Assumed Parameter Values Research Articles

Comparison between least squares and percentile methods in estimating Rayleigh Kumaraswamy distribution, a simulation study

In this research, a new generalization of the Rayleigh distribution called the Rayleigh-Kumaraswamy distribution was introduced. The extended formulas for the probability density function (PDF) and cumulative distribution function (CDF) were derived. Furthermore, some uses of distribution properties such as moments and moments generating function were also derived. The PDF property of the distribution was preserved. Additionally, A simulation study was conducted using different sample sizes and various assume .Two different methods for estimating the parameters of the new distribution are presented: the least squares method, and the method based on percentiles. Simulation studies are conducted to compare the performance of these estimation methods using different sample sizes and assumed parameter values. The comparison is based on statistical criteria such as mean square error and bias. The results indicate that the least squares method performs the best

Analysing the potential impacts of three interventions on fruit and vegetable consumption in urban Kenya using participatory systems modelling.

This study uses participatory modelling with stakeholders to assess the potential impacts of three interventions intended to increase fruit and vegetable (F&V) consumption in urban Kenya. A participatory process using Group Model Building (GMB) developed a conceptual model of the determinants of vegetable consumption. A subsequent quantitative System Dynamics model using data from primary and secondary sources simulated vegetable consumption from 2020 to 2024 under three proposed interventions suggested by stakeholders: increasing consumer awareness, reducing post-harvest losses and increasing farm yields. Model analyses assumed mean parameter values and assessed uncertainty using 200 simulations with randomised parameter values. The research was implemented in Nairobi, Kenya with simulation analyses of mean per capita consumption in this location. Workshops convened diverse F&V value chain stakeholders (farmers, government officials, NGO staff and technical experts) to develop the conceptual model, data inputs and intervention scenarios. Increasing consumer awareness was simulated to increase vegetable consumption by relatively modest amounts by 2024 (5 g/person/d from a base of 131 g/person/d) under mean assumed value of value chain response parameters. Reducing perishability was simulated to reduce consumption due to the higher costs required to reduce losses. Increasing farm yields was simulated to have the largest impact on consumption at assumed parameter values (about 40 g/person/d) but would have a negative impact on farm profits, which could undermine efforts to implement this intervention. The combination of GMB and simulation modelling informed intervention priorities for an important public health nutrition issue.

Using a General Mathematical Model to Quantify the Fontan Paradox of Elevated Central Venous Pressure and Diminished Cardiac Output

A variety of serious complications often associated with Fontan procedure to palliate single ventricle physiology are related to elevated central venous pressure (CVP) and diminished cardiac output (CO). This “Fontan Paradox” is a fundamental challenge because some interventions benefit one of these variables at the cost of the other. Animal models employed to address the Fontan Paradox are limited, and the multiple mechanical properties affecting CVP and CO are difficult to measure, control, and scale to humans. Although complex mathematical models of the cardiovascular system have provided insights, the need to solve model equations numerically require that all parameter values are known a priori—results only apply to a subject characterized by a specific set of assumed parameter values. In contrast, it has been shown that the equations characterizing minimal closed-loop models can be solved algebraically, yielding algebraic formulas for hemodynamic variables in terms of mechanical properties of the heart and vasculature. Therefore, the purpose of the present work is to derive algebraic formulas for CVP and CO to address the Fontan Paradox. First, we utilized a modified minimal closed-loop model consisting of a single ventricle, arterial and venous vascular compartments, and systemic and pulmonary resistances. The end-diastolic pressure-volume relationship was linearized, and mean arterial pressure was assumed to be regulated by renal control of blood volume. Equations were solved algebraically for CVP, CO, and venous pressures. The resulting formulas for CVP and CO incorporate only five groups of parameters characterizing the 1) efficiency of heart-vascular interaction, 2) relative cardiac contractility, 3) relative pulmonary resistance, 4) theoretical stroke volume at zero ventricular pressure, and 5) theoretical CO at zero CVP. Of these, only mean arterial pressure (controlled by blood volume) and systemic resistance require a choice to be made of either rectifying CVP or CO. Furthermore, these general formulas indicate that altering blood volume or systemic resistance to treat low CO has a greater negative impact on CVP in subjects with diastolic dysfunction or high pulmonary resistance. The present work thus provides a novel tool for clinical investigators to explore the mechanical basis of the Fontan Paradox.

