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

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.

The Confidence Interval of the Estimator of the Periodic Intensity Function in the Presence of Power Function Trend on the Nonhomogeneous Poisson Process

The nonhomogeneous Poisson process is one of the most widely applied stochastic processes. In this article, we provide a confidence interval of the intensity estimator in the presence of a periodic multiplied by trend power function. This estimator's confidence interval is an application of the formulation of the estimator asymptotic distribution that has been given in previous studies. In addition, constructive proof of the convergent in probability has been provided for all power functions.

Nonhomogeneous Poisson Process Model of Summer High Temperature Extremes Over China

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.

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

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.

Probability distributions of COVID-19 tweet posted trends uses a nonhomogeneous Poisson process

The influence of social media in disseminating information, especially during the COVID-19 pandemic, can be observed with time interval, so that the probability of number of tweets discussed by netizens on social media can be observed. The nonhomogeneous Poisson process (NHPP) is a Poisson process with dependent on time parameters and the exponential distribution having unequal parameter values and, independently of each other. The probability of no accurence an event in the initial state is one and the probability of an event in initial state is zero. Using of non-homogeneous Poisson in this paper aims to predict and count the number of tweet posts with the keyword coronavirus, COVID-19 with set time intervals every day. Posting of tweets from one time each day to the next do not affect each other and the number of tweets is not the same. The dataset used in this study is crawling of COVID-19 tweets three times a day with duration of 20 minutes each crawled for 13 days or 39 time intervals. Result of this study obtained predictions and calculated for the probability of the number of tweets for the tendency of netizens to post on the situation of the COVID-19 pandemic.