A Uniform Shrinkage Prior in Spatiotemporal Poisson Models for Count Data

2021 ◽  
pp. 83-102
Author(s):  
Krisada Lekdee ◽  
Chao Yang ◽  
Lily Ingsrisawang ◽  
Yisheng Li
Keyword(s):  
Count Data ◽  
Poisson Models ◽  
Shrinkage Prior

scholarly journals Flexible models for overdispersed and underdispersed count data

2021 ◽  
Author(s):  
Dexter Cahoy ◽  
Elvira Di Nardo ◽  
Federico Polito
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Hypergeometric Functions ◽  
Natural Generalization ◽  
Model Parameters ◽  
Probability Models ◽  
Limiting Behavior ◽  
Poisson Models ◽  
Special Cases ◽  
Flexible Models

AbstractWithin the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.

scholarly journals An Application Comparison of Two Poisson Models on Zero Count Data

2021 ◽  
Vol 1818 (1) ◽  
pp. 012165
Author(s):  
L. H. Hashim ◽  
K. H. Hashim ◽  
Mushtak A. K. Shiker
Keyword(s):  
Count Data ◽  
Poisson Models

Extended negative binomial hurdle models

2018 ◽  
Vol 28 (5) ◽  
pp. 1540-1551
Author(s):  
Maengseok Noh ◽  
Youngjo Lee
Keyword(s):  
Count Data ◽  
Negative Binomial ◽  
Random Effect ◽  
Random Effect Model ◽  
Real Data ◽  
Hurdle Models ◽  
Poisson Models ◽  
Effect Model ◽  
Zero Rate ◽  
General Statistical

Poisson models are widely used for statistical inference on count data. However, zero-inflation or zero-deflation with either overdispersion or underdispersion could occur. Currently, there is no available model for count data, that allows excessive occurrence of zeros along with underdispersion in non-zero counts, even though there have been reported necessity of such models. Furthermore, given an excessive zero rate, we need a model that allows a larger degree of overdispersion than existing models. In this paper, we use a random-effect model to produce a general statistical model for accommodating such phenomenon occurring in real data analyses.

scholarly journals On Predictive Distribution of K-Inflated Poisson Models with and Without Additional Information

2020 ◽  
Vol 43 (2) ◽  
pp. 173-182
Author(s):  
Abdolnasser Sadeghkhani ◽  
S. Ejaz Ahmed
Keyword(s):  
Count Data ◽  
Poisson Model ◽  
Random Variable ◽  
Simulation Method ◽  
Predictive Distribution ◽  
Bayesian Estimator ◽  
Additional Information ◽  
Poisson Models ◽  
Model Independent

This   paper   addresses  different   approaches  in  finding   the   Bayesian predictive distribution of a random  variable from a Poisson  model that  can handle  count data  with an inflated  value  of K ∈ N, known as the KIP  model. We explore  how we can  use  other  source  of additional information to  find such  an estimator. More specifically, we find a Bayesian estimator of future density of random  variable Y1 , based  on observable X1  from the K1 IP(p1 , λ1 ) model, with and without assuming that  there exists  another random  variable X2 , from the K2 IP(p2 , λ2 ) model, independent of X1 , provided λ1  ≥ λ2 , and compare their  performance using  simulation method.

scholarly journals The effect of data aggregation on dispersion estimates in count data models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Adam Errington ◽  
Jochen Einbeck ◽  
Jonathan Cumming ◽  
Ute Rössler ◽  
David Endesfelder
Keyword(s):  
Count Data ◽  
Data Aggregation ◽  
Random Effect ◽  
Real Data ◽  
Data Sets ◽  
Count Data Models ◽  
Response Curves ◽  
Poisson Models ◽  
Random Effect Models ◽  
Radiation Biodosimetry

Abstract For the modelling of count data, aggregation of the raw data over certain subgroups or predictor configurations is common practice. This is, for instance, the case for count data biomarkers of radiation exposure. Under the Poisson law, count data can be aggregated without loss of information on the Poisson parameter, which remains true if the Poisson assumption is relaxed towards quasi-Poisson. However, in biodosimetry in particular, but also beyond, the question of how the dispersion estimates for quasi-Poisson models behave under data aggregation have received little attention. Indeed, for real data sets featuring unexplained heterogeneities, dispersion estimates can increase strongly after aggregation, an effect which we will demonstrate and quantify explicitly for some scenarios. The increase in dispersion estimates implies an inflation of the parameter standard errors, which, however, by comparison with random effect models, can be shown to serve a corrective purpose. The phenomena are illustrated by γ-H2AX foci data as used for instance in radiation biodosimetry for the calibration of dose-response curves.

scholarly journals Hierarchical Poisson models for spatial count data

2013 ◽  
Vol 122 ◽  
pp. 393-408 ◽  
Author(s):  
Victor De Oliveira
Keyword(s):  
Count Data ◽  
Poisson Models ◽  
Spatial Count Data

scholarly journals Prediction of confirmed cases of and deaths caused by COVID-19 in Chile through time series techniques: A comparative study

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0245414
Author(s):  
Claudia Barría-Sandoval ◽  
Guillermo Ferreira ◽  
Katherine Benz-Parra ◽  
Pablo López-Flores
Keyword(s):  
Time Series ◽  
Count Data ◽  
Moving Average ◽  
Time Dependent ◽  
Training Set ◽  
Health Organizations ◽  
Autoregressive Integrated Moving Average ◽  
Poisson Models ◽  
Public Health Organizations ◽  
Containment Measures

Background Chile has become one of the countries most affected by COVID-19, a pandemic that has generated a large number of cases worldwide. If not detected and treated in time, COVID-19 can cause multi-organ failure and even death. Therefore, it is necessary to understand the behavior of the spread of COVID-19 as well as the projection of infections and deaths. This information is very relevant so that public health organizations can distribute financial resources efficiently and take appropriate containment measures. In this research, we compare different time series methodologies to predict the number of confirmed cases of and deaths from COVID-19 in Chile. Methods The methodology used in this research consisted of modeling cases of both confirmed diagnoses and deaths from COVID-19 in Chile using Autoregressive Integrated Moving Average (ARIMA henceforth) models, Exponential Smoothing techniques, and Poisson models for time-dependent count data. Additionally, we evaluated the accuracy of the predictions using a training set and a test set. Results The dataset used in this research indicated that the most appropriate model is the ARIMA time series model for predicting the number of confirmed COVID-19 cases, whereas for predicting the number of deaths from COVID-19 in Chile, the most suitable approach is the damped trend method. Conclusion The ARIMA models are an alternative to modeling the behavior of the spread of COVID-19; however, depending on the characteristics of the dataset, other methodologies can better predict the behavior of these records, for example, the Holt-Winter method implemented with time-dependent count data.

Regression Analysis of Count Data

1998 ◽  
Author(s):  
A. Colin Cameron ◽  
Pravin K. Trivedi
Keyword(s):  
Regression Analysis ◽  
Count Data
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