Estimates Of Model Parameters Research Articles

Reliability inference for a family of inverted exponentiated distributions under block progressive Type II censoring

In this article, estimation of survival characteristics is discussed when life tests are performed against different test facilities using block progressive Type-II censoring. Under the assumption that the lifetimes of test units follow a family of inverted exponentiated distributions, estimates are derived under classical and hierarchical Bayesian frameworks when the differences in different test facilities are taken into consideration. Maximum likelihood estimators are obtained and their existence and uniqueness properties are also established. In addition, Bayes estimators are provided under a hierarchical framework, and a hybrid Metropolis-Hastings sampling procedure is proposed for complex posterior computation. The performance of all the proposed approaches is compared via extensive simulation studies and two real-life data are analyzed for illustration. From numerical results we observe that the hierarchical approach provides relatively better estimates for model parameters.

Statistical Modeling of Right-Censored Spatial Data Using Gaussian Random Fields

Consider a fixed number of clustered areas identified by their geographical coordinates that are monitored for the occurrences of an event such as a pandemic, epidemic, or migration. Data collected on units at all areas include covariates and environmental factors. We apply a probit transformation to the time to event and embed an isotropic spatial correlation function into our models for better modeling as compared to existing methodologies that use frailty or copula. Composite likelihood technique is employed for the construction of a multivariate Gaussian random field that preserves the spatial correlation function. The data are analyzed using counting process and geostatistical formulation that led to a class of weighted pairwise semiparametric estimating functions. The estimators of model parameters are shown to be consistent and asymptotically normally distributed under infill-type asymptotic spatial statistics. Detailed small sample numerical studies that are in agreement with theoretical results are provided. The foregoing procedures are applied to the leukemia survival data in Northeast England. A comparison to existing methodologies provides improvement.

A constrained maximum likelihood approach to developing well-calibrated models for predicting binary outcomes.

The added value of candidate predictors for risk modeling is routinely evaluated by comparing the performance of models with or without including candidate predictors. Such comparison is most meaningful when the estimated risk by the two models are both unbiased in the target population. Very often data for candidate predictors are sourced from nonrepresentative convenience samples. Updating the base model using the study data without acknowledging the discrepancy between the underlying distribution of the study data and that in the target population can lead to biased risk estimates and therefore an unfair evaluation of candidate predictors. To address this issue assuming access to a well-calibrated base model, we propose a semiparametric method for model fitting that enforces good calibration. The central idea is to calibrate the fitted model against the base model by enforcing suitable constraints in maximizing the likelihood function. This approach enables unbiased assessment of model improvement offered by candidate predictors without requiring a representative sample from the target population, thus overcoming a significant practical challenge. We study theoretical properties for model parameter estimates, and demonstrate improvement in model calibration via extensive simulation studies. Finally, we apply the proposed method to data extracted from Penn Medicine Biobank to inform the added value of breast density for breast cancer risk assessment in the Caucasian woman population.

Abstract PO4-02-12: MDA iLobular Prognostic Tool: A Novel Approach for Risk Stratification in Invasive Lobular Carcinoma