Mathematical modeling and stability analysis of endemic equilibrium point of gaming disorder

In this article, we propose a PEAR mathematical model that describes the dynamic of a population that reacts in the spread of the E-game infection. By using Routh-Hurwitz criteria and constructing Lyapunov functions, the local stability and the global stability of endimec equilibrium point are obtained. Since there are usually errors in data collection and assumed parameter values, we also study the sensitivity analysis of the model parameters to know the parameters that have a high impact on the reproduction number R0. The stability analysis of the model that they proposed shows that the system is locally and globally asymptotically stable at endemic equilibrium point when R0 > 1. Finally, some numerical simulations are performed to verify the theoretical analysis using Matlab software.

An Adaptive Bayesian Parameter Estimation of a Synchronous Generator Under Gross Errors

Polynomial-chaos-expansion-based surrogate models have recently been advocated in the literature for power system dynamic parameter estimation. Regarding the estimation of the uncertain generator parameters, a Bayesian inference framework has been proposed based on a polynomial-based reduced-order representation of the synchronous machines using assumed parameter values. Then, the non-Gaussian posterior probability distribution functions (pdfs) of these parameters are recovered through the stochastic sampling approach efficiently. However, facing very large parameter errors, the reliability of the surrogate model decreases, yielding biased estimation results. To overcome this problem, this article develops a hierarchical Bayesian inference framework that processes the measurements provided by phasor measurement units, while making use of multifidelity surrogates together with the importance sampling method. The latter allows us to estimate in an efficient manner the posterior pdfs of the uncertain parameters through the normalized weights of the prior samples. To improve the accuracy of the posterior pdfs, an adaptive procedure is further adopted in the importance sampling for the gradual evolution of its proposal functions. The new proposals assist in fine-tuning the sample space and thereby help to construct surrogates with higher fidelity. Through an iterative process, this approach is able to estimate accurately and efficiently non-Gaussian posterior pdfs of the uncertain generator parameters subject to gross errors.

Spirometry in selected clinical situations

Spirometry is the most frequently performed functional test of the respiratory system. In pulmonological practice it is a basic tool used to diagnose ventilation disorders and to monitor treatment. The results obtained during the test are compared to predicted values, that is, assumed parameter values, computed on the basis of anthropometrical data such as: age, gender and height, with the use of complex equations. The use of additional variables including, e.g. an ethnic group or a race as well as corrective factors, enables a more exact determination of their values. Spirometry can be conducted in a sitting or standing position; however, for the subject safety reasons it is usually performed in a sitting position. It allows to eliminate the risk of fall as a result of syncope or impaired balance. Spirometry in a standing position should be considered in measurably obese patients or in patients with a wide abdominal circumference caused by other reasons. Patients with normal body weight obtain equivalent or slightly higher spirometric values in a standing position. In the selected clinical situations some problems with the measurement of the actual hight of patients in a standard way (measurement without shoes, feet together, upright position, eyes straight ahead) and with correct calculation of predicted values occur. They are, among others, silhouette-disturbing disorders or diseases causing changes in body proportions, from the less often occurring, like Marfan syndrome or achondroplasia, to more frequent posture defects and mobility impairments. These diseases influence the change of the predictive functional parameter values which are used to compare with the obtained results. The aim of the study is to demonstrate the methods of height and predicted values determination on the basis of measurements of ranges between different body points with the use of simple and complex equations in a group of patients in whom the application of standard measurement methods is impossible.

Microscopic Simulation Replicates the Capacity Drop Phenomenon

Microscopic simulation is used widely to analyze traffic networks. The outputs of such models, such as travel time and delay, depend in large part on the assumed parameter values. These parameters determine the traffic capacity, whose interpretation is not straightforward as the maximum discharge flow of a bottleneck in a freeway can be lower under congested conditions than in an uncongested situation. This phenomenon is often referred to as the capacity drop, and must be accurately portrayed by microsimulation models to simulate traffic properly for long periods of time. This is specifically problematic when the total demand is between the maximum congested and uncongested flow rates as travel times may potentially be over- or underestimated depending on prevailing traffic conditions. Here, we simulate traffic flow in a bottleneck with a combined car-following and lane-changing model and use data from the 405 freeway near Irvine, CA to calibrate the model parameters. The calibrated model tracks closely the observed data and predicts accurately the capacity drop phenomenon.

