On a class of multivariate counting processes

2016 ◽  
Vol 48 (2) ◽  
pp. 443-462 ◽  
Author(s):  
Ji Hwan Cha ◽  
Massimiliano Giorgio
Keyword(s):  
Point Processes ◽  
Dependence Structure ◽  
Counting Processes ◽  
New Class ◽  
Marginal Process ◽  
Polya Process ◽  
History Of ◽  
Pólya Process ◽  
Important Characterization

Abstract In this paper we define and study a new class of multivariate counting processes, named `multivariate generalized Pólya process'. Initially, we define and study the bivariate generalized Pólya process and briefly discuss its reliability application. In order to derive the main properties of the process, we suggest some key properties and an important characterization of the process. Due to these properties and the characterization, the main properties of the bivariate generalized Pólya process are obtained efficiently. The marginal processes of the multivariate generalized Pólya process are shown to be the univariate generalized Pólya processes studied in Cha (2014). Given the history of a marginal process, the conditional property of the other process is also discussed. The bivariate generalized Pólya process is extended to the multivariate case. We define a new dependence concept for multivariate point processes and, based on it, we analyze the dependence structure of the multivariate generalized Pólya process.

ON A MULTIVARIATE GENERALIZED POLYA PROCESS WITHOUT REGULARITY PROPERTY

2019 ◽  
Vol 34 (4) ◽  
pp. 484-506
Author(s):  
Ji Hwan Cha ◽  
F.G. Badía
Keyword(s):  
Regularity Property ◽  
Dependence Structure ◽  
Counting Processes ◽  
Multiple Events ◽  
New Class ◽  
Different Types ◽  
Polya Process ◽  
Multivariate Dependence ◽  
Pólya Process ◽  
Stochastic Properties

Most of the multivariate counting processes studied in the literature are regular processes, which implies, ignoring the types of the events, the non-occurrence of multiple events. However, in practice, several different types of events may occur simultaneously. In this paper, a new class of multivariate counting processes which allow simultaneous occurrences of multiple types of events is suggested and its stochastic properties are studied. For the modeling of such kind of process, we rely on the tool of superposition of seed counting processes. It will be shown that the stochastic properties of the proposed class of multivariate counting processes are explicitly expressed. Furthermore, the marginal processes are also explicitly obtained. We analyze the multivariate dependence structure of the proposed class of counting processes.

An analysis of the Pólya point process

1983 ◽  
Vol 15 (01) ◽  
pp. 39-53 ◽  
Author(s):  
Ed Waymire ◽  
Vijay K. Gupta
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Critical Value ◽  
General Representation ◽  
Infinitely Divisible ◽  
Generating Functional ◽  
Representation Problem ◽  
Polya Process ◽  
Pólya Process ◽  
Stochastic Point Processes

The Pólya process is employed to illustrate certain features of the structure of infinitely divisible stochastic point processes in connection with the representation for the probability generating functional introduced by Milne and Westcott in 1972. The Pólya process is used to provide a counterexample to the result of Ammann and Thall which states that the class of stochastic point processes with the Milne and Westcott representation is the class of regular infinitely divisble point processes. So the general representation problem is still unsolved. By carrying the analysis of the Pólya process further it is possible to see the extent to which the general representation is valid. In fact it is shown in the case of the Pólya process that there is a critical value of a parameter above which the representation breaks down. This leads to a proper version of the representation in the case of regular infinitely divisible point processes.

Characterization of the Generalized Pólya Process and its Applications

2014 ◽  
Vol 46 (4) ◽  
pp. 1148-1171 ◽  
Author(s):  
Ji Hwan Cha
Keyword(s):  
Joint Distribution ◽  
Arrival Times ◽  
Stochastic Intensity ◽  
Polya Process ◽  
New Type ◽  
Compound Process ◽  
Pólya Process

In this paper some important properties of the generalized Pólya process are derived and their applications are discussed. The generalized Pólya process is defined based on the stochastic intensity. By interpreting the defined stochastic intensity of the generalized Pólya process, the restarting property of the process is discussed. Based on the restarting property of the process, the joint distribution of the number of events is derived and the conditional joint distribution of the arrival times is also obtained. In addition, some properties of the compound process defined for the generalized Pólya process are derived. Furthermore, a new type of repair is defined based on the process and its application to the area of reliability is discussed. Several examples illustrating the applications of the obtained properties to various areas are suggested.

scholarly journals Event history analysis of dynamic networks

Biometrika ◽  
2020 ◽  
Author(s):  
T Sit ◽  
Z Ying ◽  
Y Yu
Keyword(s):  
Event History Analysis ◽  
Dynamic Networks ◽  
Partial Likelihood ◽  
Event History ◽  
Dependence Structure ◽  
Counting Processes ◽  
Asymptotic Results ◽  
History Analysis ◽  
History Of ◽  
Likelihood Approach

Summary Statistical analysis on networks has received growing attention due to demand from various emerging applications. In dynamic networks, one of the key interests is to model the event history of time-stamped interactions among nodes. We model dynamic directed networks via multivariate counting processes. A pseudo partial likelihood approach is exploited to capture the network dependence structure. Asymptotic results are established. Numerical experiments are performed to demonstrate the effectiveness of our proposal.

