Relevant bibliographies by topics / Linear random growth models

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Linear random growth models'

Author: Grafiati
Published: 15 March 2025

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Journal articles on the topic "Linear random growth models"

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Kohli, Nidhi, and Amanda L. Sullivan. "Linear-linear piecewise growth mixture models with unknown random knots: A primer for school psychology." Journal of School Psychology 73 (April 2019): 89–100. http://dx.doi.org/10.1016/j.jsp.2019.03.004.

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Chilyabanyama, Obvious N., Roma Chilengi, Innocent Ngaruye, Najeeha Talat Iqbal, and Samuel Bosomprah. "Statistical Models for Estimating Linear Growth Velocity." International Journal of Nutrition, Pharmacology, Neurological Diseases 11, no. 4 (October 2021): 262–66. http://dx.doi.org/10.4103/ijnpnd.ijnpnd_6_21.

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Poor linear growth among infants is still a global public health issue. Linear growth velocity has been variously suggested as a more robust measure for growth over the classical measure of attained height for age. In this study, we systematically reviewed available literature for models used in estimating linear growth velocity. We searched Medline, Embase, Cochrane methodology register, Joanna Briggs Institute EBP, through the Ovid interface, and PubMed database to identify relevant articles that used statistical models to estimate linear growth velocity among infants. Longitudinal studies published in English were included. Two reviewers independently screened the titles and abstracts to identify potentially eligible studies. Any disagreements were discussed and resolved. Full-text articles were downloaded for all the studies that met the eligibility criteria. We synthesized literature using the preferred reporting items for systematic review and meta-analyses guidelines for the most used statistical methods for modelling infant growth trajectories. A total of 301 articles were retrieved from the initial search. Fifty-six full-text articles were assessed for eligibility and 16 of which were included in the final review with a total of 303,940 infants, median sample size of 732 (interquartile range: 241–1683). Polynomial function models were the most used growth model. Three (18.8%) of the articles modelled the linear growth. Two (12.5%) articles used mixed-effects models and another two (12.5%) used the Jenss-Bayley growth models to model linear growth. Other models included residual growth model, two-stage multilevel linear spline model, joint multilevel linear spline model, and generalized least squares with random effects. We have identified linear mixed-effects models, polynomial growth models, and the Jenss-Bayley model as the used models for characterizing linear growth among infants. Linear mixed-effects model is appealing for its robustness even under violation of largely robust even to quite severe violations of model assumptions.
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Quine, M. P., and J. S. Law. "Modelling random linear nucleation and growth by a Markov chain." Journal of Applied Probability 36, no. 1 (March 1999): 273–78. http://dx.doi.org/10.1239/jap/1032374248.

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In an attempt to investigate the adequacy of the normal approximation for the number of nuclei in certain growth/coverage models, we consider a Markov chain which has properties in common with related continuous-time Markov processes (as well as being of interest in its own right). We establish that the rate of convergence to normality for the number of ‘drops’ during times 1,2,…n is of the optimal ‘Berry–Esséen’ form, as n → ∞. We also establish a law of the iterated logarithm and a functional central limit theorem.
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Quine, M. P., and J. S. Law. "Modelling random linear nucleation and growth by a Markov chain." Journal of Applied Probability 36, no. 01 (March 1999): 273–78. http://dx.doi.org/10.1017/s0021900200017034.

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In an attempt to investigate the adequacy of the normal approximation for the number of nuclei in certain growth/coverage models, we consider a Markov chain which has properties in common with related continuous-time Markov processes (as well as being of interest in its own right). We establish that the rate of convergence to normality for the number of ‘drops’ during times 1,2,…n is of the optimal ‘Berry–Esséen’ form, as n → ∞. We also establish a law of the iterated logarithm and a functional central limit theorem.
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Kumar, Amit, Sanjeev Kumar, Manjari Pandey, Chirag Chaudhari, Med Ram Verma, Chandrahas, and Anuj Chauhan. "Bertalanffy Model Reflects Growth Trajectory in Aseel Chicken." Indian Journal of Veterinary Sciences & Biotechnology 18, no. 5 (November 7, 2022): 59–62. http://dx.doi.org/10.48165/ijvsbt.18.5.12.

