Posterior consistency for partially observed Markov models

Analyzing progression of diseases is vital to monitor patient's traversal over time through a disease. Clinical study settings present modeling challenges, as patients' disease trajectories are only partially observed, and patients' disease statuses are only assessed at clinic visit times. HIV disease is a continuum of progressive damage to the immune system from the time of infection to the manifestation of severe immunologic damage. We proposed a semi-Markov model and collected data at Yirgalem General Hospital. Our study found that for an HIV/AIDS patient the transition probability from a given state to the next worse state increases within the good states as time gets optimum and then decreases with increasing time during a follow up. In a specific state of the disease a patient will stay in that state with a non- zero probability in good states and a patient will transit to the next state either to the worst or to the good state with a non-zero probability. The probability of being in same state decreases over time. With the good or alive states, the probability of being in a better state is non-zero, but less than the probability of being in worst states. The survival probabilities are decreasing with increasing time. Therefore, we recommend that increased clinical care for patients on ART services should be strengthen and patients need to regularly check their CD4 T cell count in the appropriate day based on physician order to timely know and monitor their disease status to improve the survival probability and to reduce mortality.

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A Test for the Underlying State-Structure of Hidden Markov Models: Partially Observed Capture-Recapture Data

Frontiers in Ecology and Evolution ◽

10.3389/fevo.2021.598325 ◽

2021 ◽

Vol 9 ◽

Author(s):

Anita Jeyam ◽

Rachel S. McCrea ◽

Roger Pradel

Keyword(s):

Hidden Markov Models ◽

Markov Models ◽

Hidden Markov ◽

Canada Geese ◽

State Structure ◽

Data Set ◽

Partial Observations ◽

Partially Observed ◽

Capture Recapture ◽

Special Case

Hidden Markov models (HMMs) are being widely used in the field of ecological modeling, however determining the number of underlying states in an HMM remains a challenge. Here we examine a special case of capture-recapture models for open populations, where some animals are observed but it is not possible to ascertain their state (partial observations), whilst the other animals' states are assigned without error (complete observations). We propose a mixture test of the underlying state structure generating the partial observations, which assesses whether they are compatible with the set of states observed in the complete observations. We demonstrate the good performance of the test using simulation and through application to a data set of Canada Geese.

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Quantitative Methods for Estimating the Size of a Drug-Using Population

Journal of Drug Issues ◽

10.1177/002204269302300204 ◽

1993 ◽

Vol 23 (2) ◽

pp. 185-216 ◽

Cited By ~ 31

Author(s):

Thomas D. Wickens

Keyword(s):

Drug Use ◽

System Dynamics ◽

Quantitative Methods ◽

Linear Models ◽

Markov Models ◽

Partially Observed ◽

Capture Recapture ◽

Closed Populations ◽

Log Linear ◽

Dynamics Models

The author describes several of the most important quantitative procedures for estimating the size of an unobserved or partially observed population, with specific application to the estimation of the prevalence of drug use. The methods discussed include synthetic estimation, truncated Poisson estimates, multiple-capture surveys in both closed populations (the capture-recapture model and log-linear models) and open populations (the Jolly-Seber model and Markov models), and, more briefly, system dynamics models.

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Large margin training for hidden Markov models with partially observed states

Proceedings of the 26th Annual International Conference on Machine Learning - ICML '09 ◽

10.1145/1553374.1553408 ◽

2009 ◽

Cited By ~ 64

Author(s):

Trinh-Minh-Tri Do ◽

Thierry Artières

Keyword(s):

Hidden Markov Models ◽

Markov Models ◽

Hidden Markov ◽

Large Margin ◽

Partially Observed

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Uncertainty modelling and computational aspects of data association

Statistics and Computing ◽

10.1007/s11222-021-10039-1 ◽

2021 ◽

Vol 31 (5) ◽

Author(s):

Jeremie Houssineau ◽

Jiajie Zeng ◽

Ajay Jasra

Keyword(s):

Markov Models ◽

Hidden Markov ◽

Possibility Theory ◽

Uncertainty Modelling ◽

Alternative Representation ◽

Lack Of Information ◽

Partially Observed ◽

Computational Aspects ◽

Particle Mcmc ◽

Filtering Problem

AbstractA novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted observations. In order to account for the lack of information about the different aspects of this type of complex system, an alternative representation of uncertainty based on possibility theory is considered. It is shown how analogues of usual concepts such as Markov chains and hidden Markov models (HMMs) can be introduced in this context. In particular, the considered statistical model for multiple dynamical objects can be formulated as a hierarchical model consisting of conditionally independent HMMs. This structure is leveraged to propose an efficient method in the context of Markov chain Monte Carlo (MCMC) by relying on an approximate solution to the corresponding filtering problem, in a similar fashion to particle MCMC. This approach is shown to outperform existing algorithms in a range of scenarios.

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