The perturbation bound for the Perron vector of a transition probability tensor

2013 ◽  
Vol 20 (6) ◽  
pp. 985-1000 ◽  
Author(s):  
Wen Li ◽  
Lu-Bin Cui ◽  
Michael K. Ng
Keyword(s):  
Transition Probability ◽  
Perturbation Bound ◽  
Perron Vector

scholarly journals The Diameter and Laplacian Eigenvalues of Directed Graphs

10.37236/1142 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Fan Chung
Keyword(s):  
Random Walk ◽  
Directed Graphs ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Undirected Graphs ◽  
Laplacian Eigenvalues ◽  
Strongly Connected ◽  
Perron Vector

For undirected graphs it has been known for some time that one can bound the diameter using the eigenvalues. In this note we give a similar result for the diameter of strongly connected directed graphs $G$, namely $$ D(G) \leq \bigg \lfloor {2\min_x \log (1/\phi(x))\over \log{2\over 2-\lambda}} \bigg\rfloor +1 $$ where $\lambda$ is the first non-trivial eigenvalue of the Laplacian and $\phi$ is the Perron vector of the transition probability matrix of a random walk on $G$.

scholarly journals Sensitivity of hidden Markov models

2005 ◽  
Vol 42 (03) ◽  
pp. 632-642 ◽  
Author(s):  
Alexander Yu. Mitrophanov ◽  
Alexandre Lomsadze ◽  
Mark Borodovsky
Keyword(s):  
Markov Chain ◽  
Hidden Markov Models ◽  
Stochastic Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Initial Distribution ◽  
Transition Probability Matrix ◽  
Perturbation Bound ◽  
Semi Markov Processes

We derive a tight perturbation bound for hidden Markov models. Using this bound, we show that, in many cases, the distribution of a hidden Markov model is considerably more sensitive to perturbations in the emission probabilities than to perturbations in the transition probability matrix and the initial distribution of the underlying Markov chain. Our approach can also be used to assess the sensitivity of other stochastic models, such as mixture processes and semi-Markov processes.

scholarly journals Sensitivity of hidden Markov models

2005 ◽  
Vol 42 (3) ◽  
pp. 632-642 ◽  
Author(s):  
Alexander Yu. Mitrophanov ◽  
Alexandre Lomsadze ◽  
Mark Borodovsky
Keyword(s):  
Markov Chain ◽  
Hidden Markov Models ◽  
Stochastic Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Initial Distribution ◽  
Transition Probability Matrix ◽  
Perturbation Bound ◽  
Semi Markov Processes

We derive a tight perturbation bound for hidden Markov models. Using this bound, we show that, in many cases, the distribution of a hidden Markov model is considerably more sensitive to perturbations in the emission probabilities than to perturbations in the transition probability matrix and the initial distribution of the underlying Markov chain. Our approach can also be used to assess the sensitivity of other stochastic models, such as mixture processes and semi-Markov processes.

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

Regional household poverty and mobility analysis – a transition probability approach

2020 ◽  
Vol 63 (3) ◽  
pp. 286-302
Author(s):  
Damian Mowczan ◽  
Keyword(s):  
Transition Probability ◽  
General Level ◽  
Transition Matrices ◽  
Equivalent Unit ◽  
Central Statistical ◽  
Per Capita ◽  
Probability Matrices ◽  
General Mobility ◽  
One Year ◽  
The One

The main objective of this paper was to estimate and analyse transition-probability matrices for all 16 of Poland’s NUTS-2 level regions (voivodeship level). The analysis is conducted in terms of the transitions among six expenditure classes (per capita and per equivalent unit), focusing on poverty classes. The period of analysis was two years: 2015 and 2016. The basic aim was to identify both those regions in which the probability of staying in poverty was the highest and the general level of mobility among expenditure classes. The study uses a two-year panel sub-sample of unidentified unit data from the Central Statistical Office (CSO), specifically the data concerning household budget surveys. To account for differences in household size and demographic structure, the study used expenditures per capita and expenditures per equivalent unit simultaneously. To estimate the elements of the transition matrices, a classic maximum-likelihood estimator was used. The analysis used Shorrocks’ and Bartholomew’s mobility indices to assess the general mobility level and the Gini index to assess the inequality level. The results show that the one-year probability of staying in the same poverty class varies among regions and is lower for expenditures per equivalent units. The highest probabilities were identified in Podkarpackie (expenditures per capita) and Opolskie (expenditures per equivalent unit), and the lowest probabilities in Kujawsko-Pomorskie (expenditures per capita) and Małopolskie (expenditures per equivalent unit). The highest level of general mobility was noted in Małopolskie, for both categories of expenditures.

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