We argue that our research objectives in Liechty, Pieters, and Wedel (2003) are to provide generalizable insights into covert visual attention to complex, multimodal stimuli in their natural context, through inverse inference from eye-movement data. We discuss the most important issues raised by Feng (2003) and Reichle and Nelson (2003), in particular the task definition, inclusion of ad features, object-based versus space-based attention and the evidence for the where and what streams.

This article reviews recent advances in the psychometric and econometric modeling of eye-movements during decision making. Eye movements offer a unique window on unobserved perceptual, cognitive, and evaluative processes of people who are engaged in decision making tasks. They provide new insights into these processes, which are not easily available otherwise, allow for explanations of fundamental search and choice phenomena, and enable predictions of future decisions. We propose a theoretical framework of the search and choice tasks that people commonly engage in and of the underlying cognitive processes involved in those tasks. We discuss how these processes drive specific eye-movement patterns. Our framework emphasizes the central role of task and strategy switching for complex goal attainment. We place the extant literature within that framework, highlight recent advances in modeling eye-movement behaviors during search and choice, discuss limitations, challenges, and open problems. An agenda for further psychometric modeling of eye movements during decision making concludes the review.

Liechty, Pieters & Wedel (2003) developed a hidden Markov Model (HMM) to identify the states of an attentional process in an advertisement viewing task. This work is significant because it demonstrates the benefits of stochastic modeling and Bayesian estimation in making inferences about cognitive processes based on eye movement data. One limitation of the proposed approach is that attention is conceptualized as an autonomous random process that is affected neither by the overall layout of the stimulus nor by the visual information perceived during the current fixation. An alternative model based on the input-output hidden Markov model (IOHMM; Bengio, 1999) is suggested as an extension of the HMM. The need for further studies that validate the HMM classification results is also discussed.

Hidden Markov models (HMMs) have been applied in various domains, which makes the identifiability issue of HMMs popular among researchers. Classical identifiability conditions shown in previous studies are too strong for practical analysis. In this paper, we propose generic identifiability conditions for discrete time HMMs with finite state space. Also, recent studies about cognitive diagnosis models (CDMs) applied first-order HMMs to track changes in attributes related to learning. However, the application of CDMs requires a known $\mathit{Q}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varvec{Q}$$\end{document} matrix to infer the underlying structure between latent attributes and items, and the identifiability constraints of the model parameters should also be specified. We propose generic identifiability constraints for our restricted HMM and then estimate the model parameters, including the $\mathit{Q}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varvec{Q}$$\end{document} matrix, through a Bayesian framework. We present Monte Carlo simulation results to support our conclusion and apply the developed model to a real dataset.

Maintaining a stable score scale over time is critical for all standardized educational assessments. Traditional quality control tools and approaches for assessing scale drift either require special equating designs, or may be too time-consuming to be considered on a regular basis with an operational test that has a short time window between an administration and its score reporting. Thus, the traditional methods are not sufficient to catch unusual testing outcomes in a timely manner. This paper presents a new approach for score monitoring and assessment of scale drift. It involves quality control charts, model-based approaches, and time series techniques to accommodate the following needs of monitoring scale scores: continuous monitoring, adjustment of customary variations, identification of abrupt shifts, and assessment of autocorrelation. Performance of the methodologies is evaluated using manipulated data based on real responses from 71 administrations of a large-scale high-stakes language assessment.

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.