Taboo rate and hitting time distribution of continuous-time reversible Markov chains

Xiang, Xuyan; Hai-qin, FU; Zhou, Jieming; Deng, Yingchun; Yang, Xiangqun

doi:10.1016/j.spl.2020.108969

“…For the random process { ( ), ∈ }, the Markov process expression is as follows: MC) is a random process with Markov properties, a special form of Markov process, which is discrete in state and time (Xiang et al, 2021). MC has no aftereffect of Markov process, indicating that its subsequent state is only related to the current state and has nothing to do with the previous state.…”

mentioning

confidence: 99%

Runoff forecast and analysis of the probability of dry and wet transition in the Hanjiang River Basin

Jin

¹

,

Chen

²

,

Zhong

³

2021

Stoch Environ Res Risk Assess

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Runoff prediction has an important guiding role in the planning and management of regional water resources, flood prevention and drought resistance, and can effectively predict the risk of changes in regional water resources. This study used 12 runoff prediction methods to predict the runoff of four hydrological stations in the Hanjiang River Basin (HRB). Through the MCMC method, the HRB runoff probability conversion model from low to high (high to low) is constructed. The study found that the runoff of the HRB had a decreasing trend. In the mid-1980s, the runoff had a significant decreasing trend. The smoother the runoff changes, the easier it is to make accurate prediction. On the whole, the QS-MFM, MFM, MA-MFM, CES and DNN methods have strong generalization ability and can more accurately predict the runoff of the HRB. The Logistic model can accurately simulate the change of runoff status in the HRB. Among them, the HLT station has the fastest conversion rate of drought and flood, and the flow that generates floods is 6 times that of drought. The smaller the basin area, the larger the gap between drought and flood discharge. Overall, this research provides important technical support for the prediction of change in water resources and the transition probability from drought to flood in the HRB.

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Identifying the generator matrix of a stationary Markov chain using partially observable data

Xiang,

Zhou,

Deng

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

4

0

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Given that most states in real-world systems are inaccessible, it is critical to study the inverse problem of an irreversibly stationary Markov chain regarding how a generator matrix can be identified using minimal observations. The hitting-time distribution of an irreversibly stationary Markov chain is first generalized from a reversible case. The hitting-time distribution is then decoded via the taboo rate, and the results show remarkably that under mild conditions, the generator matrix of a reversible Markov chain or a specific case of irreversibly stationary ones can be identified by utilizing observations from all leaves and two adjacent states in each cycle. Several algorithms are proposed for calculating the generator matrix accurately, and numerical examples are presented to confirm their validity and efficiency. An application to neurophysiology is provided to demonstrate the applicability of such statistics to real-world data. This means that partially observable data can be used to identify the generator matrix of a stationary Markov chain.

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Runoff Forecast and Analysis of the Probability of Dry and Wet Transition in the Hanjiang River Basin

Jin

¹

,

Chen

²

,

Zhong

³

2021

Preprint

0

View full text Add to dashboard Cite

Runoff prediction has an important guiding role in the planning and management of regional water resources, flood prevention and drought resistance, and can effectively predict the risk of changes in regional water resources. This study used 12 runoff prediction methods to predict the runoff of four hydrological stations in the Hanjiang River Basin (HRB). Through the MCMC method, the HRB runoff probability conversion model from low to high (high to low) is constructed. The study found that the runoff of the HRB had a decreasing trend. In the mid-1980s, the runoff had a significant decreasing trend. The smoother the runoff changes, the easier it is to make accurate prediction. On the whole, the QS-MFM, MFM, MA-MFM, CES and DNN methods have strong generalization ability and can more accurately predict the runoff of the HRB. The Logistic model can accurately simulate the change of runoff status in the HRB. Among them, the HLT station has the fastest conversion rate of drought and flood, and the flow that generates floods is 6 times that of drought. The smaller the basin area, the larger the gap between drought and flood discharge. Overall, this research provides important technical support for the prediction of change in water resources and the transition probability from drought to flood in the HRB.

show abstract

Taboo rate and hitting time distribution of continuous-time reversible Markov chains

Cited by 3 publications

References 18 publications

Runoff forecast and analysis of the probability of dry and wet transition in the Hanjiang River Basin

Runoff forecast and analysis of the probability of dry and wet transition in the Hanjiang River Basin

Identifying the generator matrix of a stationary Markov chain using partially observable data

Runoff Forecast and Analysis of the Probability of Dry and Wet Transition in the Hanjiang River Basin

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