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Aseel, a popular breed of native chicken, characterized by its pugnacity, fighting strength and royal gait is being used to create crosses for domestic chicken production. However, information on its growth models is scanty. An experiment was conducted to evaluate different non-linear models and to find out best fitting model in Aseel, being maintained at Central Avian Research Institute, Izatnagar, Bareilly. Data on body weights from 12-weeks of age to 20-weeks of age at biweekly intervals were recorded on a random bred single-hatched flock. Owing to the non-linear characteristic of growth, three non-linear models namely, Gompertz, Bertalanffy and Logistic models were evaluated. Goodness of fit for all the models were checked using coefficient of determination (R2), adjusted coefficient of determination (Adj-R2), mean square error (MSE), mean absolute error (MAE) and Akaike information criterion (AIC). The Bertalanffy model most accurately characterized the growth trend in males, females and pooled sex data. The study revealed that this model may be used to ascertain the average body weights in Aseel chicken under random mating. The investigation has generated baseline data on growth modelling of random bred groups and may be used in similar investigations on other native chicken breeds.
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Sarmento, José Lindenberg Rocha, Robledo de Almeida Torres, Wandrick Hauss de Sousa, Lucia Galvão de Albuquerque, Raimundo Nonato Braga Lôbo, and José Ernandes Rufino de Sousa. "Modeling of average growth curve in Santa Ines sheep using random regression models." Revista Brasileira de Zootecnia 40, no. 2 (February 2011): 314–22. http://dx.doi.org/10.1590/s1516-35982011000200012.

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Polynomial functions of age of different orders were evaluated in the modeling of the average growth trajectory in Santa Ines sheep in random regression models. Initially, the analyses were performed not considering the animal effect. Subsequently, the random regression analyses were performed including the random effects of the animal and its mother (genetic and permanent environment). The linear fit was lower, and the other orders were similar until near 100 days of age. The cubic function provided the closest fit of the observed averages, mainly at the end of the curve. Orders superior to this one tended to present incoherent behavior with the observed weights. The estimated direct heritabilities, considering the linear fit, were higher to those estimated by considering other functions. The changes in animal ranking based on predicted breeding values using linear fit and superior orders were small; however, the difference in magnitude of the predicted breeding values was higher, reaching values 77% higher than those obtained with the cubic function. The cubic polynomial function is efficient in describing the average growth curve.
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Li, Yao Xiang, and Li Chun Jiang. "Modeling Microfibril Angle of Larch Using Linear Mixed-Effects Models." Advanced Materials Research 267 (June 2011): 516–20. http://dx.doi.org/10.4028/www.scientific.net/amr.267.516.

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Earlywood microfibril angle (MFA) was determined at each growth ring from disks at breast height (1.3 m) from 6 dahurian larch (Larix gmelinii. Rupr.) trees grown in northeastern China. Significant variation in microfibril angle was observed among growth rings. MFA at breast height varied from 7.5°to 21.5°between growth rings and showed a descreasing trend from pith to bark for each tree. A second order polynomial equation with linear mixed-effects was used for modeling earlywood MFA. The LME procedure in S-Plus is used to fit the mixed-effects models for the MFA data. The results showed that the polynomial model with three random parameters could significantly improve the model performance. The fitted mixed-effects model was also evaluated using a separate dataset. The mixed model was found to predict MFA better than the original model fitted using ordinary least-squares based on absolute and relative errors.
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Codling, Edward A., Michael J. Plank, and Simon Benhamou. "Random walk models in biology." Journal of The Royal Society Interface 5, no. 25 (April 15, 2008): 813–34. http://dx.doi.org/10.1098/rsif.2008.0014.

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Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.
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Hay, El Hamidi. "Machine Learning for the Genomic Prediction of Growth Traits in a Composite Beef Cattle Population." Animals 14, no. 20 (October 18, 2024): 3014. http://dx.doi.org/10.3390/ani14203014.

