The Italian market of sparkling wines increases as volume and assortment (such as brands, appellations, typologies) mainly because of sparkling Prosecco consumption. We investigate the repeated purchase behavior of sparkling wines in two years within the supermarket channel through scanner data collected from a consumer panel. We propose a Hidden Markov Model to analyze these data, assuming an unobservable process to capture consumers’ preferences and allowing us to consider purchases sparsity over time. We consider multivariate responses defining types of purchases, namely price, appellation, and sugar content. Customers’ covariates influence the initial and transition probabilities of the latent process. We identify five market segments, and we track their evolution over time. One segment includes Prosecco-oriented consumers, and we show that loyalty to Prosecco changes strongly over time according to the region of residence, income, and family type. The findings improve the understanding of the market and may provide evidence to design successful marketing strategies. (JEL Classifications: C33, C51, D12, L66)

Human–robot interaction (HRI) is becoming more important nowadays. In this paper, a low-cost communication system for HRI is designed and implemented on the Scout robot and a robotic face. A hidden Markov model-based voice command detection system is proposed and a non-native database has been collected by Persian speakers, which contains 10 desired English commands. The experimental results confirm that the proposed system is capable to recognize the voice commands, and properly performs the task or expresses the right answer. Comparing the system with a trained system on the Julius native database shows a better true detection (about 10%).

A new method of forecasting mortality is introduced. The method is based on the continuous-time dynamics of the Lexis diagram, which given weak assumptions implies that the death count data are Poisson distributed. The underlying mortality rates are modelled with a hidden Markov model (HMM) which enables a fully likelihood-based inference. Likelihood inference is done by particle filter methods, which avoids approximating assumptions and also suggests natural model validation measures. The proposed model class contains as special cases many previous models with the important difference that the HMM methods make it possible to estimate the model efficiently. Another difference is that the population and latent variable variability can be explicitly modelled and estimated. Numerical examples show that the model performs well and that inefficient estimation methods can severely affect forecasts.

Markov processes play an important role in reliability analysis and particularly in modeling the stochastic evolution of survival/failure behavior of systems. The probability law of Markov processes is described by its generator or the transition rate matrix. In this paper, we suppose that the process is doubly stochastic in the sense that the generator is also stochastic. In our model, we suppose that the entries in the generator change with respect to the changing states of yet another Markov process. This process represents the random environment that the stochastic model operates in. In fact, we have a Markov modulated Markov process which can be modeled as a bivariate Markov process that can be analyzed probabilistically using Markovian analysis. In this setting, however, we are interested in Bayesian inference on model parameters. We present a computationally tractable approach using Gibbs sampling and demonstrate it by numerical illustrations. We also discuss cases that involve complete and partial data sets on both processes.

Let (X, Y) = (Xn, Yn)n≥1 be the output process generated by a hidden chain Z = (Zn)n≥1, where Z is a finite-state, aperiodic, time homogeneous, and irreducible Markov chain. Let LCn be the length of the longest common subsequences of X1,..., Xn and Y1,..., Yn. Under a mixing hypothesis, a rate of convergence result is obtained for E[LCn]/n.

This paper addresses the construction of digital twins (exact mirror images of real-world in cyberspace) using hidden Markov models for the futuristic manufacturing systems known as Industry 4.0. The proposed digital twin consists of two components namely model component and simulation component. The model component forms a Markov chain that encapsulates the dynamics underlying the phenomenon by using some discrete states and their transition probabilities. The simulation component recreates the phenomenon using a Monte Carlo simulation process. The efficacy of the proposed digital twin construction methodology is shown by a case study, where the digital twin of the surface roughness of a surface created by successive grinding operations is described. The developers of the cyber-physical systems will be benefitted from the outcomes of this study because these systems need the computable virtual abstractions of the manufacturing phenomena to address the issues related to the maturity index of futuristic manufacturing systems (i.e., understand, predict, decide, and adopt).

Network scholars commonly encounter multiple networks, each of which is possibly governed by distinct generation rules while sharing a node group structure. Although the stochastic blockmodeling—detecting such latent group structures with group-specific connection profiles—has been a major topic of recent research, the focus has been given to the assortative group discovery of a single network. Despite its universality, concepts, and techniques for simultaneous characterization of node traits of multilayer networks, constructed by stacking multiple networks into layers, have been limited. Here, we propose a Bayesian multilayer stochastic blockmodeling framework that uncovers layer-common node traits and factors associated with layer-specific network generating functions. Without assuming a priori layer-specific generation rules, our fully Bayesian treatment allows probabilistic inference of latent traits. We extend the approach to detect changes in block structures embedded in temporal layers of network time series. We demonstrate the method using synthetic multilayer networks with assortative, disassortative, core-periphery, and overlapping community structures. Finally, we apply the method to empirical social network datasets, and find that it detects significant latent traits and structural changepoints. In particular, we uncover endogenous historical regimes associated with distinct constellations of states in United States Senate roll call vote similarity patterns.

We establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in V-norm, allowing for unbounded test functions. The analysis is conducted in an general setup involving nonnegative kernels in a random environment which allows treatment of filters and prediction filters in a single framework. The main result is illustrated on two examples, the first showing that a total variation norm stability result obtained by Douc et al. (2009) can be extended to V-norm without any additional assumptions, the second concerning a situation in which forgetting of the initial condition holds in V-norm for the filters, but the V-norm of each prediction filter is infinite.

Motivated by the gene tree/species tree problem from statistical phylogenetics, we extend the class of Markov branching trees to a parametric family of distributions on fragmentation trees that satisfies a generalized Markov branching property. The main theorems establish important statistical properties of this model, specifically necessary and sufficient conditions under which a family of trees can be constructed consistently as sample size grows. We also consider the question of attaching random edge lengths to these trees.

The bandwidth limitation of wideband (WB) audio systems degrades the subjective quality and naturalness of audio signals. In this paper, a new method for blind bandwidth extension of WB audio signals is proposed based on non-linear prediction and hidden Markov model (HMM). The high-frequency (HF) components in the band of 7–14 kHz are artificially restored only from the low-frequency information of the WB audio. State-space reconstruction is used to convert the fine spectrum of WB audio to a multi-dimensional space, and a non-linear prediction based on nearest-neighbor mapping is employed in the state space to restore the fine spectrum of the HF components. The spectral envelope of the resulting HF components is estimated based on an HMM according to the features extracted from the WB audio. In addition, the proposed method and the reference methods are applied to the ITU-T G.722.1 WB audio codec for comparison with the ITU-T G.722.1C super WB audio codec. Objective quality evaluation results indicate that the proposed method is preferred over the reference bandwidth extension methods. Subjective listening results show that the proposed method has a comparable audio quality with G.722.1C and improves the extension performance compared with the reference methods.

Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends on the set of observations. In this paper we establish, under general assumptions on the hidden Markov model, the tightness of the sequence of asymptotic variances when considered as functions of the random observations as the number of observations tends to infinity. We discuss our assumptions on examples and provide numerical simulations.

The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, Ann. Stat. 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, Ann. Inst. Henri Poincaré 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (i.e. independent regime switches). In this framework, we give sufficient conditions to keep the LRTS tight and compute its the asymptotic distribution. Second, we consider the extension of the ideas in Gassiat [Ann. Inst. Henri Poincaré 38 (2002) 897–906] to autoregressive models with regimes switches according to a Markov chain. In this case, it is shown that the marginal likelihood is no longer a contrast function and cannot be used to select the number of regimes. Some numerical examples illustrate the results and their convergence properties.

In many countries, high somatic cell scores (SCS) in milk are used as an indicator for mastitis because they are collected on a routine basis. However, individual test-day SCS are not very accurate in identifying infected cows. Mathematical models may improve the accuracy of the biological marker by making better use of the information contained in the available data. Here, a simple hidden Markov model (HMM) is described mathematically and applied to SCS recorded monthly on cows with or without clinical mastitis to evaluate its accuracy in estimating parameters (mean, variance and transition probabilities) under healthy or diseased states. The SCS means were estimated at 1.96 (s.d. = 0.16) and 4.73 (s.d. = 0.71) for the hidden healthy and infected states, and the common variance at 0.83 (s.d. = 0.11). The probability of remaining uninfected, recovering from infection, getting newly infected and remaining infected between consecutive test days was estimated at 78.84%, 60.49%, 11.70% and 15%, respectively. Three different health-related states were compared: clinical stages observed by farmers, subclinical cases defined for somatic cell counts below or above 250 000 cells/ml and infected stages obtained from the HMM. The results showed that HMM identifies infected cows before the appearance of clinical and subclinical signs, which may critically improve the power of the studies on the genetic determinants of SCS and reduce biases in predicting breeding values for SCS.

Application of map-matching techniques to GPS positions can provide accurate vehicle location information in challenging situations. The Hidden Markov Model (HMM) is a statistical model that is well known for providing solutions to temporal recognition applications such as text and speech recognition. This paper introduces a novel map-matching algorithm based on HMM for GPS-based wheelchair navigation. Given GPS positions, a hidden Markov chain model is established by using both geometric data and the topology of sidewalk segments. The map-matching algorithm employs the Viterbi algorithm to estimate correct sidewalk segments as hidden states in a HMM in order to match GPS trajectory on the corresponding segment sequence. The HMM-based map-matching algorithm was validated on a campus sidewalk network for wheelchair navigation. The results show an improvement in tracking a wheelchair in dense urban conditions both in accuracy and in computational time.

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 process, relying on information theoretic arguments. The novelty of our work relies in the joint estimation of two structural parameters. Furthermore, the different models in competition are not nested. In an asymptotic framework, we prove that a penalized maximum likelihood estimator is strongly consistent without prior bounds on k and m. We complement our theoretical work with a simulation study of its behaviour. We also study numerically the behaviour of the BIC criterion. A theoretical proof of its consistency seems to us presently out of reach for MCMR, as such a result does not yet exist in the simpler case where m = 0 (that is for hidden Markov models).