A NOTE ON THE CLASS OF GEOMETRIC COUNTING PROCESSES

2013 ◽  
Vol 27 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Ji Hwan Cha ◽  
Maxim Finkelstein
Keyword(s):  
Poisson Process ◽  
Probabilistic Analysis ◽  
Counting Process ◽  
Geometric Distribution ◽  
Survival Models ◽  
Dependence Structure ◽  
Counting Processes ◽  
External Shocks ◽  
New Class ◽  
Independent Increments

In this paper, we suggest a new class of counting processes, called the Class of Geometric Counting Processes (CGCP), where each member of the counting process in the class has increments described by the geometric distribution. Distinct from the Poisson process, they do not possess the property of independent increments, which usually complicates probabilistic analysis. The suggested CGCP is defined and the dependence structure shared by the members of the class is discussed. As examples of useful applications, we consider stochastic survival models under external shocks. We show that the corresponding survival probabilities under reasonable assumptions can be effectively described by the CGCP without specifying the dependence structure.

Characterization of the Generalized Pólya Process and its Applications

2014 ◽  
Vol 46 (04) ◽  
pp. 1148-1171 ◽  
Author(s):  
Ji Hwan Cha
Keyword(s):  
Joint Distribution ◽  
Arrival Times ◽  
Stochastic Intensity ◽  
Polya Process ◽  
New Type ◽  
Compound Process ◽  
Pólya Process

In this paper some important properties of the generalized Pólya process are derived and their applications are discussed. The generalized Pólya process is defined based on the stochastic intensity. By interpreting the defined stochastic intensity of the generalized Pólya process, the restarting property of the process is discussed. Based on the restarting property of the process, the joint distribution of the number of events is derived and the conditional joint distribution of the arrival times is also obtained. In addition, some properties of the compound process defined for the generalized Pólya process are derived. Furthermore, a new type of repair is defined based on the process and its application to the area of reliability is discussed. Several examples illustrating the applications of the obtained properties to various areas are suggested.

An analysis of the Pólya point process

1983 ◽  
Vol 15 (1) ◽  
pp. 39-53 ◽  
Author(s):  
Ed Waymire ◽  
Vijay K. Gupta
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Critical Value ◽  
General Representation ◽  
Infinitely Divisible ◽  
Generating Functional ◽  
Representation Problem ◽  
Polya Process ◽  
Pólya Process ◽  
Stochastic Point Processes

The Pólya process is employed to illustrate certain features of the structure of infinitely divisible stochastic point processes in connection with the representation for the probability generating functional introduced by Milne and Westcott in 1972. The Pólya process is used to provide a counterexample to the result of Ammann and Thall which states that the class of stochastic point processes with the Milne and Westcott representation is the class of regular infinitely divisble point processes. So the general representation problem is still unsolved. By carrying the analysis of the Pólya process further it is possible to see the extent to which the general representation is valid. In fact it is shown in the case of the Pólya process that there is a critical value of a parameter above which the representation breaks down. This leads to a proper version of the representation in the case of regular infinitely divisible point processes.

Subversive Mobilities

Transfers ◽  
2013 ◽  
Vol 3 (1) ◽  
pp. 7-25 ◽  
Author(s):  
Mikkel Thelle
Keyword(s):  
Public Space ◽  
Cultural History ◽  
Turn Of The Century ◽  
Public Action ◽  
History Of ◽  
Urban Conflict

The article approaches mobility through a cultural history of urban conflict. Using a case of “The Copenhagen Trouble,“ a series of riots in the Danish capital around 1900, a space of subversive mobilities is delineated. These turn-of-the-century riots points to a new pattern of mobile gathering, the swarm; to a new aspect of public action, the staging; and to new ways of configuring public space. These different components indicate an urban assemblage of subversion, and a new characterization of the “throwntogetherness“ of the modern public.

Targeting IDH Mutations in AML: Wielding the Double-edged Sword of Differentiation

2020 ◽  
Vol 20 (7) ◽  
pp. 490-500 ◽  
Author(s):  
Justin S. Becker ◽  
Amir T. Fathi
Keyword(s):  
Genome Structure ◽  
Cellular Metabolism ◽  
Standard Of Care ◽  
Competitive Inhibitor ◽  
Driver Mutations ◽  
New Class ◽  
Regulatory Enzymes ◽  
Idh Mutations ◽  
Genomic Characterization

The genomic characterization of acute myeloid leukemia (AML) by DNA sequencing has illuminated subclasses of the disease, with distinct driver mutations, that might be responsive to targeted therapies. Approximately 15-23% of AML genomes harbor mutations in one of two isoforms of isocitrate dehydrogenase (IDH1 or IDH2). These enzymes are constitutive mediators of basic cellular metabolism, but their mutated forms in cancer synthesize an abnormal metabolite, 2- hydroxyglutarate, that in turn acts as a competitive inhibitor of multiple gene regulatory enzymes. As a result, leukemic IDH mutations cause changes in genome structure and gene activity, culminating in an arrest of normal myeloid differentiation. These discoveries have motivated the development of a new class of selective small molecules with the ability to inhibit the mutant IDH enzymes while sparing normal cellular metabolism. These agents have shown promising anti-leukemic activity in animal models and early clinical trials, and are now entering Phase 3 study. This review will focus on the growing preclinical and clinical data evaluating IDH inhibitors for the treatment of IDH-mutated AML. These data suggest that inducing cellular differentiation is central to the mechanism of clinical efficacy for IDH inhibitors, while also mediating toxicity for patients who experience IDH Differentiation Syndrome. Ongoing trials are studying the efficacy of IDH inhibitors in combination with other AML therapies, both to evaluate potential synergistic combinations as well as to identify the appropriate place for IDH inhibitors within existing standard-of-care regimens.

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