This paper introduces the hhsmm R package, which involves functions for initializing, fitting, and predication of hidden hybrid Markov/semi-Markov models. These models are flexible with both Markovian semi-Markovian states, applied to situations where model absorbing or macro-states. The left-to-right series/parallel networks states two states. also includes switching regression as well auto-re...

There is significant motivation to develop reduced-complexity filtering algorithms (with explicit performance bounds) for tracking maneuvering targets. Maneuvering target estimation is an important problem in target tracking due to the uncertainty in maneuvers of the target. In a hostile environment a target will try to avoid being tracked by maneuvering in such a way so that its motion is diff...

By means of two simple convexity arguments we are able to develop a general method for proving consistency and asymptotic normality of estimators that are defined by minimisation of convex criterion functions. This method is then applied to a fair range of different statistical estimation problems, including Cox regression, logistic and Poisson regression, least absolute deviation regression ou...

We suggest the use of Poisson hidden Markov models (PHMMs) in non life insurance. PHMMs are an extension of the well-known mixture models and we use them to model the dynamics of overdispersed data, in particular of the claim number. PHMMs allow us to explicitly consider unobserved factors influencing the dynamics of the claim number. This has an immediate impact on the value of the pure risk p...

We consider hidden Markov models as a versatile class of models for weakly dependent random phenomena. The topic of the present paper is likelihood-ratio testing for hidden Markov models, and we show that, under appropriate conditions, the standard asymptotic theory of likelihood-ratio tests is valid. Such tests are crucial in the specification of multivariate Gaussian hidden Markov models, whi...

Description Functions for fitting general continuous-time Markov and hidden Markov multi-state models to longitudinal data. Both Markov transition rates and the hidden Markov output process can be modelled in terms of covariates. A variety of observation schemes are supported, including processes observed at arbitrary times, completely-observed processes, and censored states.

The air transport industry is seeking to manage risks in air travels. Its main objective is to detect abnormal behaviors in various flight conditions. The current methods have some limitations and are based on studying the risks and measuring the effective parameters. These parameters do not remove the dependency of a flight process on the time and human decisions. In this paper, we used an HMM...

We consider the stochastic model of water pollution, which mathematically can be written with a stochastic partial differential equation driven by Poisson measure noise. We use a stochastic particle Markov chain method to produce an implementable approximate solution. Our main result is the annealed law of large numbers establishing convergence in probability of our Markov chains to the solutio...