Poisson Mixture Model Research Articles

COVID-19-infected cases in Thailand during the Omicron wave using the capture-recapture method

Thailand is among many countries, severely affected by the COVID-19 pandemic. In December 2021, the Thai Ministry of Public Health announced the discovery of the first imported case of the Omicron variant, and the local transmission of the Omicron variant was confirmed. The Omicron variant spread rapidly but was less dangerous than the Delta. Some patients experienced mild or no symptoms and self-treated without requiring medical assistance. Lower fatality rates during the Omicron outbreak were reported compared with previous variants. Information concerning hidden COVID-19-infected patients is beneficial and will lead to a better understanding of the disease outbreak mechanism. This study proposed the lower bound estimator under the capture-recapture (CR) method to estimate the true value of COVID-19 infections in Thailand during the Omicron wave. The Chao lower bound estimator for the Poisson mixture model was created to take into account the fact that populations can be different based on how cases and deaths have been spread out over time. The approximate variance of the estimator was constructed for a confidence interval of 95%, focusing on the ratio of total estimated infected cases to observed cases in March 2022. The average ratio was 2.99 (95% CI: 2.96 to 3.01), suggesting that for every 100 observed patients, at least 199 infected patients were underreported.

Claim Prediction and Premium Pricing for Telematics Auto Insurance Data Using Poisson Regression with Lasso Regularisation

We leverage telematics data on driving behavior variables to assess driver risk and predict future insurance claims in a case study utilising a representative telematics sample. In the study, we aim to categorise drivers according to their driving habits and establish premiums that accurately reflect their driving risk. To accomplish our goal, we employ the two-stage Poisson model, the Poisson mixture model, and the Zero-Inflated Poisson model to analyse the telematics data. These models are further enhanced by incorporating regularisation techniques such as lasso, adaptive lasso, elastic net, and adaptive elastic net. Our empirical findings demonstrate that the Poisson mixture model with the adaptive lasso regularisation outperforms other models. Based on predicted claim frequencies and drivers’ risk groups, we introduce a novel usage-based experience rating premium pricing method. This method enables more frequent premium updates based on recent driving behaviour, providing instant rewards and incentivising responsible driving practices. Consequently, it helps to alleviate cross-subsidization among risky drivers and improves the accuracy of loss reserving for auto insurance companies.

Spatial patterns in occupancy and density of larval lampreys in freshwater habitats restored to a Stage 0 condition

AbstractWe examined occupancy and density of larval lampreys (Entosphenus tridentatus and Lampetra spp.) in two rivers in Oregon (USA) restored to a Stage 0 condition 1–5 years prior, using a multiscale occupancy model and a zero‐inflated Poisson mixture model. We sampled lampreys using backpack electrofishing in randomly distributed, paired, 1‐m2 quadrats and recorded environmental data. Probabilities of occupancy and density were higher when water velocity was low, the substrate was noncompacted, and sediment was dominated by fines (<4 mm). At mean water depth (0.34 m) and velocity (0.09 m/s), estimated densities in occupied quadrats were 4.8 lampreys/m2 (95%: 3.4–6.9) when the substrate was compacted, and fines were not dominant, and 21.1 lampreys/m2 (95%: 17.7–25.3) when the substrate was noncompacted and fines were dominant. Probabilities of detecting occupancy in a 1‐m2 quadrat sampled by backpack electrofishing were 0.76 (95%: 0.64–0.87) when captured after visual observation and 0.80 (95%: 0.71–0.88) with blind sweeps (i.e., constantly moving the net regardless of observation). The probability of capturing a single lamprey in a quadrat sampled by blind sweeps was 0.32 (95%: 0.27–0.37). Sampling in paired 1‐m2 quadrats facilitated concurrent examination of patterns in occupancy and density while accounting for capture probability, which could aid temporal monitoring of restored habitats. To the best of our knowledge, this is the first study to document occupancy and estimate densities of larval lampreys in habitats that underwent valley floor restoration to Stage 0. We observed both lamprey genera within 5 years of restoration. Aquatic restoration that increases low‐velocity, noncompacted, fine sediment habitats could benefit lampreys.

Precision detection of recent HIV infections using high-throughput genomic incidence assay.