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The adoption of genomic selection is prevalent across various plant and livestock species, yet existing models for predicting genomic breeding values often remain suboptimal. Machine learning models present a promising avenue to enhance prediction accuracy due to their ability to accommodate both linear and non-linear relationships. In this study, we evaluated four machine learning models—Random Forest, Support Vector Machine, Convolutional Neural Networks, and Multi-Layer Perceptrons—for predicting genomic values related to birth weight (BW), weaning weight (WW), and yearling weight (YW), and compared them with other conventional models—GBLUP (Genomic Best Linear Unbiased Prediction), Bayes A, and Bayes B. The results demonstrated that the GBLUP model achieved the highest prediction accuracy for both BW and YW, whereas the Random Forest model exhibited a superior prediction accuracy for WW. Furthermore, GBLUP outperformed the other models in terms of model fit, as evidenced by the lower mean square error values and regression coefficients of the corrected phenotypes on predicted values. Overall, the GBLUP model delivered a superior prediction accuracy and model fit compared to the machine learning models tested.
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Wang, Weibo. "Forecasting The Population of China From 2020 To 2025 Based on Random Forest and Linear Regression." Highlights in Science, Engineering and Technology 85 (March 13, 2024): 511–18. http://dx.doi.org/10.54097/a70zsh28.

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The population dynamics of a country do play a vital role in its economic and political development. The COVID-19 epidemic has significantly affected the world's population. However, most people only care about the negative influence caused by COVID-19 but ignore the positive influence. This article uses two machine learning models, the random forest model, and the linear regression model, to predict the population change in China if there were no COVID-19 pandemic. With the predicted results, this article can compare the potential positive impact of the pandemic. This paper tries to fit two popular models, namely, Random Roest and Linear Regression to forecast the population of China from 2020 to 2025. The historical birth rate, death rate, and GDP growth rate of China are collected as features adding to the models to decline the error. For the Random Forest model, this paper set up an ensemble of decision trees to predict the future population of China. For the Linear Regression model, our features and population fit a linear connection. The findings of two models are compared in this article, and it is suggested that the random forest model is more suited for population forecasting. In addition, according to this study, the COVID-19 pandemic has some favorable effects on economic growth and birth rates. The article emphasizes the need to not only focus on the negative effects of the pandemic. Furthermore, the article points out that the linear regression model has poor fitting results for non-linear relationships. It suggests exploring more non-linear models for prediction and considering more influential parameters.
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Dissertations / Theses on the topic "Linear random growth models"

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Turnbull, Shane. "Competition within random growth models." Thesis, Lancaster University, 2018. http://eprints.lancs.ac.uk/127679/.

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This thesis is concerned with introducing competition into random models. It can be observed that there are two natural mechanisms for the evolution of a random model; either by growth or by self interactions. What we do is look at two types of models and introduce competition within them. The first model, the voter model, is an example of a self interacting model and we introduce growth into it. The second model, the Hasting-Levitov model, is a random growth model and we introduce competition within the model. In both cases we construct diffusion approximations to model these systems when the initial population is large for the first case and when the addition of incoming particles is small in the second. Once these diffusion processes have been constructed we then analyse the long term behaviour of them and find their asymptotic distribution, this is done by using the speed measure and scale function.
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Krajenbrink, Alexandre. "Beyond the typical fluctuations : a journey to the large deviations in the Kardar-Parisi-Zhang growth model." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEE021.

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Cette thèse de doctorat porte sur l'étude du modèle de croissance stochastique Kardar-Parisi-Zhang (KPZ) en 1+1 dimensions et en particulier de l'équation qui le régit. Cette thèse est d'une part destinée à effectuer un état de l'art et dresser un portrait moderne de la recherche des solutions exactes de l'équation KPZ, de leurs propriétés en terme de théorie des grandes déviations et également de leurs applications (en théorie des matrices aléatoires ou en calcul stochastique notamment). D'autre part cette thèse a pour but de formuler un certain nombre de questions ouvertes à l'interface avec la théorie de l'intégrabilité, la théorie des matrices aléatoires et la théorie des gaz de Coulomb.Cette thèse est divisée en trois parties distinctes portant (i) sur les solutions exactes de l'équation KPZ, (ii) sur les solutions à temps court sous la forme d'un principe grandes déviations et (iii) sur les solutions à temps long et leurs extensions aux statistiques linéaires au bord de spectre de matrice aléatoire.Nous présenterons les résultats de cette thèse comprenant notamment (a) une nouvelle solution de l'équation KPZ à tout temps dans un demi-espace, (b) une méthodologie générale pour établir à temps court un principe de grandes déviations pour les solutions de KPZ à partir de leur représentation sous forme de déterminant de Fredholm et (c) une unification de quatre méthodes permettant d'obtenir à temps long un principe de grandes déviations pour les solutions de l'équation KPZ et de manière plus générale d'étudier des statistiques linéaires au bord du spectre de matrices aléatoires
Throughout this Ph.D thesis, we will study the Kardar-Parisi-Zhang (KPZ) stochastic growth model in 1+1 dimensions and more particularly the equation which governs it. The goal of this thesis is two-fold. Firstly, it aims to review the state of the art and to provide a detailed picture of the search of exact solutions to the KPZ equation, of their properties in terms of large deviations and also of their applications to random matrix theory or stochastic calculus. Secondly, is it intended to express a certain number of open questions at the interface with integrability theory, random matrix theory and Coulomb gas theory.This thesis is divided in three distinct parts related to (i) the exact solutions to the KPZ equation, (ii) the short time solutions expressed by a Large Deviation Principle and the associated rate functions and (iii) the solutions at large time and their extensions to linear statistics at the edge of random matrices.We will present the new results of this thesis including (a) a new solution to the KPZ equation at all times in a half-space, (b) a general methodology to establish at short time a Large Deviation Principle for the solutions to the KPZ equation from their representation in terms of Fredholm determinant and (c) the unification of four methods allowing to obtain at large time a Large Deviation Principle for the solution to the KPZ equation and more generally to investigate linear statistics at the soft edge of random matrices
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Häggström, Lundevaller Erling. "Tests of random effects in linear and non-linear models." Doctoral thesis, Umeå universitet, Statistik, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-15.