Abstract Background: Invasive lobular carcinoma (ILC) is a distinct subtype of breast cancer that differs from the more common invasive ductal carcinoma (IDC) by its unique characteristics that influence prognosis. Recent studies have shown that ILC is associated with worse long-term outcomes compared to IDC. Risk stratification is essential in breast cancer for tailoring treatment plans to the individual patient’s needs, maximizing the chances of successful outcomes and minimizing unnecessary interventions. Although there are multiple tools available for breast cancer, there is currently not a risk stratification tool that is specific for ILC. The MDA iLobular prognostic tool is the first risk stratification tool that has been developed specifically for ILC patients. Methods: We retrospectively searched for patients treated at MD Anderson Cancer Center with a diagnosis of stage I-III ILC in our prospectively collected electronic database. The study focused on two primary endpoints: Overall Survival (OS) and Distant Recurrence Free Survival (DRFS). We utilized univariate and multivariate Cox Proportional Hazard (PH) regression models to assess the statistical significance of all variables. The univariate Cox analysis identified prognostic factors, which were further analyzed using backward and stepwise multivariate Cox proportional hazards regression analysis. This process helped identify statistically significant prognostic factors that were included in the final multivariate models. We estimated hazard ratios and 95% confidence intervals for each factor, considering a P-value of < 0.05 as statistically significant. To evaluate the performance of the fitted multivariate Cox PH regression models for OS and DRFS, we randomly divided two-thirds of the data points into a training dataset, while the remaining one-third constituted the test dataset. We assessed the discrimination capacity of each model using Harrell's C-index. Results: The study included a total of 4,216 female patients, with a median age of 56 years. The median pathological tumor size was 2 mm, and the median number of lymph nodes was one. Among these patients, 1,376 were pre-menopausal, while 2,837 were post-menopausal. The training cohort was a subset of 2,950 patients and the test cohort was a subset of 1,266 patients. After evaluating various prognostic models, we identified the model with the highest prognostic accuracy for OS and DRFS. This selected model demonstrated a Harrell's C-index of 0.704 for OS and 0.718 for DRFS on the training dataset and a Harrell's C-index of 0.702 for OS and 0.671 for DRFS on the test dataset. The model incorporated several covariates, including age at the time of diagnosis, number of lymph nodes, pathological tumor size (mm), ER status, tumor grade, ILC histology, and the presence or absence of concomitant LCIS (Table 1). Conclusion: In conclusion, the MDA iLobular prognostic tool represents a significant advancement as the first dedicated tool for risk stratifying ILC, providing valuable guidance for tailoring therapy to individual ILC patients based on their specific risk profiles. Table 1. Multivariate Cox proportional hazard model parameter estimates for OS and DRFS Citation Format: Jason Mouabbi, Sarah Pasyar, Roland Bassett, Akshara Singareeka Raghavendra, Amy Hassan, Rachel Layman, Debu Tripathy. MDA iLobular Prognostic Tool: A Novel Approach for Risk Stratification in Invasive Lobular Carcinoma [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO4-02-12.

Estimation for generalized linear cointegration regression models through composite quantile regression approach

This paper introduces a meaningful approach employing composite quantile regression (CQR) to estimate generalized linear cointegration regression models. We elucidate the fundamental structure of the proposed model by presenting its underlying expressions and derive the asymptotic distribution of the estimates of model parameters. Through extensive simulations, our findings demonstrate the superior robustness and precision of the CQR method compared to ordinary least squares (OLS) and quantile regression (QR) approaches. The application of the model to economic and financial variables highlights its significant academic and practical value.

Pedestrian injury severities resulting from vehicle/pedestrian intersection crashes: An assessment of COVID-contributing temporal shifts

Pedestrian mobility has become an increasingly important concern in transportation system analysis because of its positive impacts on the environment and healthy lifestyles. However, pedestrian safety in a vehicle-dominated transportation network remains a concern and potential barrier to pedestrian mobility, with pedestrian intersection safety being of particular concern. In addition, it is important to understand how pedestrian safety has been affected by the COVID-19 pandemic, perhaps permanently shifting pedestrian injury risks. This research seeks to provide insight into how pedestrian injury risks at intersections have changed as a result of the pandemic by estimating a series pedestrian injury severity models. To do so, unconstrained and partially constrained random parameters multinomial logit models with heterogeneity in the means of random parameters were estimated. Using Florida data, two one-year periods (one year before and one year after the COVID-19 pandemic) were defined based on vehicle miles traveled. The sample includes 3,780 single pedestrian-single vehicle crashes (2,348 from daytime and 1,432 from nighttime). A broad range of variables was considered to assess how the parameters may have shifted between the before and after periods. A series of likelihood ratio tests were conducted to examine the stability of model parameter estimates across the predefined time periods as well as to determine the differences between the daytime and nighttime crash injury severity outcomes. The results show that the nighttime crashes experienced more temporal shifts relative to daytime crashes. The findings also showed that both pedestrian and driver behavior played key temporally-shifting roles before and after the COVID-19 pandemic period. Finally, the out-of-sample simulations suggest that pedestrian injuries have become more severe after the pandemic.

