Decrement tables and the measurement of morbidity: II

1984 ◽  
Vol 111 (1) ◽  
pp. 73-86 ◽  
Author(s):  
S. Haberman
Keyword(s):  
Markov Chains ◽  
Life Tables ◽  
The Relationship

1.1. An earlier paper by the author has attempted to describe the theories of multi-state life tables and inhomogeneous Markov chains in their application to the study of morbidity as introduced by Pollard. It is the purpose of this paper to extend the model to describe the relationship between the incidence and prevalence of a disease. The implications of certain assumptions about the presence of mortality and of differentials in the level of mortality are also discussed.

Stability and exponential convergence of continuous-time Markov chains

2003 ◽  
Vol 40 (04) ◽  
pp. 970-979 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Continuous Time ◽  
Exponential Convergence ◽  
Perturbation Bounds ◽  
Continuous Time Markov Chains ◽  
The Relationship

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

3. The fathers of demographic thought

2018 ◽  
pp. 14-23
Author(s):  
Sarah Harper
Keyword(s):  
17Th Century ◽  
Life Tables ◽  
Analytical Reasoning ◽  
Thomas Malthus ◽  
Statistical Regularities ◽  
The Relationship

Demographic ideas can be traced back to antiquity, but it is generally accepted that demography originated in the middle of the 17th century with the English statistician, John Graunt (1620–74), and his primitive life tables, which were the first attempt to examine statistical regularities inherent within the numbers of births and deaths. ‘The fathers of demographic thought’ describes the diverse theorists who founded and developed the study of demography. It begins with Graunt and then outlines the input of Sir William Petty (1623–87), Edmund Halley (1656–1742), Richard Price (1723–91), and Thomas Malthus (1766–1834). Their foundations were central to developing the relationship between analytical reasoning, numerical problems, and arithmetical records.

Strong stationary times and eigenvalues

1992 ◽  
Vol 29 (01) ◽  
pp. 228-233
Author(s):  
Peter Matthews
Keyword(s):  
Markov Chains ◽  
Initial Distribution ◽  
Mixture Of Distributions ◽  
Stationary Time ◽  
Threshold Phenomenon ◽  
Strong Stationary Time ◽  
Finite Markov Chains ◽  
The Relationship ◽  
Insight Into

This note gives a new strong stationary time (SST) for reversible finite Markov chains. A modification of the initial distribution is represented as a mixture of distributions which have eigenvector interpretations, and for which good simple SSTs exist. This provides some insight into the relationship between SSTs and eigenvalues. Connections to duality and the threshold phenomenon are discussed.

scholarly journals The space of models in machine learning: using Markov chains to model transitions

2021 ◽  
Author(s):  
Vicenç Torra ◽  
Mariam Taha ◽  
Guillermo Navarro-Arribas
Keyword(s):  
Markov Chains ◽  
Statistical Learning ◽  
Data Privacy ◽  
Metric Spaces ◽  
Distribution Functions ◽  
Transition Matrices ◽  
Probabilistic Metric Spaces ◽  
Definition Of ◽  
Probabilistic Metric ◽  
The Relationship

AbstractMachine and statistical learning is about constructing models from data. Data is usually understood as a set of records, a database. Nevertheless, databases are not static but change over time. We can understand this as follows: there is a space of possible databases and a database during its lifetime transits this space. Therefore, we may consider transitions between databases, and the database space. NoSQL databases also fit with this representation. In addition, when we learn models from databases, we can also consider the space of models. Naturally, there are relationships between the space of data and the space of models. Any transition in the space of data may correspond to a transition in the space of models. We argue that a better understanding of the space of data and the space of models, as well as the relationships between these two spaces is basic for machine and statistical learning. The relationship between these two spaces can be exploited in several contexts as, e.g., in model selection and data privacy. We consider that this relationship between spaces is also fundamental to understand generalization and overfitting. In this paper, we develop these ideas. Then, we consider a distance on the space of models based on a distance on the space of data. More particularly, we consider distance distribution functions and probabilistic metric spaces on the space of data and the space of models. Our modelization of changes in databases is based on Markov chains and transition matrices. This modelization is used in the definition of distances. We provide examples of our definitions.

scholarly journals A new model for estimating district life expectancy at birth in India, with special reference to Assam state

2014 ◽  
Vol 41 (1-2) ◽  
pp. 180
Author(s):  
Rajan Sarma ◽  
Labananda Choudhury
Keyword(s):  
Life Expectancy ◽  
South Asian ◽  
Census Data ◽  
Life Tables ◽  
Important Indicator ◽  
Registration System ◽  
Life Expectancy At Birth ◽  
Sample Registration System ◽  
Using Data ◽  
The Relationship

Life expectancy at birth (e0) is considered as an important indicator of the mortality level of a population. In India, direct estimation of e0 is not possible due to incomplete death registration. The Sample Registration System (SRS) of India provides information on e0 only for the 16 major states. Estimates of e0 for the districts are not available. Using data from the Coale-Demeny West model life tables, United Nations South Asian model life tables, and SRS life tables of India and its major states, the paper shows that the relationship between life expectancy at age one (e0) and the probability of surviving to age one (l1) is linear, and the relationship between e0 and l1 is quadratic. From the quadratic relationship between e0 and l1, an attempt is made to estimate e0 for some selected districts of India for 2001 and 2010, using estimated l1 from 2001 census data and Annual Health Survey (2010–11) data.

Stability and exponential convergence of continuous-time Markov chains

2003 ◽  
Vol 40 (4) ◽  
pp. 970-979 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Continuous Time ◽  
Exponential Convergence ◽  
Perturbation Bounds ◽  
Continuous Time Markov Chains ◽  
The Relationship

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

scholarly journals Performance Analysis of IEEE 802.11p for Continuous Backoff Freezing in IoV

Electronics ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1404 ◽  
Author(s):  
Qiong Wu ◽  
Siyang Xia ◽  
Qiang Fan ◽  
Zhengquan Li
Keyword(s):  
Performance Analysis ◽  
Markov Chains ◽  
Analytical Model ◽  
Vehicular Ad Hoc Networks ◽  
Rapid Development ◽  
Probability Generating Function ◽  
Packet Delay ◽  
Ieee 802.11P ◽  
Traffic Density ◽  
The Relationship

With the rapid development of cloud computing and big data, traditional Vehicular Ad hoc Networks (VANETs) are evolving into the Internet of Vehicles (IoV). As an important communication technology in IoV, IEEE 802.11p protocols have been studied by many experts and scholars. In IEEE 802.11p, a node’s backoff counter will be frozen when the channel is detected as busy. However, most studies did not consider the possibility of continuous backoff freezing when calculating delay. Thus, in this paper, we focus on the performance analysis of IEEE 802.11p for continuous backoff freezing. Specifically, we establish an analytical model to analyze the broadcast performance in the highway scene where vehicles can obtain traffic density from roadside units through Vehicle to Infrastructure (V2I) communications. We first calculate the relationship between vehicle density and the number of vehicles. Then, we derive the relationship between the number of vehicles and packet delay according to Markov chains. Next, we utilize the probability generating function (PGF) to transform traditional Markov chains into z domain under the situation of non-saturation. Finally, we employ the Mason formula to derive packet delay. As compared with the performance without considering the continuous backoff freezing, the simulation results have demonstrated that our analytical model is more reasonable.

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