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Häggström, Lundevaller Erling. "Tests of random effects in linear and non-linear models /." Umeå : Department of Statistics, University of Umeå, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-15.

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Eberz-Wagner, Dorothea M. "Discrete growth models /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5797.

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Calbo, Sanjuán Gema. "Mean Square Analytic Solutions of Random Linear Models." Doctoral thesis, Universitat Politècnica de València, 2010. http://hdl.handle.net/10251/8721.

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El objetivo de este proyecto de tesis doctoral es el desarrollo de técnicas analítico-numéricas para resolver, en media cuadrática problemas, de valores iniciales de ecuaciones y sistemas de ecuaciones en diferencias y diferenciales aleatorias de tipo lineal. Respecto del estudio aportado sobre ecuaciones en diferencias (véase Capítulo 3), se extienden al contexto aleatorio algunos de los principales resultados que en el caso determinista se conocen para resolver este tipo de ecuaciones así como para estudiar el comportamiento asintótico de su solución. En lo que se refiere a las ecuaciones diferenciales hay que señalar que el elemento unificador del estudio realizado en esta memoria es la extensión al escenario aleatorio del método de Fröbenius para la búsqueda de soluciones de ecuaciones diferenciales en forma de desarrollos en serie de potencias. A largo de los Capítulos 4-7 se abordan problemas tanto de tipo escalar como de tipo matricial tanto de primer como de segundo orden, donde la aleatoriedad se introduce en los modelos a través de las condiciones iniciales y los coeficientes, siendo además la incertidumbre en este último caso, considerada tanto de forma aditiva como multiplicativa. Los problemas basados en ecuaciones diferenciales aleatorias tratados permiten introducir procesos estocásticos importantes como son el proceso exponencial (véase Capítulo 5), los procesos trigonométricos seno y coseno y algunas de sus propiedades algebraicas básicas (véase Capítulo 6). En el último capítulo se estudia la ecuación diferencial de Hermite con coeficientes aleatorios y, bajo ciertas condiciones, se obtienen soluciones en forma de serie aleatoria finita que definen los polinomios de Hermite aleatorios. Además de obtener las soluciones en forma de serie aleatoria convergente en el sentido estocástico de la media cuadrática, para cada uno de los problemas tratados se calculan aproximaciones de las principales propiedades estadísticas del proceso solución.
Calbo Sanjuán, G. (2010). Mean Square Analytic Solutions of Random Linear Models [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8721
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Sola, Alan. "Conformal Maps, Bergman Spaces, and Random Growth Models." Doctoral thesis, KTH, Matematik (Avd.), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-12364.