Algebraic Formula Predicting the Fraction of Absorbed Fluid Transported By Mesenteric Lymphatic Vessels

When nutrients are absorbed into the interstitial space from the intestinal lumen, they can be transported either by the intestinal capillaries to the portal circulation or by mesenteric lymphatics to the cysterna chyli. Several perturbations can alter the fraction of fluid that is transported by the mesenteric lymphatics, including nutrients present in the intestinal lumen, and microvascular and cysterna chyli hydrostatic pressures. Experimental approaches employed to elucidate the mechanisms governing the relative flow through these two parallel pathways are limited, because critical parameters are difficult to measure and cannot be controlled independently. Conventional mathematical modeling approaches are also limited, because the numerical solution of of the systems of equations are sensitive to assumed parameter values and must employ advanced computational techniques. Therefore, the purpose of the present work was to develop a general algebraic formula that predicts the fraction of fluid that is transported by the mesenteric lymphatic vessels. The basic framework was developed by equating the fluid flow into the intestinal interstitial compartment from the lumen and fluid removed by mesenteric lymph flow and microvascular absorption. Transport of fluid between the interstitium and the capillaries was characterized by the Starling‐Landis equation. Lymph flow from the intestinal interstitium to the cysterna chyli was assumed to be a linear function of interstitial and cysterna chyli hydrostatic pressures. Nutrients were assumed to be actively transported from the intestinal lumen, and water was assumed to be transported iso‐osmotically as characterized by the Starling‐Landis equation. The system of equations were solved algebraically to yield a formula for the fraction of fluid transported by the mesenteric lymphatic vessels. This simple model reproduces measured values of fluid flows, as well as the preferential transport of fluid by mesenteric lymphatic vessels when lipids are absorbed. Not only does it predict how fluid transport is affected by changes in parameters characterizing microvascular and lymphatic function, it provides a novel means to estimate critical parameter values from measured fluid flow.

Epidemic model formulation and analysis for diarrheal infections caused by salmonella

Epidemic modeling can be used to gain better understanding of infectious diseases, such as diarrhea. In the presented research, a continuous mathematical model has been formulated for diarrhea caused by salmonella. This model has been analyzed and simulated to be established in a functioning form. Elementary model analysis, such as working out the disease-free state and basic reproduction number, has been done for this model. The basic reproduction number has been calculated using the next generation matrix method. Stability analysis of the model has been done using the Routh–Hurwitz method. Sensitivity analysis and parameter estimation have been completed for the system too using MATLAB packages that work on the Latin Hypercube Sampling and Partial Rank Correlation Coefficient methods. It was established that as long as R0 < 1, there will be no epidemic. Upon simulation using assumed parameter values, the results produced comprehended the epidemic theory and practical situations. The system was proven stable using the Routh–Hurwitz criterion and parameter estimation was successfully completed. Salmonella diarrhea has been successfully modeled and analyzed in this research. This model has been flexibly built and it can be integrated onto certain platforms to be used as a predictive system to prevent further infections of salmonella diarrhea.

Two-Stage Bayesian Study Design for Species Occupancy Estimation

A problem of interest for ecology and conservation is that of determining the best allocation of survey effort in studies aimed at estimating the proportion of sites occupied by a species. Many species are difficult to detect and often remain undetected during surveys at sites where they are present. Hence, for the estimator of species occupancy to be unbiased, detectability needs to be taken into account. In such studies there is a trade-off between sampling more sites and expending more survey effort within each site. This design problem has not been addressed to date with an explicit consideration of the uncertainty in assumed parameter values. In this article we apply sequential and Bayesian design techniques and show how a simple two-stage design can significantly improve the efficiency of the study. We further investigate the optimal allocation of survey effort between the two study stages, given a prior distribution for the parameter values. We address this problem using asymptotic approximations and then explore how the results change when the sample size is small, considering second-order approximations and highlighting the value of simulations as a tool for study design. Given the efficiency gain, we recommend following the sequential design approach for species occupancy estimation. This article has supplementary material online.

