To reduce energy demand in households it is useful to know which electrical appliances are in use at what times. Monitoring individual appliances is costly and intrusive, whereas data on overall household electricity use is more easily obtained. In this paper, we consider the energy disaggregation problem where a household’s electricity consumption is disaggregated into the component appliances...

Longitudinal data, where the same set of subjects is repeatedly observed over time, are frequently analyzed by using HiddenMarkov models (HMMs). In this situation, heterogeneity may arise at individual and/or time level affecting the hidden process, i.e. the transition probabilities among hidden states. Non-homogeneous (NH) HMMs face with this problem by expressing the transition probabilities ...

A hidden Markov process (HMP) is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. The non-asymptotic equipartition property (NEP) is a bound on the probability of the sample entropy deviating from the entropy rate of a stochastic process, so it can be viewed as a refinement of Shannon-McMillan-Breiman theorem. In this report, w...

A more realistic way to describe a model is the use of intervals which contain required values parameters. In practice we estimate parameters from set data and it natural that they will be in confidence intervals. present study, study Non-Homogeneous Markov Systems (NHMS) processes for basic are We call such Set (NHMSS). First relative expected population structure memberships prove under certa...

This paper introduces a new multinomial approach unifying the computation of confidence intervals for Markovian models. Starting from a method used for homogeneous Markov chains, we show that it can be applied on models incorporating a hidden component. We consider three models derived from the basic homogeneous Markov chain: the Mixture Transition Distribution (MTD) model, the Hidden Markov Mo...

Among the class of discrete time Markovian processes, two models are widely used, the Markov chain and the Hidden Markov Model. A major di erence between these two models lies in the relation between successive outputs of the observed variable. In a visible Markov chain, these are directly correlated while in hidden models they are not. However, in some situations it is possible to observe both...