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This thesis consists of an introduction and five research papers on topics related to conformal mapping, the Loewner equation and its applications, and Bergman-type spaces of holomorphic functions. The first two papers are devoted to the study of integral means of derivatives of conformal mappings. In Paper I, we present improved upper estimates of the universal means spectrum of conformal mappingsof the unit disk. These estimates rely on inequalities  obtained by Hedenmalm and Shimorin using Bergman space techniques, and on computer calculations. Paper II is a survey of recent results on the universal means spectrum, with particular emphasis on Bergman spacetechniques.Paper III concerns Bergman-type spaces of holomorphic functions in subsets of $\textbf{C}^d$ and their reproducing kernel functions. By expanding the norm of a function in a Bergman space along the zero variety of a polynomial, we obtain a series expansion of reproducing kernel functions in terms of kernels associated with lower-dimensionalspaces of holomorphic functions. We show how this general approach can be used to explicitly compute kernel functions for certain weighted Bergman and Bargmann-Fock spaces defined in domains in $\textbf{C}^2$.The last two papers contribute to the theory of Loewner chains and theirapplications in the analysis of planar random growth model defined in terms of compositions of conformal maps.In Paper IV, we study Loewner chains generated by unimodular L\'evy processes.We first establish the existence of a capacity scaling limit for the associated growing hulls in terms of whole-plane Loewner chains driven by a time-reversed process. We then analyze the properties of Loewner chains associated with a class of two-parameter compound Poisson processes, and we describe the dependence of the geometric properties of the hulls on the parameters of the driving process. In Paper V, we consider a variation of the Hastings-Levitov growth model, with anisotropic growth. We again establish results concerning scaling limits, when the number of compositions increases and the basic conformal mappings tends to the identity. We show that the resulting limit sets can be associated with solutions to the Loewner equation.We also prove that, in the limit, the evolution of harmonic measure on the boundary is deterministic and is determined by the flow associated with an ordinary differential equation, and we give a description of the fluctuations around this deterministic limit flow.

QC 20100414

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Mostafa, S. M. "Estimation of variance components in balanced random and mixed linear models." Thesis, University of Strathclyde, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382394.

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Siegert, Wolfgang. "Local Lyapunov exponents sublimiting growth rates of linear random differential equations." Berlin Heidelberg Springer, 2007. http://d-nb.info/991321065/04.

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Mendis, Ruchini Dilinika. "Sensitivity Analyses for Tumor Growth Models." TopSCHOLAR®, 2019. https://digitalcommons.wku.edu/theses/3113.

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This study consists of the sensitivity analysis for two previously developed tumor growth models: Gompertz model and quotient model. The two models are considered in both continuous and discrete time. In continuous time, model parameters are estimated using least-square method, while in discrete time, the partial-sum method is used. Moreover, frequentist and Bayesian methods are used to construct confidence intervals and credible intervals for the model parameters. We apply the Markov Chain Monte Carlo (MCMC) techniques with the Random Walk Metropolis algorithm with Non-informative Prior and the Delayed Rejection Adoptive Metropolis (DRAM) algorithm to construct parameters' posterior distributions and then obtain credible intervals.
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Books on the topic "Linear random growth models"

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Damron, Michael, Firas Rassoul-Agha, and Timo Seppäläinen, eds. Random Growth Models. Providence, Rhode Island: American Mathematical Society, 2018. http://dx.doi.org/10.1090/psapm/075.

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Lee, Youngjo. Generalized Linear Models with Random Effects. Second edition. | Boca Raton, Florida : CRC Press, [2017] |: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315119953.

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Srivastava, M. S. Growth curve models. Toronto: University of Toronto, Dept. of Statistics, 1998.

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Stanley, H. Eugene, and Nicole Ostrowsky, eds. Random Fluctuations and Pattern Growth: Experiments and Models. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2653-0.

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1941-, Stanley H. Eugene, Ostrowsky Nicole 1943-, Institut d'études scientifiques de Cargèse., and North Atlantic Treaty Organization. Scientific Affairs Division., eds. Random fluctuations and pattern growth: Experiments and models. Dordrecht [Netherlands]: Kluwer Academic Publishers, 1988.

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Kshirsagar, Anant M. Growth curves. New York: M. Dekker, 1995.

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M. C. M. de Gunst. A random model for plant cell population growth. [Amsterdam, the Netherlands]: Centrum voor Wiskunde en Informatica, 1989.

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Kaufman, Robert L. Interaction Effects in Linear and Generalized Linear Models: Examples and Applications Using Stata. California, USA: SAGE Publications, Incorporated, 2018.

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Cisilino, Adrián. Linear and nonlinear crack growth using boundary elements. Southampton, UK: WIT Press, 2000.

