Related papers: Asymptotically Efficient Identification of Known-S…
As saturated output observations are ubiquitous in practice, identifying stochastic systems with such nonlinear observations is a fundamental problem across various fields. This paper investigates the asymptotically efficient identification…
Herein, the Hidden Markov Model is expanded to allow for Markov chain observations. In particular, the observations are assumed to be a Markov chain whose one step transition probabilities depend upon the hidden Markov chain. An…
We consider a unified framework of sequential change-point detection and hypothesis testing modeled by means of hidden Markov chains. One observes a sequence of random variables whose distributions are functionals of a hidden Markov chain.…
Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…
The problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered. Assuming a Markov evolution of the system (in particular, the pair…
Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…
We consider probabilistic systems with hidden state and unobservable transitions, an extension of Hidden Markov Models (HMMs) that in particular admits unobservable {\epsilon}-transitions (also called null transitions), allowing state…
State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…
In this paper, we develop methods of nonlinear filtering and prediction of an unobservable Markov chain with a finite set of states. This Markov chain controls coefficients of AR(p) model. Using observations generated by AR(p) model we have…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
In this paper, we propose an algorithm for estimating the parameters of a time-homogeneous hidden Markov model from aggregate observations. This problem arises when only the population level counts of the number of individuals at each time…
We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden…
Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small…
The partially observable hidden Markov model is an extension of the hidden Markov Model in which the hidden state is conditioned on an independent Markov chain. This structure is motivated by the presence of discrete metadata, such as an…
We consider the estimation of the transition matrix of a hidden Markovian process by using information geometry with respect to transition matrices. In this paper, only the histogram of $k$-memory data is used for the estimation. To…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…
The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we…
Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques…