scholarly journals Recognizing duration effects in multistate population models

Genus ◽  
2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Robert Schoen
Keyword(s):  
Markov Models ◽  
General Procedure ◽  
Transition Probability ◽  
Population Data ◽  
Cross Product ◽  
Transition Probability Matrix ◽  
Current State ◽  
State Duration ◽  
Markov Transition ◽  
Data Limitations

AbstractThe risk of many demographic events varies by both current state and duration in that state. However, the use of such semi-Markov models has been substantially constrained by data limitations. Here, a new specification of the semi-Markov transition probability matrix in terms of the underlying rates is provided, and a general procedure is developed to estimate semi-Markov probabilities and rates from adjacent population data.Multistate models recognizing marriage and divorce by duration in state are constructed for United States Females, 1995. The results show that recognizing duration in the married and divorced states adds significantly to the model’s analytical value. Extending the constant-α method to semi-Markov models, 2000–2005 U.S. population data and 1995 cross-product ratios are employed to estimate 2000–2005 duration-dependent transfer probabilities and rates.The present analyses provide new relationships between probabilities and rates in semi-Markov models. Extending the constant cross-product ratio estimation approach opens new sources of data and expands the range of data susceptible to state-duration analyses.

scholarly journals Hidden Semi-Markov Models for Predictive Maintenance

2015 ◽  
Vol 2015 ◽  
pp. 1-23 ◽  
Author(s):  
Francesco Cartella ◽  
Jan Lemeire ◽  
Luca Dimiccoli ◽  
Hichem Sahli
Keyword(s):  
Markov Models ◽  
Real Data ◽  
Information Criterion ◽  
Absolute Error ◽  
Predictive Maintenance ◽  
Average Absolute Error ◽  
Current State ◽  
Automatic Model Selection ◽  
State Duration ◽  
Useful Lifetime

Realistic predictive maintenance approaches are essential for condition monitoring and predictive maintenance of industrial machines. In this work, we propose Hidden Semi-Markov Models (HSMMs) with (i) no constraints on the state duration density function and (ii) being applied to continuous or discrete observation. To deal with such a type of HSMM, we also propose modifications to the learning, inference, and prediction algorithms. Finally, automatic model selection has been made possible using the Akaike Information Criterion. This paper describes the theoretical formalization of the model as well as several experiments performed on simulated and real data with the aim of methodology validation. In all performed experiments, the model is able to correctly estimate the current state and to effectively predict the time to a predefined event with a low overall average absolute error. As a consequence, its applicability to real world settings can be beneficial, especially where in real time the Remaining Useful Lifetime (RUL) of the machine is calculated.

scholarly journals On the evolution of corruption patterns in the post-communist countries

Equilibrium ◽  
2015 ◽  
Vol 10 (1) ◽  
pp. 33 ◽  
Author(s):  
Andrzej Cieślik ◽  
Łukasz Goczek
Keyword(s):  
Transition Probability ◽  
Transition Probability Matrix ◽  
Markov Transition Probability ◽  
Long Run ◽  
Markov Transition ◽  
Corruption Index ◽  
Communist Countries ◽  
Control Of Corruption ◽  
Over Time

In this paper, we study the evolution of corruption patterns in 27 post-communist countries during the period 1996-2012 using the Control of Corruption Index and the corruption category Markov transition probability matrix. This method allows us to generate the long-run distribution of corruption among the post-communist countries. Our empirical findings suggest that corruption in the post-communist countries is a very persistent phenomenon that does not change much over time. Several theoretical explanations for such a result are provided.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models

2018 ◽  
Vol 28 (5) ◽  
pp. 1552-1563 ◽  
Author(s):  
Tunny Sebastian ◽  
Visalakshi Jeyaseelan ◽  
Lakshmanan Jeyaseelan ◽  
Shalini Anandan ◽  
Sebastian George ◽  
...  
Keyword(s):  
Logistic Regression ◽  
Markov Chain ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Passage Time ◽  
Transition Probability Matrix ◽  
Ordinal Logistic Regression ◽  
The Mean

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as ‘Low’, ‘Moderate’ and ‘High’ with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

scholarly journals Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models

2021 ◽  
Author(s):  
Giorgio Eduardo Montanari ◽  
Marco Doretti ◽  
Maria Francesca Marino
Keyword(s):  
Random Effects ◽  
Markov Models ◽  
Transition Probability ◽  
Random Effect ◽  
Transition Probability Matrix ◽  
Probability Vector ◽  
Physical Health Status ◽  
Model Based ◽  
Latent Markov Model ◽  
Special Case

AbstractIn this paper, an ordinal multilevel latent Markov model based on separate random effects is proposed. In detail, two distinct second-level discrete effects are considered in the model, one affecting the initial probability vector and the other affecting the transition probability matrix of the first-level ordinal latent Markov process. To model these separate effects, we consider a bi-dimensional mixture specification that allows to avoid unverifiable assumptions on the random effect distribution and to derive a two-way clustering of second-level units. Starting from a general model where the two random effects are dependent, we also obtain the independence model as a special case. The proposal is applied to data on the physical health status of a sample of elderly residents grouped into nursing homes. A simulation study assessing the performance of the proposal is also included.

scholarly journals Variational Beta Process Hidden Markov Models with Shared Hidden States for Trajectory Recognition

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1290
Author(s):  
Jing Zhao ◽  
Yi Zhang ◽  
Shiliang Sun ◽  
Haiwei Dai
Keyword(s):  
Dirichlet Process ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Beta Process ◽  
Shared Information ◽  
Long Time ◽  
Real World Datasets ◽  
Hidden States

Hidden Markov model (HMM) is a vital model for trajectory recognition. As the number of hidden states in HMM is important and hard to be determined, many nonparametric methods like hierarchical Dirichlet process HMMs and Beta process HMMs (BP-HMMs) have been proposed to determine it automatically. Among these methods, the sampled BP-HMM models the shared information among different classes, which has been proved to be effective in several trajectory recognition scenes. However, the existing BP-HMM maintains a state transition probability matrix for each trajectory, which is inconvenient for classification. Furthermore, the approximate inference of the BP-HMM is based on sampling methods, which usually takes a long time to converge. To develop an efficient nonparametric sequential model that can capture cross-class shared information for trajectory recognition, we propose a novel variational BP-HMM model, in which the hidden states can be shared among different classes and each class chooses its own hidden states and maintains a unified transition probability matrix. In addition, we derive a variational inference method for the proposed model, which is more efficient than sampling-based methods. Experimental results on a synthetic dataset and two real-world datasets show that compared with the sampled BP-HMM and other related models, the variational BP-HMM has better performance in trajectory recognition.

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