Hypergeometric Model Research Articles

Portfolio problem for the α−hypergeometric stochastic volatility model with consumption

This paper solves the finite horizon optimal consumption-investment problem for an investor that trades in the α−hypergeometric stochastic volatility model, with preferences based on a power utility function. To find the optimal strategy, we follow the dynamic programming approach. First, we perform a suitable change of variables in order to fully transform the non-linear Hamilton-Jacobi-Bellman (HJB) equation into a semilinear one. Next, we apply the Girsanov theorem to deduce an implicit Feynman-Kac formula depending upon the volatility process. The operator defined by the Feynman-Kac representation is shown to be a contraction operator on a designed function space. Finally, the Banach fixed point theorem yields the existence of a solution to the HJB equation in the designed space. Moreover, we apply a verification theorem to guarantee that the solution of the HJB equation coincides with the value function.

A universal canopy gap fraction model for forests with various tree distributions based on Nilson's models considering directional overlaps among crowns

An accurate estimation of forest canopy gap fraction (GF) is a prerequisite for remote sensing retrievals of several associated canopy parameters e.g. leaf area index, fAPAR (fraction of photosynthetically active radiation absorbed by the canopy), clumping index, etc. A universal canopy GF model for forests is required for various tree distribution patterns on flat and slopping terrains, yet existing models so far do not possess all these abilities simultaneously. For example, the Neyman type-A model, the Poisson model, and the hypergeometric model are suitable only to forests with clumped, random, and regular tree distributions, respectively. In this regard, the suite of Nilson's canopy GF models developed for forests with various tree distributions have the potential to become universal models. For this purpose, this study attempts to overcome the following limitations of these models to make them be true universally applicable: (1) canopy GF calculated by the Nilson's models is mostly accurate for various tree distributions at nadir; whereas at it is either underestimated for clumped tree distributions or overestimated for regular tree distributions at off-nadir; and (2) Nilson's models were developed for flat terrains and untested for sloping terrains. Herein, two Nilson's models are modified by expanding the calculation of overlaps among crowns (OAC) at nadir to the whole hemispherical space. The results show that all canopy GF simulations in the new models (New91 and New99) show higher consistency with ray-tracing results than those in original Nilson's models in all directions, highlighting the need to consider directional OAC. The modified models (especially for New99) are validated in two RAMI forest stands and a Saihanba forest stand: the relative error in canopy GF between the modified models and a ray-tracing model is less than 10 % in all forest stands. The modified models (especially New99) are suitable for various tree distributions on flat and slopping terrains and therefore increased the universality of the original Nilson's models suitable for a wide-range of remote sensing applications. New99 can be deemed as a universal canopy GF model for forests with various tree distributions.

Hypergeometric viable models in f(R) gravity

A cosmologically viable hypergeometric model within the framework of the modified gravity theory f(R) has been derived based on the requirements of asymptotic behavior towards ΛCDM, the presence of an inflection point in the f(R) curve, and the viability conditions dictated by the phase space curves (m, r), where m and r denote characteristic functions of the model. To examine the constraints associated with these viability criteria, the models were expressed in terms of a dimensionless variable, namely R → x and f(R) → y(x) = x + h(x) + λ, where h(x) represents the deviation of the model from General Relativity. By employing the geometric properties imposed by the inflection point, differential equations were formulated to establish the relationship between and h″(x). The resulting solutions yielded models of the Starobinsky (2007) and Hu-Sawicki types. However, it was subsequently discovered that these differential equations correspond to specific cases of a hypergeometric differential equation, indicating that these models can be derived from a more general hypergeometric model. The parameter domains of this model were thoroughly analyzed to ensure its viability.

Compactly-Supported Isotropic Covariances on Spheres Obtained from Matrix-Valued Covariances in Euclidean Spaces

Let p, d be positive integers, with d odd. Let \(\varvec{\phi }:[0,+\infty ) \rightarrow {\mathbb {R}}^{p \times p}\) be the isotropic part of a matrix-valued and isotropic covariance function (a positive semidefinite matrix-valued function) that is defined over the d-dimensional Euclidean space. If \(\varvec{\phi }\) is compactly supported over \([0,\pi ]\), then we show that the restriction of \(\varvec{\phi }\) to \([0,\pi ]\) is the isotropic part of a matrix-valued covariance function defined on a d-dimensional sphere, where isotropy in this case means that the covariance function depends on the geodesic distance. Our result does not need any assumption of continuity for the mapping \(\varvec{\phi }\). Further, when \(\varvec{\phi }\) is continuous, we provide an analytical expression of the d-Schoenberg sequence associated with the compactly-supported covariance on the sphere, which only requires knowledge of the Fourier transform of its isotropic part, and illustrate with the Gauss hypergeometric covariance model, which encompasses the well-known spherical, cubic, Askey and generalized Wendland covariances, and with a hole effect covariance model. Special cases of the results presented in this paper have been provided by other authors in the past decade.