Bayesian modeling of quantiles of body mass index among under-five children in Ethiopia

BackgroundBody Mass Index (BMI) is a measurement of nutritional status, which is a vital pre-condition for good health. The prevalence of childhood malnutrition and the potential long-term health risks associated with obesity in Ethiopia have recently increased globally. The main objective of this study was to investigate the factors associated with the quantiles of under-five children’s BMI in Ethiopia.MethodsData on 5,323 children, aged between 0-59 months from March 21, 2019, to June 28, 2019, were obtained from the Ethiopian Mini Demographic Health Survey (EMDHS, 2019), based on the standards set by the World Health Organization. The study used a Bayesian quantile regression model to investigate the association of factors with the quantiles of under-five children’s body mass index. Markov Chain Monte Carlo (MCMC) with Gibbs sampling was used to estimate the country-specific marginal posterior distribution estimates of model parameters, using the Brq R package.ResultsOut of a total of 5323 children included in this study, 5.09% were underweight (less than 12.92 BMI), 10.05% were overweight (BMI: 17.06 – 18.27), and 5.02% were obese (greater than or equal to 18.27 BMI) children’s. The result of the Bayesian quantile regression model, including marginal posterior credible intervals (CIs), showed that for the prediction of the 0.05 quantile of BMI, the current age of children [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document}= -0.007, 95% CI :(-0.01, -0.004)], the region Afar [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = - 0.32, 95% CI: (-0.57, -0.08)] and Somalia[β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = -0.72, 95% CI: (-0.96, -0.49)] were negatively associated with body mass index while maternal age [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = 0.01, 95% CI: (0.005, 0.02)], mothers primary education [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document}= 0.19, 95% CI: (0.08, 0.29)], secondary and above [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = 0.44, 95% CI: (0.29, 0.58)], and family follows protestant [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = 0.22, 95% CI: (0.07, 0.37)] were positively associated with body mass index. In the prediction of the 0.95 (or 0.85?) quantile of BMI, in the upper quantile, still breastfeeding [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = -0.25, 95% CI: (-0.41, -0.10)], being female [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = -0.13, 95% CI: (-0.23, -0.03)] were negatively related while wealth index [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = 0.436, 95% CI: (0.25, 0.62)] was positively associated with under-five children’s BMI.ConclusionsIn conclusion, the research findings indicate that the percentage of lower and higher BMI for under-five children in Ethiopia is high. Factors such as the current age of children, sex of children, maternal age, religion of the family, region and wealth index were found to have a significant impact on the BMI of under-five children both at lower and upper quantile levels. Thus, these findings highlight the need for administrators and policymakers to devise and implement strategies aimed at enhancing the normal or healthy weight status among under-five children in Ethiopia.

How robust are estimates of key parameters in standard viral dynamic models?

Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.

CovXtreme : MATLAB software for non-stationary penalised piecewise constant marginal and conditional extreme value models

The covXtreme software provides functionality for estimation of marginal and conditional extreme value models, non-stationary with respect to covariates, and environmental design contours. Generalised Pareto (GP) marginal models of peaks over threshold are estimated, using a piecewise-constant representation for the variation of GP threshold and scale parameters on the (potentially multidimensional) covariate domain of interest. The conditional variation of one or more associated variates, given a large value of a single conditioning variate, is described using the conditional extremes model of Heffernan and Tawn (2004), the slope term of which is also assumed to vary in a piecewise constant manner with covariates. Optimal smoothness of marginal and conditional extreme value model parameters with respect to covariates is estimated using cross-validated roughness-penalised maximum likelihood estimation. Uncertainties in model parameter estimates due to marginal and conditional extreme value threshold choice, and sample size, are quantified using a bootstrap resampling scheme. Estimates of environmental contours using various schemes, including the direct sampling approach of Huseby et al. 2013, are calculated by simulation or numerical integration under fitted models. The software was developed in MATLAB for metocean applications, but is applicable generally to multivariate samples of peaks over threshold data. The software and case study data can be downloaded from GitHub, with an accompanying user guide.

Statistical inference of comparative generalized inverted exponential populations under joint adaptive progressive type-II censored samples

Design of efficient test plans to assessing product reliability rapidly, is a critical step to obtain product reliability accurately. In this paper, we are adopted the problem of statistical inference of two generalized inverted exponential populations in a competing duration. To save the balance between the optimal test time and the number of failures needing for statistical inference, joint adaptive type-II hybrid progressive censoring scheme is applied. The model parameters are estimated with classical methods (maximum likelihood and bootstrap) for point estimate and the corresponding confidence intervals. Also, Bayes estimators of model parameters are computed under importance sample technique with the corresponding Bayes credible intervals. A real data sets are analyzed for illustrating purposes. The results are compared and assessed through Monte Carlo simulation study.

