Empirical Distribution Models Research Articles

Forecast-Based Newsvendor Models for Hospital Bed Capacity Management

Hospitals worldwide share common challenges in finding the optimal number of patient beds in advance, which is referred to as the bed capacity management problem. Effective management cannot be achieved without an appropriate understanding of the stochastic nature of patient demands. In light of the widespread usage of newsvendor models in inventory management and the increasingly available operational data, we propose a data-driven approach to tackling the supply-demand matching problem under uncertainty, factoring in the observation that daily hospitalization demands are not independent and identically distributed. We develop forecast-based newsvendor models that use autoregressive integrated moving average (ARIMA) to make predictions, and determine the optimal bed capacity during the designated forecast periods. The performance of this approach is tested using real-world data from the West China Hospital. Our analysis affirms the superiority of the forecast-based models in practical settings and further enlightens the situations where forecast might not be effective - when the normality assumption of the noise distribution does not strictly hold, the empirical distribution model can be a computationally cost-effective choice.

Probabilistic prediction of short term wind power considering temporal and spatial dependence of prediction error

The short-term probabilistic prediction of wind power has the characteristics of spatial dependence and time-series dependence. Considering the two characteristics at the same time can improve the prediction level. In this paper, a probabilistic short-term wind power prediction model considering the temporal and spatial dependence of prediction error is proposed. Considering the coupling relationship between the two properties, the NWP(Numerical Weather Prediction) wind speed point prediction error in the historical period is hierarchical clustering, and the empirical distribution model is used to fit the probability distribution of the error under different wind conditions; the cumulative empirical distribution probability value corresponding to the NWP wind speed at the time to be predicted is bootstrap sampling; under the given confidence level, the possible wind speed at each time point to be predicted in the short term is calculated The power fluctuation range of the generator. The test results show that this method can ensure the statistical significance and fitting stability of the sub sample set at the same time, and improve the classification accuracy of the days to be predicted. Compared with considering a single property, the result of probability prediction performs better on multiple evaluation indexes.

Comparisons suggest more efforts are required to parameterize wind flow around shrub vegetation elements for predicting aeolian flux

Upon interacting with the atmosphere, vegetation could alter the wind distribution and consequently the erodibility of nearby region. The parameterization of wind distribution around vegetation is crucial for the prediction of surface aeolian flux. This paper compared the performances of existing empirical distribution models in the estimation of aeolian flux for shrub vegetation, focusing on distribution pattern and vegetation porosity (main parameter of distribution function). Predicted dust fluxes directly entrained by air flow show weak sensitivity to both distribution pattern and porosity in the case of low vegetation density, which suggests some aspects in dust forecast models might be simplified. However, both distribution pattern and porosity show significant effect on sand saltation transport rate in the lee of vegetation element and, consequently, on the formation and evolution of surface aeolian landforms. The contribution of dust fluxes released in wind increase zone to the total emission by using current parameterizations increases with both the decrease of wind speed and the increase of vegetation density. Nevertheless, the parameterization of wind increase zone needs to be validated and improved by further experimental and numerical investigations.

Experimental analysis of sea clutter using airborne circular scanning SAR in medium grazing angle

The theoretical statistical model of sea clutter is a key issue for maritime surveillance. In recent years, the statistical model of sea clutter has attracted much attention to design the detector well. Meanwhile, the circular scanning synthetic aperture radar (SAR) has been applied to wide surveillance of the sea surface. Therefore, the paper analyzes the validity of available sea clutter models for range Doppler images from different scan angles for moderate sea state in the medium grazing angle. The parameter estimation method for different distribution models employs the method of logarithmic cumulant (MoLC) based on Mellin transform uniformly. By the analysis of the fitting performance between the histogram of real data and the amplitude probability density function (PDF) of empirical distribution models and the goodness-of-fit (GoF) test for real data from different scan angles, it is indicated the generalized K (GK) distribution with generalized Gamma texture distribution can fit the sea clutter well for different scan angles in the medium grazing angle.