Risk assessment for norovirus foodborne illness by raw oyster (Ostreidae) consumption and economic burden in Korea

The objective of this study was to evaluate the probability of norovirus foodborne illness by raw oyster consumption. One hundred fifty-six oyster samples were collected to examine the norovirus prevalence. The oyster samples were inoculated with murine norovirus and stored at 4°C-25°C. A plaque assay determined norovirus titers. The norovirus titers were fitted with the Baranyi model to calculate shoulder period (h) and death rate (Log PFU/g/h). These kinetic parameters were fitted to a polynomial model as a function of temperature. Distribution temperature and time were surveyed, and consumption data were surveyed. A dose-response model was also searched through literature. The simulation model was prepared with these data in @RISK to estimate the probability of norovirus foodborne. One sample of 156 samples was norovirus positive. Thus, the initial contamination level was estimated by the Beta distribution (2, 156), and the level was .5.3 Log PFU/g. The developed predictive models showed that the norovirus titers decreased in oysters under the storage conditions simulated with the Uniform distribution (0.325, 1.643) for time and the Pert distribution (10, 18, 25) for temperature. Consumption ratio of raw oyster was 0.98%, and average consumption amount was 1.82 g, calculated by the Pert distribution [Pert {1.8200, 1.8200, 335.30, Truncate (0, 236.8)}]. 1F1 hypergeometric dose-response model [1 -(1 + 2.55 × 10−3 × dose)-0.086] was appropriate to evaluate dose-response. The simulation showed that the probability of norovirus foodborne illness by raw oyster consumption was 5.90 × 10−10 per person per day. The annual socioeconomic cost of consuming raw oysters contaminated with norovirus was not very high.

Functional Enrichment Analysis of Regulatory Elements.

Statistical methods for enrichment analysis are important tools to extract biological information from omics experiments. Although these methods have been widely used for the analysis of gene and protein lists, the development of high-throughput technologies for regulatory elements demands dedicated statistical and bioinformatics tools. Here, we present a set of enrichment analysis methods for regulatory elements, including CpG sites, miRNAs, and transcription factors. Statistical significance is determined via a power weighting function for target genes and tested by the Wallenius noncentral hypergeometric distribution model to avoid selection bias. These new methodologies have been applied to the analysis of a set of miRNAs associated with arrhythmia, showing the potential of this tool to extract biological information from a list of regulatory elements. These new methods are available in GeneCodis 4, a web tool able to perform singular and modular enrichment analysis that allows the integration of heterogeneous information.

Application of a Hypergeometric Model in Simulating Canopy Gap Fraction and BRF for Forest Plantations on Sloping Terrains

The influence of tree distribution and slope on canopy gap fraction (GF) and bidirectional reflectance factor (BRF) is shown here to be non-negligible. Trees are often assumed to be randomly distributed in natural forests due to random distribution of natural resources, but this assumption is not valid for forest plantations. A geometric optical model for forest plantations (GOFP) is a geometric optical model for forest plantations on horizontal surfaces based on the theory of exclusion distance among crowns. Sloping terrains change the exclusion distance among crowns, and inevitably affect the canopy GF and BRF. In this article, GOFP with a hypergeometric model (distances among trees are considered) on horizontal surfaces is modified as GOFP-T to simulate BRF for forest plantations on sloping terrains under two scenarios: (horizontal distances among crowns remain unchanged with slope) and (sloping distances among crowns remain unchanged with slope). Two three-dimensional (3-D) radiative transfer models (DART and LESS) and field measurements are used to evaluate and validate GOFP-T simulations. The results show that 1) the canopy GF, four component area ratios, and canopy BRF simulated by GOFP-T show high consistency with results from the two 3-D model: root-mean-square errors in GF, sunlit foliage, and sunlit ground are less than 0.02, 0.06, and 0.03, respectively; 2) forest coverage and canopy reflectance in GOFP-T are compared well with point cloud results from an airboard LiDAR system and Landsat 8 OLI surface reflectance products, respectively, indicating that GOFP-T has ability in simulating canopy reflectance for forest plantations on sloping terrains. GOFP-T with the hypergeometric model in this article is the first simple model to simulate canopy GF and BRF for forest plantations on sloping terrains.