Influence of spectral bandwidth on the working curve in vat photopolymerization

In vat photopolymerization, 3-dimensional parts are fabricated by using patterned light to spatially cure a liquid resin. One of the foundational measurements for vat photopolymerization is known as the working curve whereby the depth (i.e. thickness) of cured resin is measured as a function of radiant exposure. The commonly applied mathematical model for the working curve – known widely as the Jacobs model – assumes a monochromatic light source. The Jacobs model has been widely used, but in many cases significant deviations between the Jacobs model and the data have been observed. Herein, we extend the Jacobs model by deriving a polychromatic model that accounts for broadband light sources (e.g. light emitting diodes, LEDs). We demonstrate through experiment and theory that in certain cases the deviations from Jacobs’ original model can be explained and understood as an optical ‘inner filter’ effect. The ability of the Jacobs model to capture the working curve behavior is shown to be dependent on the bandwidth of the light source in conjunction with the gradient in the absorption spectrum of the resin in the vicinity of the light source spectrum. Additionally, we offer an empirical model function that better fits experimental data and allows for an improved estimate of model parameters. Broadly, this work aims to strengthen the conceptual link between the working curve measurement and the photophysical parameters that are intrinsic to vat photopolymerization printing.

MbDecoda: a debiased approach to compositional data analysis for microbiome surveys.

Potentially pathogenic or probiotic microbes can be identified by comparing their abundance levels between healthy and diseased populations, or more broadly, by linking microbiome composition with clinical phenotypes or environmental factors. However, in microbiome studies, feature tables provide relative rather than absolute abundance of each feature in each sample, as the microbial loads of the samples and the ratios of sequencing depth to microbial load are both unknown and subject to considerable variation. Moreover, microbiome abundance data are count-valued, often over-dispersed and contain a substantial proportion of zeros. To carry out differential abundance analysis while addressing these challenges, we introduce mbDecoda, a model-based approach for debiased analysis of sparse compositions of microbiomes. mbDecoda employs a zero-inflated negative binomial model, linking mean abundance to the variable of interest through a log link function, and it accommodates the adjustment for confounding factors. To efficiently obtain maximum likelihood estimates of model parameters, an Expectation Maximization algorithm is developed. A minimum coverage interval approach is then proposed to rectify compositional bias, enabling accurate and reliable absolute abundance analysis. Through extensive simulation studies and analysis of real-world microbiome datasets, we demonstrate that mbDecoda compares favorably with state-of-the-art methods in terms of effectiveness, robustness and reproducibility.

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

AbstractIn this paper, we harness a result in point process theory, specifically the expectation of the weighted K-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an estimation method to derive parameter estimates for a particular model assumed for the data. The underlying motivation is to avoid the difficulties associated with dealing with complex likelihoods in point process models and their maximization. The exploited result makes our method theoretically applicable to any model specification. In this paper, we restrict our study to Poisson models, whose likelihood represents the base for many more complex point process models. In this context, our proposed method can estimate the vector of local parameters that correspond to the points within the analyzed point pattern without introducing any additional complexity compared to the global estimation. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes and show complex scenarios based on the Poisson model through the analysis of two real datasets concerning environmental problems.

Abstract 2390: Longitudinal assessment of circulating tumor DNA in patients with advanced colorectal cancer: A proposed general statistical framework and visualization tool