HIV incidence is a key measure for tracking disease spread and identifying populations and geographic regions where new infections are most concentrated. The HIV sequence population provides a robust signal for the stage of infection. Large-scale and high-precision HIV sequencing is crucial for effective genomic incidence surveillance. We produced 1,034 full-length envelope gene sequences from a seroconversion cohort by conducting HIV microdrop sequencing and measuring the genomic incidence assay's genome similarity index (GSI) dynamics. The measured dynamics of 9 of 12 individuals aligned with the GSI distribution estimated independently using 417 publicly available incident samples. We enhanced the capacity to identify individuals with recent infections, achieving predicted detection accuracies of 92% (89%-94%) for cases within 6 months and 81% (74%-87%) for cases within 9 months. These accuracy levels agreed with the observed detection accuracy intervals of an independent validation data set. Additionally, we produced 131 full-length envelope gene sequences from eight individuals with chronic HIV infection. This analysis confirmed a false recency rate (FRR) of 0%, which was consistent with 162 publicly available chronic samples. The mean duration of recent infection (MDRI) was 238 (209-267) days, indicating an 83% improvement in performance compared to current recent infection testing algorithms. The shifted Poisson mixture model was then used to estimate the time since infection, and the model estimates showed an 88% consistency with the days post infection derived from HIV RNA test dates and/or seroconversion dates. HIV microdrop sequencing provides unique prospects for large-scale incidence surveillance using high-throughput sequencing. IMPORTANCE Accurate identification of recently infected individuals is vital for prioritizing specific populations for interventions, reducing onward transmission risks, and optimizing public health services. However, current HIV-specific antibody-based methods have not been satisfactory in accurately identifying incident cases, hindering the use of HIV recency testing for prevention efforts and partner protection. Genomic incidence assays offer a promising alternative for identifying recent infections. In our study, we used microdroplet technologies to produce a large number of complete HIV envelope gene sequences, enabling the accurate detection of early infection signs. We assessed the dynamics of the incidence assay's metrics and compared them with statistical models. Our approach demonstrated high accuracy in identifying individuals with recent infections, achieving predicted detection rates exceeding 90% within 6 months and over 80% within 9 months of infection. This high-resolution method holds significant potential for enhancing the effectiveness of HIV incidence screening for case-based surveillance in public health initiatives.

Distributed online expectation-maximization algorithm for Poisson mixture model

Traffic flow data, in the form of multiple time series of aggregated traffic volume observed from various vehicle detector stations, are investigated as a motivating example. By the very nature of the traffic volume observations, we model the traffic volume data from each station by a Poisson mixture model. We then propose a distributed online expectation-maximization algorithm to fit the traffic volume data under the Poisson mixture model, with the results to be used to make inference about the population attributes of the traffic flows. Apart from the finite mixture Poisson model, two forms of infinite mixture Poisson – Poisson-inverse-Gaussian model and Poisson-Gamma model – are specifically considered and analyzed in detail. Simulation study and real data analysis are also undertaken to confirm the theoretical properties that we have derived for the proposed distributed online expectation-maximization algorithms.

Robust Online Modeling of Counts in Agent Networks

Many real-world processes of interest produce nonnegative integer values standing for counts. For instance, we count packets in computer networks, people in monitored areas, or particles incident on detectors. Often, the ultimate goal is the modeling of these counts. However, standard techniques are computationally demanding and sensitive to the amount of available information. In our quest to solve the objective, we consider two prominent features of the contemporary world: online processing of streaming data, and the rapidly evolving ad-hoc agent networks. We propose a novel algorithm for a collaborative online estimation of the zero-inflated Poisson mixture models in diffusion networks. Its main features are low memory and computational requirements, and the capability of running in inhomogeneous networks. There, the agents possibly observe different processes, and locally decide which of their neighbors provide useful information. Two simulation examples demonstrate that the algorithm attains good stability and estimation performance even under slowly varying parameters.

An improved EMS simulation-optimization model with Poisson mixture distribution

A Discrete Event System (DES) simulation and optimization model is proposed for the ambulance allocation problem in an Emergency Medical Service (EMS) system. The accuracy of the proposed model was improved by estimation of input parameters using the Poisson mixture model and the Expectation Maximization Algorithm. The results were proven by Mann–Whitney and Kolmogorov–Smirnov tests. The DES model was run by the OptQuest program embedded in Arena software. The response times of the cases within the urban and rural regions were improved by 40% and 45%, respectively, and the station success rates in urban and rural areas were raised to 95% and 96%, respectively. Our results indicated that the number of ambulances must be revised, and their allocations to stations in the real system need to be reorganized to achieve the required EMS system performance standards.