$\alpha$-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs

In this article we propose a $\alpha$-hypergeometric model with uncertain volatility (UV) where we derive a worst-case scenario for option pricing. The approach is based on the connexion between a certain class of nonlinear partial differential equations of HJB-type (G-HJB equations), that govern the nonlinear expectation of the UV model and that provide an alternative to the difficult model calibration problem of UV models, and second-order backward stochastic differential equations (2BSDEs). Using asymptotic analysis for the G-HJB equation and the equivalent 2BSDE representation, we derive a limit model that provides an accurate description of the worst-case price scenario in cases when the bounds of the UV model are slowly varying. The analytical results are tested by numerical simulations using a deep learning based approximation of the underlying 2BSDE.

Evaluation of GOFP over four forest plots using RAMI and UAV measurements

ABSTRACT Comparison and validation of canopy reflectance (CR) models are two important steps to ensure their reliability. Pure forest plantations are an ideal type of forest for validating CR models because of their simple background and the low variance in the crown structures which are usually assumed to be identical in most CR models. A Geometric Optical Model for Forest Plantations (GOFP) was compared using dataset in two radiation transfer model intercomparison exercise (RAMI) stands and validated using in situ dataset of detailed optical and structural data of two forest plantations in the Saihanba Forestry Center, China. The results show that (1) the tree distributions in stands described by the hypergeometric model in GOFP show good consistencies with the dataset in the two RAMI stands and measurements from the two Saihanba forest stands; and (2) the CRs simulated with GOFP are also compared well in the two RAMI stands and validated with measurements collected with unmanned aerial vehicles in the two Saihanba stands. GOFP shows a better consistency with the CR measurements than those from CR models for natual forestsbecause the tree distribution in forest plantations is described more reasonably in GOFP.

Denoising Distantly Supervised Named Entity Recognition via a Hypergeometric Probabilistic Model

Denoising is the essential step for distant supervision based named entity recognition. Previous denoising methods are mostly based on instance-level confidence statistics, which ignore the variety of the underlying noise distribution on different datasets and entity types. This makes them difficult to be adapted to high noise rate settings. In this paper, we propose Hypergeometric Learning (HGL), a denoising algorithm for distantly supervised NER that takes both noise distribution and instance-level confidence into consideration. Specifically, during neural network training, we naturally model the noise samples in each batch following a hypergeometric distribution parameterized by the noise-rate. Then each instance in the batch is regarded as either correct or noisy one according to its label confidence derived from previous training step, as well as the noise distribution in this sampled batch. Experiments show that HGL can effectively denoise the weakly-labeled data retrieved from distant supervision, and therefore results in significant improvements on the trained models.

A comparison of hypothesis tests for homogeneity in meta-analysis with focus on rare binary events.

Analysis of rare binary events is an important problem for biomedical researchers. Due to the sparsity of events in such problems, meta-analysis that integrates information across multiple studies can be applied to increase the efficiency of statistical inference. Although it is critical to examine whether the effect sizes are homogeneous across all studies, a comprehensive review of homogeneity tests has been lacking, and in particular, no attention has been paid to infrequent dichotomous outcomes. We systematically review statistical methods for homogeneity testing. By conducting an extensive simulation analysis and two case studies, we examine the performance of 30 tests in meta-analysis of rare binary outcomes. When using log-odds ratio as the association measure, our simulation results suggest that there is no uniform winner. However, we recommend the test proposed by Kulinskaya and Dollinger (BMC Med Res Methodol, 2015, 15), which uses a gamma distribution to approximate the null distribution, for its generally good performance; for very rare events coupled with small within-study sample sizes, in addition to the Kulinskaya-Dollinger test, we further recommend the conditional score test based on the random-effects hypergeometric model proposed by Liang and Self (Biometrika, 1985, 72:353-358). One should be cautious about the use of the Wald tests, the Lipsitz tests (Biometrics, 1998, 54:148-160), and tests proposed by Bhaumik et al (J Am Stat Assoc, 2012, 107:555-567).

Optimal Portfolio for the $\alpha$-Hypergeometric Stochastic Volatility Model

In this article we study an optimal portfolio problem for an investor with constant relative risk aversion that trades in a market with asset prices described by the $\alpha$-hypergeometric stochas...

