Performance evaluation of faulty iterative decoders using absorbing Markov chains

2016 ◽  
Author(s):  
Predrag Ivanis ◽  
Bane Vasic ◽  
David Declercq
Keyword(s):  
Performance Evaluation ◽  
Markov Chains ◽  
Iterative Decoders ◽  
Absorbing Markov Chains

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

Absorbing Markov chains for analyzing COVID-19 infections

2021 ◽  
pp. 2250008
Author(s):  
Safaa K. Kadhem ◽  
Sadeq A. Kadhim
Keyword(s):  
Markov Chains ◽  
Markov Model ◽  
Dynamical Model ◽  
Health State ◽  
Random Movement ◽  
Expected Time ◽  
Absorbing Markov Chains ◽  
Death State ◽  
Key Aspects ◽  
Model Approach

Recently, there are many works that proposed modeling approaches to describe the random movement of individuals for COVID-19 infection. However, these models have not taken into account some key aspects for disease such the prediction of expected time of patients remaining at certain health state before entering an absorption state (e.g., exit out of the system for ever such as death state or recovery). Therefore, we propose a dynamical model approach called the absorbing Markov chains for analyzing COVID-19 infections. From this modeling approach, we seek to focus and predict two states of absorption: recovery and death, as these two conditions are considered as important indicators in assessment of the health level. Based on the absorbing Markov model, the study suggested that there is a gradually increase in the predicted death number, while a decrease in the number of recovered individuals.

scholarly journals ADVANCED DYNAMIC ALGORITHMS FOR THE DECAY OF METASTABLE PHASES IN DISCRETE SPIN MODELS: BRIDGING DISPARATE TIME SCALES

1999 ◽  
Vol 10 (08) ◽  
pp. 1483-1493 ◽  
Author(s):  
M. A. NOVOTNY
Keyword(s):  
Monte Carlo ◽  
Markov Chains ◽  
Transfer Matrix ◽  
Time Scales ◽  
System Size ◽  
Metastable Phases ◽  
Spin Models ◽  
Dynamic Algorithms ◽  
Absorbing Markov Chains

An overview of advanced dynamical algorithms capable of spanning the widely disparate time scales that govern the decay of metastable phases in discrete spin models is presented. The algorithms discussed include constrained transfer-matrix, Monte Carlo with Absorbing Markov Chains (MCAMC), and projective dynamics (PD) methods. The strengths and weaknesses of each of these algorithms are discussed, with particular emphasis on identifying the parameter regimes (system size, temperature, and field) in which each algorithm works best.

Quasistationary distributions for continuous time Markov chains when absorption is not certain

1999 ◽  
Vol 36 (01) ◽  
pp. 268-272 ◽  
Author(s):  
P. K. Pollett
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Initial Distribution ◽  
Probabilistic Interpretation ◽  
Continuous Time Markov Chains ◽  
Absorbing Markov Chains ◽  
Present Context ◽  
Conditional State ◽  
Quasistationary Distributions ◽  
Definition Of

Recently, Elmes et al. (see [2]) proposed a definition of a quasistationary distribution to accommodate absorbing Markov chains for which absorption occurs with probability less than 1. We will show that the probabilistic interpretation pertaining to cases where absorption is certain (see [13]) does not hold in the present context. We prove that the state probabilities at time t conditional on absorption taking place after t, generally depend on t. Conditions are derived under which there is no initial distribution such that the conditional state probabilities are stationary.

Quantifying the probability of a shot in women’s collegiate soccer through absorbing Markov chains

2018 ◽  
Vol 14 (3) ◽  
pp. 103-115
Author(s):  
Devyn Norman Woodfield ◽  
Gilbert W. Fellingham
Keyword(s):  
Markov Process ◽  
Markov Chains ◽  
Web Application ◽  
Transition Probabilities ◽  
Transient State ◽  
Marginal Probability ◽  
Skill Area ◽  
Absorbing State ◽  
Probability Estimates ◽  
Absorbing Markov Chains

Abstract A Bayesian model is used to evaluate the probability that a given skill performed in a specified area of the field will lead to a predetermined outcome by using discrete absorbing Markov chains. The transient states of the Markov process are defined by unique skill-area combinations. The absorbing states of the Markov process are defined by a shot, turnover, or bad turnover. Defining the states in this manner allows the probability of a transient state leading to an absorbing state to be derived. A non-informative prior specification of transition counts is used to permit the data to define the posterior distribution. A web application was created to collect play-by-play data from 34 Division 1 NCAA Women’s soccer matches for the 2013–2014 seasons. A prudent construction of updated transition probabilities facilitates a transformation through Monte Carlo simulation to obtain marginal probability estimates of each unique skill-area combination leading to an absorbing state. For each season, marginal probability estimates for given skills are compared both across and within areas to determine which skills and areas of the field are most advantageous.

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