Empirical approaches in prediction of reservoir sediment distribution—An experience of 57 reservoirs in the USA and India

An accurate prediction of sediment distribution may minimize economic losses through proper and timely planning of the functional activities of a reservoir. This study assesses different temporal and spatial factors that affect for sediment deposition in a reservoir and its distribution. This study also focuses on evaluation of two popular distribution prediction methodologies, Area Increment and Empirical Area Reduction, based on experience with sediment distribution in 57 reservoirs in the USA and India. A non-iterative processed empirical distribution model (NPEDM) and a linear regression trend model (LRTM) are proposed to predict sediment distribution. Silt contributing area and inflow entering a reservoir are found to be the most significant factors affecting in reservoir sediment deposition. Compared to the Empirical Area Reduction method, the Area Increment method provided better prediction. The reservoir classification approach and empirical design distribution type curves given by Borland and Miller (1960) are found to be rational. Shape factor values for different periods indicate that reservoir shape (type) changes with time. Thus, long term prediction is not desirable in Type-II & III reservoirs using the Empirical Area Reduction method. Newly developed the NPEDM shows reasonably good prediction of sediment distribution. The NPEDM is very easy to apply and can be used in any reservoir of any size. Extrapolation of the trend of sediment distribution obtained from the LRTM indicates an accurate short term prediction in a few reservoirs as causes of temporal and spatial variations of sediment distribution including the factors of uncertainties of sediment deposition are implicit within the methodology.

THE DISTRIBUTION MODELS ADEQUACY ESTIMATION FOR USING IN SUBSCRIBER LOCATION DETERMINATION

In corporate networks with a large number of subscribers it is an important aspect to provide quality and timely service to provide information services and monitoring the movement of subscribers within the network. To solve this problem it is necessary to provide location determination. The article describes the method of position determining of the subscriber by measuring the radio signal strength at the mobile station. The article analyzes the existing empirical distribution models that operate in a given frequency range. An experimental research of the signal power measurement for a variety of determination conditions, namely indoor and outdoor space. Verification of empirical model with experimental data was made. The optimal model was defined for calculating the subscriber location for indoor and outdoor space.

Red clump stars from the LAMOST data I: identification and distance

We present a sample of about 120 000 red clump candidates selected from the LAMOST DR2 catalog based on the empirical distribution model in the effective temperature vs. surface gravity plane. Although, in general, red clump stars are considered as standard candles, they do not exactly stay in a narrow range of absolute magnitude, but may have a range of more than one magnitude depending on their initial mass. Consequently, conventional oversimplified distance estimations with the assumption of a fixed luminosity may lead to systematic bias related to the initial mass or age, which can potentially affect the study of the evolution of the Galaxy with red clump stars. We therefore employ an isochrone-based method to estimate the absolute magnitude of red clump stars from their observed surface gravities, effective temperatures and metallicities. We verify that the estimation removes the systematics well and provides initial mass/age estimates that are independent of distance with accuracy better than 10%.

Maximum‐Likelihood Recurrence Parameters and Conditional Probability of a Ground‐Rupturing Earthquake on the Southern Alpine Fault, South Island, New Zealand

Abstract The Alpine fault in south Westland, New Zealand, releases strains of Pacific–Australian relative plate motion in large earthquakes with an average interevent spacing of ∼330 years. A new record of earthquake recurrence has been developed at Hokuri Creek, with evidence for 22 events. The youngest Hokuri Creek earthquake overlaps in time and is believed to be the same as the oldest of another site about 100 km to the northwest near Haast. The combined record spans the last 7900 years and includes 24 events. We study the recurrence rate and conditional probability of ground ruptures from this record using a new likelihood‐based approach for estimation of recurrence model parameters. Paleoseismic parameter estimation includes both dating and natural recurrence uncertainties. Lognormal and Brownian passage time (BPT) models are considered. The likelihood surface has distribution location and width parameters as axes, the mean and standard deviation of the log recurrence for the lognormal, and the mean and coefficient of variation for the BPT. The maximum‐likelihood (ML) point gives the parameters most likely to have given rise to the data. The ML point, 50‐year conditional probabilities of a ground‐rupturing earthquake are 26.8% and 26.1% for the lognormal and BPT models, respectively. Contours of equal likelihood track the parameter pairs that are equally probable to have given rise to the observed data. Conditional probabilities on the lognormal 95% boundary around the ML point range from 18.2% to 35.8%. An empirical distribution model completely based on past recurrence times gives a similar conditional probability of 27.1% (9.6%–50.2%). In contrast, the time‐independent conditional probability estimate of 13.6% (8.8%–19.1%) is about half that of the time‐dependent models. A nonparametric test of earthquake recurrence at Hokuri Creek indicates that time‐dependent recurrence models best represent the southern Alpine fault of the South Island, New Zealand.