The Control Method of Marine Environment Monitoring Data Quality Based on Computer

Han, C., 2020. The control method of marine environment monitoring data quality based on computer. In: Li, L. and Huang, X. (eds.), Sustainable Development in Coastal Regions: A Perspective of Environment, Economy, and Technology. Journal of Coastal Research, Special Issue No. 112, pp. 390-393. Coconut Creek (Florida), ISSN 0749-0208.In the face of ocean big data with multi-source, multi-type, multi-dimensional, and dynamic characteristics, how to quickly and effectively obtain an optimized quality control method and perform quality control on it is one of the key issues that restrict the rapid application of ocean data. Introduce computer into the choice of marine data quality optimization control method; use hypergeometric distribution model to give the residual set of various marine quality control methods; based on computer algorithm, search and compare the residual set of each quality control method, and finally select Optimized marine data quality control method. Finally, the feasibility of the method is verified through the quality control of marine data at a certain sea area monitoring station.

Is higher power shorter duration radiofrequency energy is better than lower power longer duration strategy in catheter ablation of atrial fibrillation A meta-analysis

Abstract Background An ideal strategy for radiofrequency ablation (RFA) of atrial fibrillation (AF) in the left atrium should be efficient enough to achieve transmural lesions in left atrium with no or minimal collateral tissue damage. Resistive heating of high power short duration (HPSD) RFA has been found to result in lesions larger in width but lesser in depth compared to lower power longer duration (LPLD) RFA in some experimental studies. Purpose This meta-analysis was performed to compare procedural, short-term and long-term outcomes of HPSD versus LPLD RFA of AF. Methods PubMed, Embase and Cochrane databases were systematically reviewed. Five observational studies meeting criteria were included in the meta-analysis. All the studies scored six or more points in the New-castle Ottawa scale. There were considerable variations in the ablation strategies across the studies. However, radiofrequency power more than 40W was considered as high power. Hypergeometric model with exact likelihood function was utilized for statistical analysis. Results Baseline parameters and ablation details have been depicted in Table 1. 740 patients with HPSD and 287 patients with LPLD ablation strategies, were followed up from 6 to 30 months. Total procedural time (P value <0.0001) and ablation time (P value <0.0001) were significantly lower in the HPSD group than LPLD group. However, the fluoroscopy time was similar (P value = 0.09) in both the groups (Table 2). There were no occurrences of atrio-esophageal fistula or pulmonary venous stenosis in any of the studies. Cardiac tamponade (P value = 0.56), stroke (P value = 0.70) and AF recurrences (P value = 0.81), were similar in both groups (Table 2). Conclusion Newer HPSD and conventional LPLD RFA, both the strategies are very safe procedure for treatment of RFA with low to no procedural complications. AF recurrence rates were reasonably high irrespective of ablation strategies, however, no strategy scored statistically better over the other one. Large randomized multi-centric studies with long-term follow up are needed to test the theoretical advantage of HPSD ablation over the traditional ablation strategy of AF. Funding Acknowledgement Type of funding source: None

Improved strategy to collect sensitive data by using negative binomial and negative hypergeometric distribution as randomization devices

In this paper, we improve upon the negative binomial randomized response model by implementing a two-stage randomization process. Using the modified estimator of the proportion of members of a population possessing a sensitive attribute, we claim to achieve both better efficiency and better protection. The findings are verified based on extensive simulation study. Then we improvise the technique of use of negative hypergeometric distribution by introducing two-stage randomization response process. Using our new technique, we also assess the efficiency and protection of the respondents as compared to the negative hypergeometric model through extensive simulation studies. We also provide SAS codes used in the evaluations of the strategies considered.

On testing for seed sample heterogeneity with the exact probability distribution of the germination count range

AbstractSeed lot heterogeneity is often evaluated through the range between germination percentages of four seed samples, considering normal and binomial approximations for calculating the tolerated range (S). In this paper, an exact test for the germination count range (R) is derived based on the hypergeometric and the binomial probability model for germination count. Through Monte Carlo simulations, the empirical distribution of R is built to evaluate the quantiles of the exact distributions. Moreover, a power analysis is performed by simulation. Sample size and germination rate effects are evaluated. In lots with a high germination rate, the proposed test based on the hypergeometric model is about 20% more powerful than the test based on the S-value. A table containing the critical values is presented and recommended to be used in off-range heterogeneity testing.

Asymptotic versus exact methods in the analysis of contingency tables: Evidence-based practical recommendations

Controversy over the validity of significance tests in the analysis of contingency tables is motivated by the disagreement between asymptotic and exact p values and its dependence on the magnitude of expected frequencies. Variants of Pearson's X2 statistic and their asymptotic distributions were proposed to overcome the difficulties, but several approaches also exist to conduct exact tests. This paper shows that discrepant asymptotic and exact results may or may not occur whether expected frequencies are large or small: Eventual inaccuracy of asymptotic p values is instead caused by idiosyncrasies of the discrete distribution of X2. More importantly, discrepancies are also artificially created by the hypergeometric sampling model used to perform exact tests. Exact computations under the alternative full-multinomial or product-multinomial models require eliminating nuisance parameters and we propose a novel method that integrates them out. The resultant exact distributions are very accurately approximated by the asymptotic distribution, which eliminates concerns about the accuracy of the latter. We also discuss that the two-stage approach that tests for significance of residuals conditional on a significant X2 test is inadvisable and that an alternative single-stage test preserves Type-I error rates and further eliminates concerns about asymptotic accuracy.