Assessing a Binary Measurement System With Varying Misclassification Rates When a Gold Standard Is Available

In manufacturing, we often use a binary measurement system (BMS) for 100% inspection to protect customers from receiving nonconforming product. We can assess the performance of a BMS by estimating the consumer's and producer's risks, the two misclassification rates. Here, we consider assessment plans and their analysis when a gold standard system (GSS) is available for the assessment study but is too expensive for everyday use. We propose a random-effects model to allow for variation in the misclassification rates within the populations of conforming and nonconforming parts. One possibility, here denoted the standard plan, is to randomly sample n parts and measure them once with the GSS and r times with the inspection system. We provide a simple analysis and planning advice for standard plans. In practice, the misclassification rates are often low and the underlying process has high capability. This combination of conditions makes the assessment of the BMS challenging. We show that we need a very large number of measurements with the standard plan in order to get precise estimators of the average misclassification rates and the true process performance. We consider an alternate design, here denoted the conditional assessment plan, where we select random samples from the sets of previously passed and failed parts. The sampled parts are measured once with the GSS and r times with the inspection system. When we augment the data from the conditional plans with available baseline information on the overall pass rate, we show that we can precisely estimate the parameters of interest with many fewer measurements. In the online supplementary materials, we provide R code to find maximum likelihood estimates and corresponding approximate standard errors, and to find the asymptotic standard deviation of the estimators with a selected plan size and assumed parameter values for both the standard and the conditional sampling plans.

Balancing Complexity and Simplicity in Mathematical Models of Fontan Circulations

Characterizing heart‐arterial‐venous interaction in the healthy adult is quite complicated. Blood pressures and flows depend on a large number of critical parameters, including compliances and contractilities of two ventricles, as well as arterial compliances, venous compliances and resistances of both systemic and pulmonary circulations. The additional complexity of the staged Fontan to palliate single ventricle physiology has made characterization insurmountable—the single ventricle and vasculature adapt not only to large changes in pressure after each of three surgeries, but also to large changes in blood volume in a rapidly growing infant. Mathematical models promising to elucidate the physiology of Fontan circulations have been too simple, lacking adaptive responses to altered hemodynamics. They also have been too complex, requiring numerical solutions that are exquisitely sensitive to assumed parameter values and are notoriously difficult to interpret. We therefore modified standard minimal models of each of the stages of the Fontan procedure to simplify the model equations. We then added select adaptive processes that modify cardiac and vascular properties. Because the resulting model solutions are algebraic, mean pressures and volumes are expressed explicitly in terms of critical cardiovascular parameters. The result is a novel tool that is complex enough to trust, yet simple enough to use.

Dynamic process model of mass effects on travel demand

Whereas transportation planners commonly predict the negative impacts of mass transportation, there is increasing empirical evidence of the existence of positive mass effects, whereby increased use of a mode by the ‘mass’ will generally increase its attractiveness for future travellers. In this paper we consider the dynamic impact of such an effect on the problem of travel demand forecasting, with particular regards to social network effects. Our proposed modelling approach is inspired by literature from social physics, evolutionary game theory and marketing. For simplicity of exposition, our model is specified for a scenario in which (a) there is a binary choice between two mobility lifestyles, referred to as car-oriented and transit-oriented, and (b) there are two population groups, where one is the “leading” or “innovative” population group and the other the “following” or “imitating” population group. This latter distinction follows the rather well-known Bass model from the marketing literature (1969). We develop the transition probabilities and transition dynamics. We illustrate with a numerical case study that despite lower intrinsic utility for the transit lifestyle, significant changes towards this lifestyle can be achieved by considering congestion, service improvements and mass effects. We further illustrate that mass effects can be positive or negative. In all cases we explore the sensitivity of our conclusions to the assumed parameter values.