Abstract Background: Understanding how ctDNA levels change over time can act as a surrogate marker for disease progression. Since ctDNA evolution is complicated—exhibiting variability within and between patients—we propose a rigorous and flexible statistical framework that comprehensively represents these types of time-varying biomarkers. We propose employing a hierarchal random effects cubic spline model due to its advantages over traditional longitudinal modeling approaches such as the former’s ability to incorporate patient characteristics and create patient-specific results. Visualization of individual patient trajectories may provide clinical utility in precision oncology settings. Methods: 167 patients with CRC were selected from GuardantINFORM, a real-world database linking genomic and claims data. All patients received chemotherapy and had at least three serial liquid biopsy tests completed via Guardant360. To meet model assumptions, ctDNA levels, measured by maximum variant allele frequency on each test, were transformed into logits. Due to the model’s hierarchal structure, an unconditional cubic spline model was fit first, producing an estimated response pattern for the cohort. Next, as patient-level results are of interest, the unconditional model was built upon by fitting a conditional model that incorporated covariates consisting of demographic, health status, and mortality information, which provided numerous patient-level response patterns. The best fitting conditional model was guided by Akaike’s information criteria. Results: Since model parameter estimates are uninterpretable, and because numerous patient-level projections are generated (each covariate value combination produces a unique projection), an R-Shiny application was developed to visually present and compare results in an intuitive interactive fashion. Additionally, to enhance the understanding of patient response patterns, velocity plots, which provides the instantaneous rate of change in ctDNA levels at different time points, are also provided. Conclusions: We demonstrate that the proposed method can successfully be applied to genomic data to describe and explore complex patient-level temporal ctDNA patterns while accounting for the impact of covariate values have on these patterns. We implemented the proposed methodology as a visualization tool that can be used in a wide variety of settings, ranging from hypothesis testing in clinical trials to patient monitoring. Results from the model can further our basic conceptualization of ctDNA dynamics and enhance our ability to integrate these results into targeted, patient centric, clinical decision-making. Citation Format: Christopher R. Pretz, Jiemin Liao, Leylah Drusbosky, Amar Das. Longitudinal assessment of circulating tumor DNA in patients with advanced colorectal cancer: A proposed general statistical framework and visualization tool [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 2390.

Analysis of Relatively Short Variable Rate “Noisy” Well Test Data Using Non-Linear Deconvolution

Short well test data are pressure-rate-time data that are not long enough to be used to infer the reservoir boundary model and are very common in the oil and gas industry. Short rate well test data may occur when companies try to cut costs of well test jobs or mostly due to improper well test design. Nevertheless, one may wish to extract the most amount of information from this limited data because the de-convolve response can allow the reservoir engineer to make the best use of the available data in selecting a suitable interpretation model by narrowing down the possible boundary models and also providing a reliable estimates of model parameters. The aim of this study is to demonstrate the usefulness and significance of pressure-rate deconvolution in analyzing relatively short variable rate data using a hypothetical case study. The simulation was carried out using Sapphire’s test design module by assuming the presence of an exploratory well in an oil reservoir above bubble point pressure. Further assumption is that the reservoir is homogenous, therefore the possibility of a changing wellbore model was neglected from the analysis. The computer codes for the simulation were inputted using python programming language. We observed from the study that although pressure and flow rate relationship can be nonlinear, the problem can be formulated as a linear problem and the nonlinearity is expressed in the features of the reservoir. The simulation results were satisfactory using the test case and deviations between model parameters and actual reservoir parameters used in simulation was shown to have an absolute value less than 8% which is within acceptable engineering limits.

A Problem with Distance Variables and Alternatives for Their Use

Researchers commonly use distance variables to: (i) estimate the direct influence of a landmark on an outcome of interest, such as a neighborhood park on home price; or (ii) control for omitted spatial influences that affect predictions of key policy variables. While both uses continue, the use of distance as a control, such as distance to Central Business District (CBD), is now more common. Using distance to a given position such as CBD is added to multivariate analysis as a method to capture all remaining, or omitted spatial effects that influence the dependent variable. We show that there is a latent and inherent identification problem with the distance variable; and we show that this extends to the use of distance as a control. These biases affect more than the distance variable. They generate inconsistent estimates for all other spatially distributed variables in a model. We then introduce an alternative control that captures unmodeled influences that vary across space, and we show that this fully stabilizes all model parameter estimates and measures of model efficiency.

Combining Recurrent Neural Network and Sigmoid Growth Models for Short-Term Temperature Forecasting and Tomato Growth Prediction in a Plastic Greenhouse

Compared with open-field cultivation, greenhouses can provide favorable conditions for crops to grow through environmental control. The prediction of greenhouse microclimates is a way to reduce environmental monitoring costs. This study used several recurrent neural network models, including long short-term memory (LSTM), gated recurrent unit, and bi-directional LSTM, with varying numbers of hidden layers and units, to establish a temperature forecasting model for a plastic greenhouse. To assess the generalizability of the proposed model, the most accurate forecasting model was used to predict the temperature in a greenhouse with different specifications. During a test period of four months, the best proposed model’s R2, MAPE, and RMSE values were 0.962, 3.216%, and 1.196 °C, respectively. Subsequently, the outputs of the temperature forecasting model were used to calculate growing degree days (GDDs), and the predicted GDDs were used as an input variable for the sigmoid growth models to simulate the leaf area index, fresh fruit weight, and aboveground dry matter of tomatoes. The R2 values of the growth model for the three growth traits were all higher than 0.80. Moreover, the fitted values and the parameter estimates of the growth models were similar, irrespective of whether the observed GDD (calculated using the actual observed data) or the predicted GDD (calculated using the temperature forecasting model output) was used. These results indicated that the proposed temperature forecasting model could accurately predict the temperature changes inside a greenhouse and could subsequently be used for the growth prediction of greenhouse tomatoes.