Quality Control of “As Built” BIM Datasets Using the ISO 19157 Framework and a Multiple Hypothesis Testing Method Based on Proportions

Building information model (BIM) data are digital and geometric-based data that are enriched thematically, semantically, and relationally, and are conceptually very similar to geographic information. In this paper, we propose both the use of the international standard ISO 19157 for the adequate formulation of the quality control for BIM datasets and a statistical approach based on a binomial/multinomial or hypergeometric (univariate/multivariate) model and a multiple hypothesis testing method. The use of ISO 19157 means that the definition of data quality units conforms to data quality elements and well-defined scopes, but also that the evaluation method and conformity levels use standardized measures. To achieve an accept/reject decision for quality control, a statistical model is needed. Statistical methods allow one to limit the risks of the parties (producer and user risks). In this way, several statistical models, based on proportions, are proposed and we illustrate how to apply several quality controls together (multiple hypothesis testing). All use cases, where the comparison of a BIM dataset versus reality is needed, are appropriate situations in which to apply this method in order to supply a general digital model of reality. An example of its application is developed to control an “as-built” BIM dataset where sampling is needed. This example refers to a simple residential building with four floors, composed of a basement garage, two commercial premises, four apartments, and an attic. The example is composed of six quality controls that are considered simultaneously. The controls are defined in a rigorous manner using ISO 19157, by means of categories, scopes, data quality elements, quality measures, compliance levels, etc. The example results in the rejection of the BIM dataset. The presented method is, therefore, adequate for controlling BIM datasets.

SPARSim single cell: a count data simulator for scRNA-seq data.

Single cell RNA-seq (scRNA-seq) count data show many differences compared with bulk RNA-seq count data, making the application of many RNA-seq pre-processing/analysis methods not straightforward or even inappropriate. For this reason, the development of new methods for handling scRNA-seq count data is currently one of the most active research fields in bioinformatics. To help the development of such new methods, the availability of simulated data could play a pivotal role. However, only few scRNA-seq count data simulators are available, often showing poor or not demonstrated similarity with real data. In this article we present SPARSim, a scRNA-seq count data simulator based on a Gamma-Multivariate Hypergeometric model. We demonstrate that SPARSim allows to generate count data that resemble real data in terms of count intensity, variability and sparsity, performing comparably or better than one of the most used scRNA-seq simulator, Splat. In particular, SPARSim simulated count matrices well resemble the distribution of zeros across different expression intensities observed in real count data. SPARSim R package is freely available at http://sysbiobig.dei.unipd.it/? q=SPARSim and at https://gitlab.com/sysbiobig/sparsim. Supplementary data are available at Bioinformatics online.

Study of changing statistics model’s influence on the exploitation and conformity of results in the new standard version ISO 14644 part 1.

Recently, the first two parts of the standard ISO 14644-1 and 2 were updated. This followed a 9-year process of revision. The standard is applicable across several industries covering healthcare, pharmaceuticals and electronics; and it outlines the approach for the design, classification and operation of cleanrooms. This article assesses the influence of the changing ISO 14644-1 on the conformity of the results. The initial version of Part 1 was based on the wrong hypothesis of a Gaussian distribution of particle concentration (in reality, the spatial distribution of particles is random). It is a hypergeometric model that has been selected for the revision of this standard. If you have seen in the standard ISO 14644-1 of 1999 you will notice that all the calculations are made according to the normal law, like the average, the mean of the averages, the standard deviation and 95% upper confidence limit... then in reality the distribution of the particles in the air in a cleanroom it's random, for this reason in this new version, it is a hypergeometric model that has been selected for the revision of this standard. In this article we have given a comparison between the two versions of the standard ISO 14644 part 1 and then it has been demonstrated by real case studies that the old version of the standard was based on the wrong hypothesis. After the comparison and study that we have done we encountered a contradiction among two versions of the standard IOS14644-1 (1999 and 2015), that we have treated in the same room, by the end of this experiment we drew out that the room is declared compliant in the new version 2015 and not compliant in the old version 1999, which aroused our curiosity to detect the error in the old version by this real case study.