scholarly journals A Hidden Markov Model to Address Measurement Errors in Ordinal Response Scale and Non-Decreasing Process

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 622 ◽  
Author(s):  
Lizbeth Naranjo ◽  
Luz Judith R. Esparza ◽  
Carlos J. Pérez
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Latent Variables ◽  
Measurement Errors ◽  
Hidden Markov ◽  
Response Scale ◽  
Ordinal Response ◽  
Continuous State Space ◽  
Continuous State ◽  
Categorical Response

A Bayesian approach was developed, tested, and applied to model ordinal response data in monotone non-decreasing processes with measurement errors. An inhomogeneous hidden Markov model with continuous state-space was considered to incorporate measurement errors in the categorical response at the same time that the non-decreasing patterns were kept. The computational difficulties were avoided by including latent variables that allowed implementing an efficient Markov chain Monte Carlo method. A simulation-based analysis was carried out to validate the approach, whereas the proposed approach was applied to analyze aortic aneurysm progression data.

A hidden Markov model addressing measurement errors in the response and replicated covariates for continuous nondecreasing processes

Biostatistics ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 743-757 ◽  
Author(s):  
Lizbeth Naranjo ◽  
Carlos J Pérez ◽  
Ruth Fuentes-García ◽  
Jacinto Martín
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Measurement Errors ◽  
Hidden Markov ◽  
Model Performance ◽  
Continuous Response ◽  
Continuous State Space ◽  
Continuous State ◽  
Simulation Based ◽  
Subject Variability

Summary Motivated by a study tracking the progression of Parkinson’s disease (PD) based on features extracted from voice recordings, an inhomogeneous hidden Markov model with continuous state-space is proposed. The approach addresses the measurement error in the response, the within-subject variability of the replicated covariates and presumed nondecreasing response. A Bayesian framework is described and an efficient Markov chain Monte Carlo method is developed. The model performance is evaluated through a simulation-based example and the analysis of a PD tracking progression dataset is presented. Although the approach was motivated by a PD tracking progression problem, it can be applied to any monotonic nondecreasing process whose continuous response variable is subject to measurement errors and where replicated covariates play a key role.

A mixed hidden Markov model for multivariate monotone disease processes in the presence of measurement errors

2020 ◽  
pp. 1471082X2097347
Author(s):  
Lizbeth Naranjo ◽  
Emmanuel Lesaffre ◽  
Carlos J. Pérez
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Conditional Independence ◽  
Hidden Markov ◽  
Caries Experience ◽  
Binary Outcomes ◽  
Model Parameters ◽  
Longitudinal Response ◽  
Continuous State ◽  
Latent Scale

Motivated by a longitudinal oral health study, the Signal-Tandmobiel® study, an inhomogeneous mixed hidden Markov model with continuous state-space is proposed to explain the caries disease process in children between 6 and 12 years of age. The binary caries experience outcomes are subject to misclassification. We modelled this misclassification process via a longitudinal latent continuous response subject to a measurement error process and showing a monotone behaviour. The baseline distributions of the unobservable continuous processes are defined as a function of the covariates through the specification of conditional distributions making use of the Markov property. In addition, random effects are considered to model the relationships among the multivariate responses. Our approach is in contrast with a previous approach working on the binary outcome scale. This method requires conditional independence of the possibly corrupted binary outcomes on the true binary outcomes. We assumed conditional independence on the latent scale, which is a weaker assumption than conditional independence on the binary scale. The aim of this article is therefore to show the properties of a model for a progressive longitudinal response with misclassification on the manifest scale but modelled on the latent scale. The model parameters are estimated in a Bayesian way using an efficient Markov chain Monte Carlo method. The model performance is shown through a simulation-based example, and the analysis of the motivating dataset is presented.

Analysis of demand in steel and iron industry – latent variables model

2020 ◽  
Vol 66 (4) ◽  
pp. 247-269
Author(s):  
Magdalena Barska
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Latent Variables ◽  
Hidden Markov ◽  
Second Order ◽  
Model Parameters ◽  
Iron Industry ◽  
Economic Cycles ◽  
Multiple Factors ◽  
Analysis Of Time Series

Demand in the steel and iron industry is influenced by multiple factors. Not all of them can be identified and measured. The paper presents the results of the analysis of the levels of demand achieved by a selected enterprise from this sector in the years 2010–2014. The aim of the study is to build a hidden Markov model which would reflect the turning points of this demand, thus making it possible to forecast its future levels. The model’s forecasting properties and stability have been examined. A simulation has been carried out that involved generating a high number of series for selected model parameters and checking their properties. This demonstrated that a three-state second order hidden Markov model was most relevant to the purpose of the study. Thanks to the model’s application, it was possible to describe states which could potentially shape the demand. Moreover, taking the transition state into consideration allowed spotting the signal about the upcoming replacement of the growth phase with the decline phase, and vice versa. The presented second order hidden Markov model can serve as an alternative to the traditional methods of the analysis of time series. The forecast generated by the model informs about the shaping of a trend in demand and serves as an indication of the shifts in economic cycles.

scholarly journals A Transformer-Based Hierarchical Variational Autoencoder Combined Hidden Markov Model for Long Text Generation

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1277
Author(s):  
Kun Zhao ◽  
Hongwei Ding ◽  
Kai Ye ◽  
Xiaohui Cui
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Latent Variables ◽  
Latent Variable ◽  
Hidden Markov ◽  
Variable Structure ◽  
Text Generation ◽  
Short Text ◽  
Variational Autoencoder ◽  
Generation Network

The Variational AutoEncoder (VAE) has made significant progress in text generation, but it focused on short text (always a sentence). Long texts consist of multiple sentences. There is a particular relationship between each sentence, especially between the latent variables that control the generation of the sentences. The relationships between these latent variables help in generating continuous and logically connected long texts. There exist very few studies on the relationships between these latent variables. We proposed a method for combining the Transformer-Based Hierarchical Variational Autoencoder and Hidden Markov Model (HT-HVAE) to learn multiple hierarchical latent variables and their relationships. This application improves long text generation. We use a hierarchical Transformer encoder to encode the long texts in order to obtain better hierarchical information of the long text. HT-HVAE’s generation network uses HMM to learn the relationship between latent variables. We also proposed a method for calculating the perplexity for the multiple hierarchical latent variable structure. The experimental results show that our model is more effective in the dataset with strong logic, alleviates the notorious posterior collapse problem, and generates more continuous and logically connected long text.

Auscultating Diagnosis for Hemodialysis Shunt Stenosis using a Self-Organizing Map and Hidden Markov Model

2012 ◽  
Vol 132 (10) ◽  
pp. 1589-1594 ◽  
Author(s):  
Hayato Waki ◽  
Yutaka Suzuki ◽  
Osamu Sakata ◽  
Mizuya Fukasawa ◽  
Hatsuhiro Kato
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov ◽  
Self Organizing Map ◽  
Self Organizing
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