Implementing and interpreting local‐scale invasive species distribution models

AbstractAimUse of local‐scale non‐native plant species (NNS) distribution models has the potential to decrease survey effort and improve population prioritization for management. We developed and evaluated data collection methods and minimum sampling requirements to inform local‐scale models of NNS distribution. We also evaluated overall model predictive performance for 16 species at two sites and determined how classes of variables contributed to model performance and suggest invasion drivers.LocationWyoming and Idaho, USAMethodsA simulation study was used to test the efficiency of different sampling methods to predict imposed species distributions. Empirical distribution models of species occurrence data from two environmentally disparate sites were cross‐validated at increasing sample sizes, and the asymptotic maximum predictive performance and relative contribution of classes of variables were determined for 16 NNS.ResultsTransect sampling was the most efficient method for maximizing model performance after accounting for logistics. Minimum sample sizes to reach model maximum predictive performance were similar for the simulation (< 0.5% of study area) and empirical studies (mean of 0.13% using transects). Maximum predictive performance tended to be greater at the site with steeper environmental gradients, and topo‐climatic/biotic variables were most important to model improvement.Main conclusionsLocal‐scale SDMs can be useful to NNS managers. Using transect methodology, enough data can be collected (ca. 0.13% of the management area) to fit models within logistical/budgetary constraints. These models are most predictive for well‐established species as opposed to new invaders and in areas with steeper environmental gradients. Finally, topo‐climatic/biotic predictors are the most important variables for predicting more established species, but disturbance and dispersal limitation should be considered and quantified to ensure variables associated with dominant processes are included in the SDM.

Optimizing invasive species control across space: willow invasion management in the Australian Alps

Summary1. A key problem facing invasive species management is how best to allocate surveillance and control effort. Models of the establishment and spread of invasive species are widely used to predict species’ occurrence across space and inform resource prioritization. However, the way they should be used to direct control effort is less clear. Managers could exhaustively search and treat the few highest priority locations or apply less thorough effort more broadly. The choice between these options is a question of balancing resources to maximize local success while minimizing further spread.2. We link a spatial model predicting the likelihood of occurrence with a decision model to efficiently allocate human resources to control the weed Salix cinerea in south‐eastern Australia. Using data collected during an ongoing control programme, we construct a species distribution model, empirically estimate control effectiveness and perform a budget‐constrained optimization that identifies priority regions for control.3. Two alternative scenarios were explored against two seasonal budgets: control is equally valued in all areas or control is doubly valuable in conservation areas.4. Optimal control effort per site varied according to the likelihood of occurrence and site‐specific benefits of control. Prioritizing conservation areas led to a reduction in area treated because of greater allocation of control effort.5. Quantifying control effectiveness was critical for realistically allocating control effort. Targeting obvious individuals and then moving to new sites was more cost‐effective than attempting to control every individual at a high‐priority site.6. Synthesis and applications. We have developed a method to identify priority locations for invasive species control across a landscape. By integrating a decision model with an empirical distribution model, our method offers a better management outcome by maximizing the efficiency of control efforts. It identifies where and how much control effort should be allocated for maximum effect within a season. Effort is expressed as control staff time spent per site with the allocation readily visualized as a map. In general, a strategy of visiting sites where the species is most likely to occur and exerting a moderate amount of effort at these sites is most efficient.

Modelling groundwater-dependent vegetation patterns using ensemble learning

Abstract. Vegetation patterns arise from the interplay between intraspecific and interspecific biotic interactions and from different abiotic constraints and interacting driving forces and distributions. In this study, we constructed an ensemble learning model that, based on spatially distributed environmental variables, could model vegetation patterns at the local scale. The study site was an alluvial floodplain with marked hydrologic gradients on which different vegetation types developed. The model was evaluated on accuracy, and could be concluded to perform well. However, model accuracy was remarkably lower for boundary areas between two distinct vegetation types. Subsequent application of the model on a spatially independent data set showed a poor performance that could be linked with the niche concept to conclude that an empirical distribution model, which has been constructed on local observations, is incapable to be applied beyond these boundaries.

