Bivariate modelling of precipitation and temperature using a non-homogeneous hidden Markov model

Aiming to generate realistic synthetic times series of the bivariate process of daily mean temperature and precipitations, we introduce a non-homogeneous hidden Markov model. The non-homogeneity lies in periodic transition probabilities between the hidden states, and time-dependent emission distributions. This enables the model to account for the non-stationary behaviour of weather variables. By carefully choosing the emission distributions, it is also possible to model the dependance structure between the two variables. The model is applied to several weather stations in Europe with various climates, and we show that it is able to simulate realistic bivariate time series

Hidden Markov Models and their Application for Predicting Failure Events

We show how Markov mixed membership models (MMMM) can be used to predict the degradation of assets. We model the degradation path of individual assets, to predict overall failure rates. Instead of a separate distribution for each hidden state, we use hierarchical mixtures of distributions in the exponential family. In our approach the observation distribution of the states is a finite mixture distribution of a small set of (simpler) distributions shared across all states. Using tied-mixture observation distributions offers several advantages. The mixtures act as a regularization for typically very sparse problems, and they reduce the computational effort for the learning algorithm since there are fewer distributions to be found. Using shared mixtures enables sharing of statistical strength between the Markov states and thus transfer learning. We determine for individual assets the trade-off between the risk of failure and extended operating hours by combining a MMMM with a partially observable Markov decision process (POMDP) to dynamically optimize the policy for when and how to maintain the asset.Comment: Will be published in the proceedings of ICCS 2020; @Booklet{EasyChair:3183, author = {Paul Hofmann and Zaid Tashman}, title = {Hidden Markov Models and their Application for Predicting Failure Events}, howpublished = {EasyChair Preprint no. 3183}, year = {EasyChair, 2020}

Short note on two output-dependent hidden Markov models

The purpose of this note is to study the assumption of mutual information independence", which is used by Zhou (2005) for deriving an output-dependent hidden Markov model, the so-called discriminative HMM (D-HMM), in the context of determining a stochastic optimal sequence of hidden states. The assumption is extended to derive its generative counterpart, the G-HMM. In addition, state-dependent representations for two output-dependent HMMs, namely HMMSDO (Li, 2005) and D-HMM, are presented