scholarly journals A sufficient condition for a unique invariant distribution of a higher-order Markov chain

2017 ◽  
Vol 130 ◽  
pp. 49-56
Author(s):  
Bernhard C. Geiger
Keyword(s):  
Markov Chain ◽  
Higher Order ◽  
Invariant Distribution ◽  
Sufficient Condition ◽  
Order Markov Chain ◽  
Higher Order Markov Chain

Higher-order Markov chain models for categorical data sequences

2004 ◽  
Vol 51 (4) ◽  
pp. 557-574 ◽  
Author(s):  
Wai Ki Ching ◽  
Eric S. Fung ◽  
Michael K. Ng
Keyword(s):  
Markov Chain ◽  
Categorical Data ◽  
Higher Order ◽  
Markov Chain Models ◽  
Order Markov Chain ◽  
Higher Order Markov Chain

scholarly journals An Efficacy Predictive Method for Diabetic Ulcers Based on Higher-Order Markov Chain-Set Pair Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Le Kuai ◽  
Xiao-ya Fei ◽  
Jia-qi Xing ◽  
Jing-ting Zhang ◽  
Ke-qin Zhao ◽  
...  
Keyword(s):  
Markov Chain ◽  
Higher Order ◽  
Effect Evaluation ◽  
Curative Effect ◽  
Diabetic Ulcers ◽  
First Order ◽  
Order Markov Chain ◽  
Higher Order Markov Chain ◽  
Pair Analysis ◽  
Spa Model

Background. Clinical comprehensive decision-making of diabetic ulcers includes curative effect evaluation and curative effect prediction. Nevertheless, there are few studies on the prediction of diabetic ulcers. Methods. Set pair analysis (SPA) was used to assess the curative effect evaluation, and therapeutic effect was evaluated by connection degree (CD). The higher-order Markov chain-SPA curative effect prediction model was established to predict the future curative effect development. The predicted results with higher-order Markov chain-SPA and traditional first-order Markov-SPA model were compared with the actual results of the patients to verify the effectiveness of prediction. Results. The connection degree of index levels I and II of 15 patients with diabetic ulcers after traditional Chinese medicine (TCM) treatment increased with time, while that of index levels IV and V decreased, indicating that the curative effect tends to improve. The higher-order Markov chain-SPA model was used to predict the curative effect. The results showed that the relative errors were fewer than the traditional first-order Markov-SPA model. Conclusions. The present study suggests that a method of SPA combined with higher-order Markov-SPA is relatively effective and can be applied to the clinical prediction of diabetic ulcers, which has higher accuracy than traditional first-order curative effect prediction model.

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