Pseudo-document simulation for comparing LDA, GSDMM and GPM topic models on short and sparse text using Twitter data

Topic models are a useful and popular method to find latent topics of documents. However, the short and sparse texts in social media micro-blogs such as Twitter are challenging for the most commonly used Latent Dirichlet Allocation (LDA) topic model. We compare the performance of the standard LDA topic model with the Gibbs Sampler Dirichlet Multinomial Model (GSDMM) and the Gamma Poisson Mixture Model (GPM), which are specifically designed for sparse data. To compare the performance of the three models, we propose the simulation of pseudo-documents as a novel evaluation method. In a case study with short and sparse text, the models are evaluated on tweets filtered by keywords relating to the Covid-19 pandemic. We find that standard coherence scores that are often used for the evaluation of topic models perform poorly as an evaluation metric. The results of our simulation-based approach suggest that the GSDMM and GPM topic models may generate better topics than the standard LDA model.

Gibbs spatial process for characterization of filament interaction in ReRAM devices via photon emission microscopy

In this work, we investigate spatial statistical properties of filament patterns in resistive random-access memory (ReRAM) devices measured from a newly developed near-infrared photon emission microscopy (PEM) [Stellari et al., IEEE Electron Device Lett. 42, 828 (2021); Stellari et al., in Proceedings of the 47th International Symposium for Testing and Failure Analysis Conference (ISTFA) (ASM International, 2021), pp. 115–121]. Unlike previous reports on uncorrelated filaments [Stellari et al., IEEE Electron Device Lett. 42, 828 (2021); Wu et al., Appl. Phys. Lett. 99, 093502 (2011)], we report a strong clustering and non-Poisson pattern of filaments constructed from individual devices. A Poisson-mixture model incorporating the clustering (attractive) effect is introduced with an excellent agreement with the PEM data for global and nearest-neighbor spatial statistics. On the other hand, a two-filament pattern is also detected within the ReRAM devices. We found that both attractive and repulsive interactions among the filaments are required in a Gibbs process to explain the filament spatial distribution. We implemented a birth-death algorithm using a Markov-chain Monte Carlo approach and achieve good agreement with the PEM data using a generalized Morse potential.

Statistical process control of overdispersed count data based on one‐parameter Poisson mixture models

AbstractThe Poisson distribution is a discrete model widely used to analyze count data. Statistical control charts based on this distribution, such as the and charts, are relatively well‐established in the literature. Nevertheless, many studies suggest the need for alternative approaches that allow for modeling overdispersion, a phenomenon that can be observed in several fields, including biology, ecology, healthcare, marketing, economics, and industry. The one‐parameter Poisson mixture distributions, whose literature is extensive and essential, can model extra‐Poisson variability, accommodating different overdispersion levels. The distributions belonging to this class of models, including the Poisson‐Lindley (PL), Poisson‐Shanker (PSh), and Poisson‐Sujatha (PSu) models, can thus be used as interesting alternatives to the usual Poisson and COM‐Poisson distributions for analyzing count data in several areas. In this paper, we consider the class of probabilistic models mentioned above (as well as the cited three members of such a class) to develop novel and useful statistical control charts for counting processes, monitoring count data that exhibit overdispersion. The performance of the so‐called one‐parameter Poisson mixture charts, namely the ‐, ‐, and ‐ charts, is measured by the average run length in exhaustive numerical simulations. Some data sets are used to illustrate the applicability of the proposed methodology.

Mental Practice as an Additional Step Before Simulation Practice Facilitates Training in Bronchoscopic Intubation.

Learning bronchoscopy is challenging for novices, as it requires navigation in a 3-dimensional space under 2-dimensional viewing conditions and execution of complex motor skills with an unfamiliar instrument. Mental practice exercises are based on repeated visualization of motor actions without physically performing them, thereby promoting the learning of skills. We aimed to evaluate whether a teaching intervention including mental practice exercise modules for the acquisition of bronchoscopy skills improves fiberoptic intubation performance of novice learners. In this prospective cohort study, 24 pediatric intensive care trainees and respiratory therapists participating in a bronchoscopy learning curriculum in 2016-2017 attended a theoretical lecture followed by self-guided learning. Subsequently, the learners were randomly assigned to either participating in a teaching intervention including mental practice exercises or not (control group). The primary outcome was time to complete their first bronchoscopic intubation using a virtual reality simulator. Secondary outcomes were the occurrence of "red outs" (ie, the anatomy could no longer be visualized) or collisions with the airway wall. Bayesian Poisson Mixture models were used to estimate the effect of the intervention on outcomes. Furthermore, participation in the teaching intervention was examined in short interviews and with descriptive thematic analysis. Subjects in the intervention group completed the bronchoscopy on average 1.2 times faster (rate ratio 1.2 [95% credible intervals 1.1-1.3]). The posterior probability that the teaching intervention reduced the occurrence of "red outs" by more than half was 86%. No differences were found regarding the odds of colliding with the airway wall. Everyone except 1 trainee in the mental practice group engaged with and found the mental practice modules helpful. A teaching intervention including mental practice exercises represents a valuable additional learning strategy promoting the performance and complex skill acquisition of novice learners in the initial stages of learning bronchoscopy procedures.