Estimations of tidal characteristics and aquifer parameters via tide-induced head changes in coastal observation wells

Abstract. The groundwater fluctuations due to tidal variations at an observation well in a coastal aquifer can be used to determine the tidal characteristics and aquifer parameters without conducting an aquifer test. In this study, a method, comprised of Jeng et al.'s solution (2005) and simulated annealing (SA) algorithm, is developed to determine the coastal aquifer parameters (hydraulic diffusivity, beach slope, and aquifer thickness) as well as the tidal characteristics (bichromatic-tide amplitudes, bichromatic-tide wave frequencies, and tidal phase lag) from the analysis of the tide-induced well-water-level (WWL) data. The synthetic WWL data generated from Jeng et al.'s solution (2005) with assumed parameter values and field data obtained from Barrenjoey beach, Australia, are analyzed. The estimated parameter values obtained from analyzing synthetic WWL data by the present method show good agreements with the previously assumed parameter values. The parameter estimation procedure may however fail in the case of a large shallow water parameter which in fact violates the constraint on the use of Jeng et al.'s solution (2005). In the analysis of field WWL data, the results indicate that the aquifer parameters estimated from the present method with single or multiple well data are significantly different from those given in Nielsen (1990). Inspecting the observed WWL data and the WWL data predicted from Jeng et al.'s solution (2005) reveals that the present method may provide better estimations for the aquifer parameters than those given in Nielsen (1990).

Sample Size and Power for Cost-Effectiveness Analysis (Part 1)

Basic sample size and power formulae for cost-effectiveness analysis have been established in the literature. These formulae are reviewed and the similarities and differences between sample size and power for cost-effectiveness analysis and for the analysis of other continuous variables such as changes in blood pressure or weight are described. The types of sample size and power tables that are commonly calculated for cost-effectiveness analysis are also described and the impact of varying the assumed parameter values on the resulting sample size and power estimates is discussed. Finally, the way in which the data for these calculations may be derived are discussed.

Comment on Barclay and Vreysen: Published dynamic population model for tsetse cannot fit field data

The structure, and assumed parameter values, of a recent dynamic population model for tsetse (Diptera: Glossinidae) render it unable to fit published data on tsetse control programs using odor-baited targets, insecticide-treated cattle and the sterile insect technique (SIT). The underlying problem is a mismatch between the small size of the mapped cells (1 ha) and the long time-step, which allows flies to move only once every 5 days, and then only to an adjacent cell. Assumed rates of tsetse dispersal and killing by odor-baited targets are consequently at least an order of magnitude lower than observed in the field. Suggestions that Glossina pallidipes could be eradicated more rapidly with SIT, than using hundreds of targets per km2, is contradicted both by the field data and by three other independent modeling studies.

Evaluation of metabolism models for free‐water dissolved oxygen methods in lakes

Free‐water measurements of dissolved oxygen (DO) in lakes are becoming common and provide opportunities for estimating ecosystem processes, such as gross primary production (GPP) and ecosystem respiration (R). The models used to estimate metabolism often subsume biological processes into one parameter each for GPP and R. However, high‐frequency DO observations made over days show diverse patterns at multiple time scales, suggesting a complex suite of processes controls DO dynamics. Can we improve metabolism estimates and predictive ability for DO at diel scales by adding complexity to the models? In this study, we use data from two north temperate lakes to test a variety of metabolism models representing a suite of non‐linear metabolic processes. To test whether alternative models can be discriminated, we simulated DO with assumed parameter values and auto‐regressive noise, and fit the models to the simulated DO. The most complex model could be discriminated from simpler models and provided the most accurate and precise predictions. However, when models were fit to observed DO data from the sensor network, the simplest model predicted DO as well as the most complex one. The added complexity did not improve model performance. An analysis of the model residuals indicates that physics may explain some of the DO pattern not predicted, especially high‐frequency oscillations and anomalies that appear to coincide with weather patterns. Under reasonably stable weather conditions and at scales of a few days, simple metabolism models explain the bulk of diel DO variability.

Using solar energy to arrest the increasing rate of fossil-fuel consumption: The southwestern states of the USA as case studies

The paper first reviews some recently introduced ideas concerning the feasibility of realizing concentrator photovoltaic systems on a very large (state-wide) scale. In particular, energy and cost assumptions are re-discussed, the concepts of double and triple sustainability are recalled and used to perform a sensitivity study of the various assumed parameter values. The model is then applied to each of the southwestern states of the USA in order to assess the economic potential for each state to freeze its fossil fuel consumption at present levels and to provide all future electricity needs entirely from solar. It is found that the scheme is economically feasible for all of the states considered, varying in attractiveness from Utah (where low electricity tariffs are problematic), to California and Nevada, where the economics are by far the most attractive among all the states.

