scholarly journals A Spatial Nonhomogeneous Poisson Process Model Using Bayesian Approach on a Space-Time Geostatistical Data

2021 ◽  
Vol 4 (3) ◽  
pp. 186-198
Author(s):  
Anggun Y.Q. ◽  
Subanar .
Keyword(s):  
Poisson Process ◽  
Bayesian Approach ◽  
Process Model ◽  
Goodness Of Fit ◽  
Nonhomogeneous Poisson Process ◽  
Mcmc Method ◽  
Good Convergence ◽  
Time Component ◽  
Study Case ◽  
Special Region

In this research, we propose the nonhomogeneous Poisson process on geostatistical data by adding a time component to be applied in the study case of air pollution in the Special Region of Yogyakarta. We use the Bayesian approach to inference the model using the MCMC method. And to generate samples of the posterior distribution, we wield the Metropolis-Hastings algorithm, and we obtained it has good convergence for this case. And to show the goodness of fit of this model, we had the value of DIC.

scholarly journals Bayesian modeling and prediction of accrual in multi-regional clinical trials

2014 ◽  
Vol 26 (2) ◽  
pp. 752-765 ◽  
Author(s):  
Yi Deng ◽  
Xiaoxi Zhang ◽  
Qi Long
Keyword(s):  
Clinical Trials ◽  
Poisson Process ◽  
Process Model ◽  
Nonhomogeneous Poisson Process ◽  
Modeling And Prediction ◽  
Accuracy And Precision ◽  
Start Up ◽  
Accrual Rate ◽  
Model Region ◽  
Over Time

In multi-regional trials, the underlying overall and region-specific accrual rates often do not hold constant over time and different regions could have different start-up times, which combined with initial jump in accrual within each region often leads to a discontinuous overall accrual rate, and these issues associated with multi-regional trials have not been adequately investigated. In this paper, we clarify the implication of the multi-regional nature on modeling and prediction of accrual in clinical trials and investigate a Bayesian approach for accrual modeling and prediction, which models region-specific accrual using a nonhomogeneous Poisson process and allows the underlying Poisson rate in each region to vary over time. The proposed approach can accommodate staggered start-up times and different initial accrual rates across regions/centers. Our numerical studies show that the proposed method improves accuracy and precision of accrual prediction compared to existing methods including the nonhomogeneous Poisson process model that does not model region-specific accrual.

scholarly journals Nonhomogeneous Poisson Process Model of Summer High Temperature Extremes Over China

2021 ◽  
Author(s):  
Meng Gao ◽  
Han Zhang ◽  
Aidi Zhang ◽  
Yueqi Wang
Keyword(s):  
High Temperature ◽  
Poisson Process ◽  
Poisson Regression ◽  
Process Model ◽  
Value Theory ◽  
Nonhomogeneous Poisson Process ◽  
Occurrence Rate ◽  
Temperature Extremes ◽  
Teleconnection Patterns ◽  
High Temperature Extremes

Abstract In this study, nonhomogeneous Poisson process (NHPP) models arising from the extreme value theory have been fitted to summer high temperature extremes (HTEs) at 359 meteorological stations over China. The seasonality and six prominent atmospheric teleconnection patterns in Northern Hemisphere are incorporated in the NHPP models reflecting the non-stationarity in occurrence rate in Poisson process of HTEs. In addition, Poisson regression model has also been applied to link HTEs and teleconnection patterns. The linkages of HTEs and teleconnection patterns have been identified in both NHPP modeling and Poisson regression. Composite maps of differences of 500-hPa geopotential height and wind fields in the positive and negative phases of teleconnection patterns are constructed to show the impacts of atmospheric circulation patterns on extreme heat events. The spatial pattern of the associated anticyclonic or cyclonic circulations with teleconnection patterns partly explains the spatial variability of the occurrences of summer HTEs over China.

scholarly journals A Reliability Growth Process Model with Time-Varying Covariates and Its Application

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 905
Author(s):  
Xin-Yu Tian ◽  
Xincheng Shi ◽  
Cheng Peng ◽  
Xiao-Jian Yi
Keyword(s):  
Poisson Process ◽  
Process Model ◽  
Growth Process ◽  
Nonhomogeneous Poisson Process ◽  
Reliability Growth ◽  
Time Varying ◽  
Repairable Systems ◽  
Martingale Theory ◽  
Amsaa Model ◽  
Time Varying Covariates

The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of the product under different operational environments. In this paper we introduce an AMSAA-based model considering the covariate effects to measure the influence of the time-varying environmental condition. The parameter estimation of the model is typically performed using maximum likelihood on the failure data. The statistical properties of the estimation in the model are comprehensively derived by the martingale theory. Further inferences including confidence interval estimation and hypothesis tests are designed for the model. The performance and properties of the method are verified in a simulation study, compared with the classical AMSAA model. A case study is used to illustrate the practical use of the model. The proposed approach can be adapted for a wide class of nonhomogeneous Poisson process based models.

Applying the Anderson-Darling Test to Suicide Clusters

Crisis ◽  
2013 ◽  
Vol 34 (6) ◽  
pp. 434-437 ◽  
Author(s):  
Donald W. MacKenzie
Keyword(s):  
Poisson Process ◽  
Goodness Of Fit ◽  
Small Samples ◽  
Massachusetts Institute Of Technology ◽  
Homogeneous Poisson Process ◽  
Cornell University ◽  
The Difference ◽  
Suicide Clusters ◽  
Institute Of Technology ◽  
Anderson Darling

Background: Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. Aim: This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Method: Suicide dates were collected for MIT and Cornell for 1990–2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Results: Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). Conclusions: The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability

2005 ◽  
Vol 288 (1) ◽  
pp. H424-H435 ◽  
Author(s):  
Riccardo Barbieri ◽  
Eric C. Matten ◽  
AbdulRasheed A. Alabi ◽  
Emery N. Brown
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Gaussian Model ◽  
Quantitative Measure ◽  
Local Maximum ◽  
Inverse Gaussian ◽  
Design Of Algorithms

Heart rate is a vital sign, whereas heart rate variability is an important quantitative measure of cardiovascular regulation by the autonomic nervous system. Although the design of algorithms to compute heart rate and assess heart rate variability is an active area of research, none of the approaches considers the natural point-process structure of human heartbeats, and none gives instantaneous estimates of heart rate variability. We model the stochastic structure of heartbeat intervals as a history-dependent inverse Gaussian process and derive from it an explicit probability density that gives new definitions of heart rate and heart rate variability: instantaneous R-R interval and heart rate standard deviations. We estimate the time-varying parameters of the inverse Gaussian model by local maximum likelihood and assess model goodness-of-fit by Kolmogorov-Smirnov tests based on the time-rescaling theorem. We illustrate our new definitions in an analysis of human heartbeat intervals from 10 healthy subjects undergoing a tilt-table experiment. Although several studies have identified deterministic, nonlinear dynamical features in human heartbeat intervals, our analysis shows that a highly accurate description of these series at rest and in extreme physiological conditions may be given by an elementary, physiologically based, stochastic model.

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