scholarly journals Parameter Synthesis for Probabilistic Hyperproperties

10.29007/37lf ◽  
2020 ◽  
Author(s):  
Erika Abraham ◽  
Ezio Bartocci ◽  
Borzoo Bonakdarpour ◽  
Oyendrila Dobe
Keyword(s):  
Markov Chain ◽  
Temporal Logic ◽  
Discrete Time ◽  
Differential Privacy ◽  
Transition Probabilities ◽  
Synthesis Problem ◽  
Discrete Time Markov Chain ◽  
Parameter Synthesis ◽  
Computation Trees

In this paper, we study the parameter synthesis problem for probabilistic hyperproper- ties. A probabilistic hyperproperty stipulates quantitative dependencies among a set of executions. In particular, we solve the following problem: given a probabilistic hyperprop- erty ψ and discrete-time Markov chain D with parametric transition probabilities, compute regions of parameter configurations that instantiate D to satisfy ψ, and regions that lead to violation. We address this problem for a fragment of the temporal logic HyperPCTL that allows expressing quantitative reachability relation among a set of computation trees. We illustrate the application of our technique in the areas of differential privacy, probabilistic nonintereference, and probabilistic conformance.

scholarly journals Markov Chain Modeling of HIV, Tuberculosis, and Hepatitis B Transmission in Ghana

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Clement Twumasi ◽  
Louis Asiedu ◽  
Ezekiel N. N. Nortey
Keyword(s):  
Markov Chain ◽  
Hepatitis B ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Chain Model ◽  
Disease Dynamics ◽  
Epidemiological Models ◽  
Discrete Time Markov Chain ◽  
Expected Time

Several mathematical and standard epidemiological models have been proposed in studying infectious disease dynamics. These models help to understand the spread of disease infections. However, most of these models are not able to estimate other relevant disease metrics such as probability of first infection and recovery as well as the expected time to infection and recovery for both susceptible and infected individuals. That is, most of the standard epidemiological models used in estimating transition probabilities (TPs) are not able to generalize the transition estimates of disease outcomes at discrete time steps for future predictions. This paper seeks to address the aforementioned problems through a discrete-time Markov chain model. Secondary datasets from cohort studies were collected on HIV, tuberculosis (TB), and hepatitis B (HB) cases from a regional hospital in Ghana. The Markov chain model revealed that hepatitis B was more infectious over time than tuberculosis and HIV even though the probability of first infection of these diseases was relatively low within the study population. However, individuals infected with HIV had comparatively lower life expectancies than those infected with tuberculosis and hepatitis B. Discrete-time Markov chain technique is recommended as viable for modeling disease dynamics in Ghana.

General transition probabilities for finite Markov chains

1964 ◽  
Vol 60 (1) ◽  
pp. 83-91 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Finite Number ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Initial State ◽  
Discrete Time Markov Chain ◽  
Finite Markov Chains

We consider a stationary discrete-time Markov chain with a finite number m of possible states which we designate by 1,…,m. We assume that at time t = 0 the process is in an initial state i with probability (i = 1,…, m) and such that and .

Probability of maintaining or attaining a structure in one step

1987 ◽  
Vol 24 (4) ◽  
pp. 1006-1011 ◽  
Author(s):  
G. Abdallaoui
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Chain Model ◽  
Discrete Time Markov Chain ◽  
One Step ◽  
Manpower System

Our concern is with a particular problem which arises in connection with a discrete-time Markov chain model for a graded manpower system. In this model, the members of an organisation are classified into distinct classes. As time passes, they move from one class to another, or to the outside world, in a random way governed by fixed transition probabilities. In this paper, the emphasis is placed on evaluating exact values of the probabilities of attaining and maintaining a structure.

scholarly journals ONE DIMENSIONAL ASYNCHRONOUS COOPERATIVE PARRONDO'S GAMES

2003 ◽  
Vol 03 (04) ◽  
pp. L389-L398 ◽  
Author(s):  
ZORAN MIHAILOVIĆ ◽  
MILAN RAJKOVIĆ
Keyword(s):  
Computer Simulation ◽  
Markov Chain ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Mean Field ◽  
Discrete Time Markov Chain ◽  
One Dimensional ◽  
Field Approach ◽  
The Mean ◽  
The One

A discrete-time Markov chain solution with exact rules for general computation of transition probabilities of the one-dimensional cooperative Parrondo's games is presented. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.

Probability of maintaining or attaining a structure in one step

1987 ◽  
Vol 24 (04) ◽  
pp. 1006-1011 ◽  
Author(s):  
G. Abdallaoui
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Chain Model ◽  
Discrete Time Markov Chain ◽  
One Step ◽  
Manpower System

Our concern is with a particular problem which arises in connection with a discrete-time Markov chain model for a graded manpower system. In this model, the members of an organisation are classified into distinct classes. As time passes, they move from one class to another, or to the outside world, in a random way governed by fixed transition probabilities. In this paper, the emphasis is placed on evaluating exact values of the probabilities of attaining and maintaining a structure.

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