Comment on “The wrinkle-like slip pulse is not important in earthquake dynamics” by D. J. Andrews and R. A. Harris

[1] Andrews and Harris [2005] (hereinafter referred to as AH) found in several numerical simulations that effects associated with prescribed stress heterogeneities and timeweakening friction can suppress those generated dynamically by rupture on a bimaterial interface, and concluded that the wrinkle-like rupture mode is generally not important for earthquake dynamics. Their results are based on selective cases, rather than a systematic parameter-space study, and they do not form the basis for a general conclusion. Moreover, most of their cases are associated with conditions for which the bimaterial effects are weak due to combination of assumed parameter values, mixed rupture modes, relatively small propagation distance, and coarse grid. Considerations of a larger body of theoretical results and observations suggest that the wrinkle-like rupture may be relevant to earthquake dynamics. [2] Weertman [1980] showed analytically that mode II slip pulse on a bimaterial interface governed by Coulomb friction produces dynamic changes of normal stress that depend on the slip function, material properties and direction of rupture propagation. Subsonic propagation in the direction of slip of the compliant solid reduces dynamically the normal stress, whereas propagation in the opposite direction increases the normal stress. Adams [1995] showed analytically that mode II rupture on a bimaterial Coulomb interface has a strong dynamic instability that transfers energy during propagation to shorter wavelengths, leading to pulse sharpening and increasing slip velocity with propagation distance. The discussed effects are pure mode II phenomena on a bimaterial interface, and they do not exist for mode III rupture or in a homogeneous solid. For additional theoretical background, see Ranjith and Rice [2001] and Ben-Zion [2001]. [3] The analytical properties of mode II slip pulse on a bimaterial interface render numerical simulations of such rupture highly challenging. Very fine grid is needed to capture the sharp features associated with the pulse, while large propagation distance is required to reach a dynamic regime that is relatively free of initial transients and reflects the attractor of the evolving dynamic behavior. Andrews and Ben-Zion [1997] simulated mode II ruptures on a bimaterial Coulomb interface with a nucleation consisting of a localized stress drop having a favored propagation direction. They observed wrinkle-like slip pulses with properties compatible to the analytical results of Weertman and Adams. Similar pulses were found in subsequent simulations with increasing refinements and incorporation of additional physical ingredients, including a nucleation mechanism that generalizes the procedure of Andrews and Ben-Zion to a symmetrically expanding source without a preferred direction and slip-weakening friction [Shi and Ben-Zion, 2006]. [4] An assessment of the possible relevance of the wrinkle-like pulse to earthquake dynamics should focus on situations associated with mode II ruptures. Important such cases are large earthquakes on plate-bounding strikeslip faults. These earthquakes (referred to below as the ‘‘target’’ earthquakes) saturate the seismogenic zone, propagate predominately as mode II rupture, and are likely to be affected primarily by the elastic properties of the bounding crustal blocks (rather than the myriad of possible smallscale heterogeneities). As discussed below, the simulations of AH address in a rather limited way the dynamics of the large target earthquakes.

Multipoint Linkage Disequilibrium Mapping Using Multilocus Allele Frequency Data

This paper describes a likelihood based fine scale linkage disequilibrium mapping method for estimating the position of a disease predisposing gene relative to a battery of typed marker loci. The method uses multilocus allele frequency data from a sample of unrelated diseased individuals and from a sample of unrelated control individuals, that is, a case and control type design. This type of data could be obtained by typing DNA pools, which is less expensive than typing individuals separately. The method described uses a nonparametric model that makes it robust to the shape of the genealogy at the disease locus. It can be implemented efficiently, making a multipoint analysis of a data set of a thousand markers feasible. An example power analysis uses simulations to estimate the amount of information that can be extracted from fully resolved haplotype data, relative to multilocus allele frequency data. For the assumed parameter values and a battery of 10 markers, roughly three times narrower region estimates can be derived from haplotype data than from allele frequency data only. Depending on how we choose to measure information, allele frequency data at an additional approximately 18 or approximately 33 markers is needed to compensate for this loss of information.