scan, the next step often involves candidate region studies or fine mapping using dense markers. Dense genotyping, however, introduces linkage disequilibrium (LD). Traditional linkage analysis assuming no LD leads to increased false positive rates. Hence, we develop models to incorporate linkage disequilibrium, focusing on the sib pair desig...

Markov Decision Processes (MDPs) [7] have developed lately as a standard method for representing uncertainty in decision-theoretic planning. Traditional MDP solution techniques have the drawback that they require an explicit state space, limiting their applicability to real-world problems due to the large number of world states occurring in such problems. Recent work addresses this drawback via...