Application of mixture distributions for identifying thresholds of frequent and high inpatient mental health service use in longitudinal data

Background There is a need for greater understanding about frequent and high use of inpatient mental health services, and those with ongoing increased needs. Most studies employ a threshold of frequent use (e.g. numbers of admissions) and high use (e.g. lengthy stays) without justification. Aims To identify model-driven thresholds for frequent/high inpatient mental health service use and contrast characteristics of patients identified using various models and thresholds. Method Retrospective population-based study using 12 years of longitudinal data for 5631 patients admitted with a mental health diagnosis. Two-component negative binomial and poisson mixture (truncated/untruncated) models identified thresholds for frequent/high use in a 12-month period. Results The two-component negative binomial mixture model resulted in the best model fit. Using negative binomial-derived thresholds, 5.3% of patients had a period of frequent use (admitted six or more times), 15.8% of high use (hospitalised for 45 or more days) and 3.5% of heavy use (both frequent and high use). The prevalence of specific mental health disorders (e.g. mood disorder and schizophrenia) among frequent and high use cohorts varied across thresholds. Conclusions This model-driven approach can be applied to identify thresholds in other cohorts. Threshold choice may depend on the magnitude and focus of potential interventions.

Prediction and optimization of sharing bikes queuing model in grid of Geohash coding

Dockless bike-sharing systems provide parking anywhere feature and environment-friendly approach for commuter. It is booming all over the world. Different from dockless bike-sharing systems, for example, previous studies focus on rental mode and docking stations planning. Yet, due to the fact that human mobility patterns of temporal and geographic lead to bike imbalance problem, we modeled human mobility patterns, predicted bike usage, and optimized management of the bike-sharing service. First, we proposed adaptive Geohash-grid clustering to classify bike flow patterns. For simplicity and rapid modeling, we defined three queuing models: over-demand, self-balance, and over-supply. Second, we improved adaptive Geohash-grid clustering-support vector machine algorithm to recognize self-balance pattern. Third, based on the result of adaptive Geohash-grid clustering-support vector machine, we proposed Markov state prediction model and Poisson mixture model expectation-maximization algorithm. Based on data set from Mobike and OFO, we conduct experiments to evaluate models. Results show that our models offer better prediction and optimization performance.

An exploration of gender gap using advanced data science tools: actuarial research community

This paper explores the role of gender gap in the actuarial research community with advanced data science tools. The web scraping tools were employed to create a database of publications that encompasses six major actuarial journals. This database includes the article names, authors’ names, publication year, volume, and the number of citations for the time period 2005–2018. The advanced tools built as part of the R software were used to perform gender classification based on the author’s name. Further, we developed a social network analysis by gender in order to analyze the collaborative structure and other forms of interaction within the actuarial research community. A Poisson mixture model was used to identify major clusters with respect to the frequency of citations by gender across the six journals. The analysis showed that women’s publishing and citation networks are more isolated and have fewer ties than male networks. The paper contributes to the broader literature on the “Matthew effect” in academia. We hope that our study will improve understanding of the gender gap within the actuarial research community and initiate a discussion that will lead to developing strategies for a more diverse, inclusive, and equitable community.

A self-consistent method to estimate the rate of compact binary coalescences with a Poisson mixture model

The recently published GWTC-1 (Abbott B P et al (LIGO Scientific Collaboration and Virgo Collaboration) 2019 Phys. Rev. X 9 031040)—a journal article summarizing the search for gravitational waves (GWs) from coalescing compact binaries in data produced by the LIGO-Virgo network of ground-based detectors during their first and second observing runs—quoted estimates for the rates of binary neutron star, neutron star black hole binary, and binary black hole mergers, as well as assigned probabilities of astrophysical origin for various significant and marginal GW candidate events. In this paper, we delineate the formalism used to compute these rates and probabilities, which assumes that triggers above a low ranking statistic threshold, whether of terrestrial or astrophysical origin, occur as independent Poisson processes. In particular, we include an arbitrary number of astrophysical categories by redistributing, via mass-based template weighting, the foreground probabilities of candidate events, across source classes. We evaluate this formalism on synthetic GW data, and demonstrate that this method works well for the kind of GW signals observed during the first and second observing runs.

The one-inflated positive Poisson mixture model for use in population size estimation.