Statistical inference for a novel distribution using ranked set sampling with applications

Working on symmetrical or asymmetrical data is complicated since each requires a different probability density function. Many statistical distributions can be used for these data types, where choosing one should be satisfied with the correct data type. So, we apply the ranked set sampling technique, which is essential in gaining data when dealing with units in a population is expensive. However, their classification is simple according to the variable of interest. The Unit Generalized Rayleigh distribution has recently played a crucial role in analyzing symmetrical or asymmetrical complex data sets specifically in modeling claim and risk data used in actuarial and financial studies, and its density can take different symmetric and asymmetric possible shapes. It is proposed in various areas, such as reliability, survival, economics, actuarial science, and insurance. We applied the ranked set sampling design in this article for gaining the model parameter estimations of the unit generalized Rayleigh model. Different estimation procedures and risk measures are computed. Moreover, the performance of these measures is illustrated via numerical simulation experiments. Under different proposed estimators, we conduct the validation of the suggested ranked set sampling design via numerous Monte Carlo simulation experiments by computing average bias and mean squared errors. At the end, we illustrated two real applications of the financial area for demonstrating the potential and the supremacy of the proposed ranked set sampling estimators.

An integrative mechanistic model of thymocyte dynamics.

The thymus plays a central role in shaping human immune function. A mechanistic, quantitative description of immune cell dynamics and thymic output under homeostatic conditions and various patho-physiological scenarios are of particular interest in drug development applications, e.g., in the identification of potential therapeutic targets and selection of lead drug candidates against infectious diseases. We here developed an integrative mathematical model of thymocyte dynamics in human. It incorporates mechanistic features of thymocyte homeostasis as well as spatial constraints of the thymus and considerations of age-dependent involution. All model parameter estimates were obtained based on published physiological data of thymocyte dynamics and thymus properties in mouse and human. We performed model sensitivity analyses to reveal potential therapeutic targets through an identification of processes critically affecting thymic function; we further explored differences in thymic function across healthy subjects, multiple sclerosis patients, and patients on fingolimod treatment. We found thymic function to be most impacted by the egress, proliferation, differentiation and death rates of those thymocytes which are most differentiated. Model predictions also showed that the clinically observed decrease in relapse risk with age, in multiple sclerosis patients who would have discontinued fingolimod therapy, can be explained mechanistically by decreased thymic output with age. Moreover, we quantified the effects of fingolimod treatment duration on thymic output. In summary, the proposed model accurately describes, in mechanistic terms, thymic output as a function of age. It may be further used to perform predictive simulations of clinically relevant scenarios which combine specific patho-physiological conditions and pharmacological interventions of interest.

A tutorial on fitting joint models of M/EEG and behavior to understand cognition.

We present motivation and practical steps necessary to find parameter estimates of joint models of behavior and neural electrophysiological data. This tutorial is written for researchers wishing to build joint models of human behavior and scalp and intracranial electroencephalographic (EEG) or magnetoencephalographic (MEG) data, and more specifically those researchers who seek to understand human cognition. Although these techniques could easily be applied to animal models, the focus of this tutorial is on human participants. Joint modeling of M/EEG and behavior requires some knowledge of existing computational and cognitive theories, M/EEG artifact correction, M/EEG analysis techniques, cognitive modeling, and programming for statistical modeling implementation. This paper seeks to give an introduction to these techniques as they apply to estimating parameters from neurocognitive models of M/EEG and human behavior, and to evaluate model results and compare models. Due to our research and knowledge on the subject matter, our examples in this paper will focus on testing specific hypotheses in human decision-making theory. However, most of the motivation and discussion of this paper applies across many modeling procedures and applications. We provide Python (and linked R) code examples in the tutorial and appendix. Readers are encouraged to try the exercises at the end of the document.