Non-Homogeneous Markov Set Systems
A more realistic way to describe a model is the use of intervals which contain the required values of the parameters. In practice we estimate the parameters from a set of data and it is natural that they will be in confidence intervals. In the present study, we study Non-Homogeneous Markov Systems (...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/471 |
| _version_ | 1827588293806522368 |
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| author | P.-C.G. Vassiliou |
| author_facet | P.-C.G. Vassiliou |
| author_sort | P.-C.G. Vassiliou |
| collection | DOAJ |
| description | A more realistic way to describe a model is the use of intervals which contain the required values of the parameters. In practice we estimate the parameters from a set of data and it is natural that they will be in confidence intervals. In the present study, we study Non-Homogeneous Markov Systems (NHMS) processes for which the required basic parameters are in intervals. We call such processes Non-Homogeneous Markov Set Systems (NHMSS). First we study the set of the relative expected population structure of memberships and we prove that under certain conditions of convexity of the intervals of the parameters the set is compact and convex. Next, we establish that if the NHMSS starts with two different initial distributions sets and allocation probability sets under certain conditions, asymptotically the two expected relative population structures coincide geometrically fast. We continue proving a series of theorems on the asymptotic behavior of the expected relative population structure of a NHMSS and the properties of their limit set. Finally, we present an application for geriatric and stroke patients in a hospital and through it we solve problems that surface in an application. |
| first_indexed | 2024-03-09T00:32:24Z |
| format | Article |
| id | doaj.art-58d102118b9d40fda2856dd220ddada7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T00:32:24Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-58d102118b9d40fda2856dd220ddada72023-12-11T18:23:39ZengMDPI AGMathematics2227-73902021-02-019547110.3390/math9050471Non-Homogeneous Markov Set SystemsP.-C.G. Vassiliou0Department of Statistical Science, University College London, Gower St, London WC1E 6BT, UKA more realistic way to describe a model is the use of intervals which contain the required values of the parameters. In practice we estimate the parameters from a set of data and it is natural that they will be in confidence intervals. In the present study, we study Non-Homogeneous Markov Systems (NHMS) processes for which the required basic parameters are in intervals. We call such processes Non-Homogeneous Markov Set Systems (NHMSS). First we study the set of the relative expected population structure of memberships and we prove that under certain conditions of convexity of the intervals of the parameters the set is compact and convex. Next, we establish that if the NHMSS starts with two different initial distributions sets and allocation probability sets under certain conditions, asymptotically the two expected relative population structures coincide geometrically fast. We continue proving a series of theorems on the asymptotic behavior of the expected relative population structure of a NHMSS and the properties of their limit set. Finally, we present an application for geriatric and stroke patients in a hospital and through it we solve problems that surface in an application.https://www.mdpi.com/2227-7390/9/5/471Non-Homogeneous Markov SystemsMarkov Set Systemslimiting set |
| spellingShingle | P.-C.G. Vassiliou Non-Homogeneous Markov Set Systems Mathematics Non-Homogeneous Markov Systems Markov Set Systems limiting set |
| title | Non-Homogeneous Markov Set Systems |
| title_full | Non-Homogeneous Markov Set Systems |
| title_fullStr | Non-Homogeneous Markov Set Systems |
| title_full_unstemmed | Non-Homogeneous Markov Set Systems |
| title_short | Non-Homogeneous Markov Set Systems |
| title_sort | non homogeneous markov set systems |
| topic | Non-Homogeneous Markov Systems Markov Set Systems limiting set |
| url | https://www.mdpi.com/2227-7390/9/5/471 |
| work_keys_str_mv | AT pcgvassiliou nonhomogeneousmarkovsetsystems |