The one-inflated positive Poisson mixture model (OIPPMM) is presented, for use as the truncated count model in Horvitz-Thompson estimation of an unknown population size. The OIPPMM offers a way to address two important features of some capture-recapture data: one-inflation and unobserved heterogeneity. The OIPPMM provides markedly different results than some other popular estimators, and these other estimators can appear to be quite biased, or utterly fail due to the boundary problem, when the OIPPMM is the true data-generating process. In addition, the OIPPMM provides a solution to the boundary problem, by labelling any mixture components on the boundary instead asone-inflation.

A Bayesian approach for some zero-modified Poisson mixture models

In this article, we propose a class of zero-modified Poisson mixture models as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros. A relevant feature of this class is that the zero modification can be incorporated using a zero truncation process and consequently, the proposed models can be expressed in the hurdle version. This procedure leads to the fact that the proposed models can be fitted without any previous information about the zero modification present in agiven dataset. A fully Bayesian approach has been considered for estimation and inference concerns. Three different simulation studies have been conducted to illustrate the performance of the developed methodology. The usefulness of the proposed class of models has been assessed by using three real datasets provided by the literature. A general model comparison with some well-known discrete distributions has been presented.

A zero-inflated Poisson mixture model to analyse spread and abundance of the Western Corn Rootworm in Austria

The Western Corn Rootworm (WCR, Diabrotica virgifera virgifera) has become one of the main maize pests in Europe. Our objective was to develop a model for mapping spread and abundance of WCR in Austria as a function of the natural spread, climatic conditions and the maize share in crop rotations. Records of a total of 5,338 WCR monitoring traps spread over Austria are available for the period 2002–2015, with 2,520 (47.2%) showing zero counts. We developed a spatial zero-inflated Poisson mixture (ZIP) model to relate WCR counts to climatic conditions and maize shares and account for zero-inflation, and spatial correlation in the count data. The model was validated by a 40-fold cross validation procedure and applied to Austrian cropland on a spatial resolution of 1 km. Results show that increased probabilities of WCR occurrence and abundance are associated with higher maize shares in crop rotations combined with a positive influence of higher winter temperatures and summer precipitation. The developed model provides a scientifically sound basis for analysing impacts of future climate change scenarios and crop rotational maize restrictions on the spread and abundance of WCR. It supports the development of WCR control measures.

Spatial–temporal traffic outlier detection by coupling road level of service

Traffic outlier detection is an essential topic in city management and data mining. Most traffic outliers are caused by accidents, control, protests, disasters, and many other events. Recently, traffic outlier detection methods are based on counting traffic flow, where the detection is inherited from the periodical changes of road flow. However, these approaches fail to detect the impact from upstream roads. Furthermore, the mappings between traffic congestion level and traffic flow are distinct from road to road. In this study, a Poisson mixture model (PMM) – coupled hidden Markov model (CHMM) outlier detection method would be introduced for detecting traffic anomalies which are from taxi global positioning system data. To make a finer-grained outlier detection method, road traffic congestion estimation, as well as the impact from upstream roads, are considered. PMM serves as an estimator to determine the congestion level for every road and CHMM is used to couple the road's impact. The experiment applies both semi-synthetic and real outlier data from the Beijing map, and the results reveal the advantages of both datasets.

Measuring the complexity of social associations using mixture models

We propose a method for examining and measuring the complexity of animal social networks that are characterized using association indices. The method focusses on the diversity of types of dyadic relationship within the social network. Binomial mixture models cluster dyadic relationships into relationship types, and variation in the preponderance and strength of these relationship types can be used to estimate association complexity using Shannon’s information index. We use simulated data to test the method and find that models chosen using integrated complete likelihood give estimates of complexity that closely reflect the true complexity of social systems, but these estimates can be downwardly biased by low-intensity sampling and upwardly biased by extreme overdispersion within components. We also illustrate the use of the method on two real datasets. The method could be extended for use on interaction rate data using Poisson mixture models or on multidimensional relationship data using multivariate mixture models.Significance statementAnimals from many species interact socially with multiple individuals, and these interactions form a social network. Pairs of individuals have social relationships that differ in their strength and type. This social complexity has long interested behavioural biologists, particularly in the context of social cognition. Measuring social complexity, however, presents challenges. We propose a new method for measuring the complexity of animal social networks. Our approach is based on quantifying variation in the strengths of social connections (measured using association indices) which we use to classify different types of pairwise relationships. We, then, use the number, strength and prevalence of these different types of relationships to measure association complexity. Our approach can be used to compare association complexity between populations and/or species. We provide code that researchers can use with their own datasets.