The effects of species’ range sizes on the accuracy of distribution models: ecological phenomenon or statistical artefact?

Summary Conservation scientists and resource managers increasingly employ empirical distribution models to aid decision‐making. However, such models are not equally reliable for all species, and range size can affect their performance. We examined to what extent this effect reflects statistical artefacts arising from the influence of range size on the sample size and sampling prevalence (proportion of samples representing species presence) of data used to train and test models. Our analyses used both simulated data and empirical distribution models for 32 bird species endemic to South Africa, Lesotho and Swaziland. Models were built with either logistic regression or non‐linear discriminant analysis, and assessed with four measures of model accuracy: sensitivity, specificity, Cohen's kappa and the area under the curve (AUC) of receiver‐operating characteristic (ROC) plots. Environmental indices derived from Fourier‐processed satellite imagery served as predictors. We first followed conventional modelling practice to illustrate how range size might influence model performance, when sampling prevalence reflects species’ natural prevalences. We then demonstrated that this influence is primarily artefactual. Statistical artefacts can arise during model assessment, because Cohen's kappa responds systematically to changes in prevalence. AUC, in contrast, is largely unaffected, and thus a more reliable measure of model performance. Statistical artefacts also arise during model fitting. Both logistic regression and discriminant analysis are sensitive to the sample size and sampling prevalence of training data. Both perform best when sample size is large and prevalence intermediate. Synthesis and applications. Species’ ecological characteristics may influence the performance of distribution models. Statistical artefacts, however, can confound results in comparative studies seeking to identify these characteristics. To mitigate artefactual effects, we recommend careful reporting of sampling prevalence, AUC as the measure of accuracy, and fixed, intermediate levels of sampling prevalence in comparative studies.

Empirical Distribution Models for Escherichia coli 57:H7 in Ground Beef Produced by a Mid‐size Commercial Grinder

ABSTRACT: The purpose of this research was to develop empirical models that describe the amount and distribution of ground beef contaminated with Escherichia coli O157:H7 when a contaminated beef trim is introduced into a batch of uncontaminated beef before processing in a mid‐size commercial grinder (34 g/s). A beef trim was inoculated with a rifampacin‐resistant strain of E. coli O157:H7 and added to a batch of noncontaminated trims at the grinding step. To study the distribution of the E. coli O157:H7rif in the ground beef, 6 treatments with different inoculum levels (1 to 6 log10 colony‐forming units [CFU]) were tested. Removal or pick up of the residual contamination with E. coli O157:H7rif left in the grinder was evaluated. E. coli O157:H7rif was detected in 9% to 86% of the total ground beef for the 1 to 6 log10 CFU inoculum levels, respectively. E. coli O157:H7rif contamination was detected in the collar that fixes the grinder's die and blade to the hub. An exponential algorithm described the relationship between the quantities of ground beef containing E. coli O157:H7rif and the inoculum level (R2= 0.82). Distribution models based on a Chi‐squared algorithm were developed for each inoculum level describing the contamination level as a function of the batch fraction processed (R2= 0.81 to 0.99). The results of this study corroborate that when beef processors test for pathogenic contamination in a mid‐scale grinder, they should test the beef residues in the collar that fixes the grinder's die and blade to the hub.

Hemlock Woolly Adelgid (Homoptera: Adelgidae) Dispersion and the Failure of Binomial Sampling to Estimate Population Density

Data collected in 1994 and 1995 from eastern hemlock stands in Pennsylvania and Virginia were used to evaluate the binomial sampling method for hemlock woolly adelgid. An empirical distribution model and a model based on the negative binomial distribution were used to describe the relationship between mean hemlock woolly adelgid density ( x ) and the proportion of samples with at least T hemlock woolly adelgid ( PT ). There were significant differences in the x versus PT relationship between locations and hemlock woolly adelgid generations regardless of the value of T (1–10) or model used. The inconsistency of the relationship may be a result of the respective phenologies of hemlock woolly adelgid and eastern hemlock, and of the effect that continued hemlock woolly adelgid feeding has on the production of new foliage. Binomial sampling procedures have been successfully developed for many pests of agricultural crops. The technique may not be suitable for long-lived hosts where pest attack significantly alters the food resource.