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Grafarend, Erik. Linear and Nonlinear Models: Fixed effects, random effects, and total least squares. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Book chapters on the topic "Linear random growth models"

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Bunde, Armin, Shlomo Havlin, and H. Eugene Stanley. "Anomalous Transport in Random Linear Structures." In Random Fluctuations and Pattern Growth: Experiments and Models, 37–41. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2653-0_7.

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Laird, N. M. "Analysis of Linear and Non-Linear Growth Models with Random Parameters." In Advances in Statistical Methods for Genetic Improvement of Livestock, 329–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-74487-7_15.

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Brinda, W. D. "Background: Random Vectors." In Visualizing Linear Models, 63–80. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-64167-2_3.

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Duflo, Marie. "Linear Identification and Tracking." In Random Iterative Models, 133–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-12880-0_5.

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Fahrmeir, Ludwig, and Gerhard Tutz. "Random Effects Models." In Multivariate Statistical Modelling Based on Generalized Linear Models, 283–329. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3454-6_7.

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Fahrmeir, Ludwig, and Gerhard Tutz. "Random effects models." In Multivariate Statistical Modelling Based on Generalized Linear Models, 219–55. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4899-0010-4_7.

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Sevestre, Patrick, and Alain Trognon. "Linear Models with Random Regressors." In Advanced Studies in Theoretical and Applied Econometrics, 100–119. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0137-7_6.

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West, Brady T., Kathleen B. Welch, Andrzej T. Gałecki, and Brenda W. Gillespie. "Random Coefficient Models for Longitudinal Data: The Autism Example." In Linear Mixed Models, 263–322. 3rd ed. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003181064-6.

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West, Brady T., Kathleen B. Welch, Andrzej T. Gałecki, and Brenda W. Gillespie. "Models for Data with Crossed Random Factors: The SAT Score Example." In Linear Mixed Models, 389–418. 3rd ed. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003181064-8.

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Boguslavskiy, Josif A. "Linear Estimators of a Random Parameter Vector." In Dynamic Systems Models, 1–18. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-04036-3_1.

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Conference papers on the topic "Linear random growth models"

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Shiao, Michael, Tzikang Chen, and Anindya Ghoshal. "A Probabilistic Approach for Reliability Quantification of Propulsion Materials." In Vertical Flight Society 71st Annual Forum & Technology Display, 1–7. The Vertical Flight Society, 2015. http://dx.doi.org/10.4050/f-0071-2015-10252.

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A new probabilistic approach to assess the reliability of brittle materials for high temperature engine components was developed. The probability of failure due the fracture of a randomly oriented damage inherent from manufacturing process was determined by a hybrid probabilistic method (HPM) for computational efficiency and accuracy. The random variables considered by this approach for overall component failure probability include fracture toughness, loads, geometric factor, initial damage size, damage growth rate, damage orientation and damage occurrence in a unit volume. HPM consists of four modules: (1) an efficient reliability algorithm, (2) a surrogate model, (3) a bi-linear interpolation scheme and (4) a random simulation method. Seven cases with various types of loads and failure mechanisms were performed by both the hybrid approach and traditional Monte Carlo simulations (MCS). For all the cases studied, the results by HPM compare very well with that by traditional MCS. HPM also shows great efficiency over traditional Monte Carlo simulations. In addition, this new probabilistic framework allows further improvement in computational efficiency by exploring other efficient simulation methods.
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Kourennyi, Eduard G., Victor A. Petrosov, and Lidiya V. Chemikova. "Linear Filtration of Random Processes in EMC Models: The “Partial Reaction” Method." In EMC_2000_Wroclaw, 587–90. IEEE, 2000. https://doi.org/10.23919/emc.2000.10842093.

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Kunderu, Pranav, and Shivm Patel. "Cardiovascular Machine Learning: Interpreting Maximum Heart Rate Values from Patient Biometrics Using Linear Regression and Random Forest Models." In 2024 9th International Conference on Intelligent Informatics and Biomedical Sciences (ICIIBMS), 236–38. IEEE, 2024. https://doi.org/10.1109/iciibms62405.2024.10792778.

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Zhang, S., W. Zhou, S. Kariyawasam, and M. Al-Amin. "Characterization of the Growth of Corrosion Defects on Energy Pipelines Using Bayesian Dynamic Linear Model." In 2014 10th International Pipeline Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/ipc2014-33215.

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This paper describes the use of the second-order polynomial dynamic linear model (DLM) to characterize the growth of the depth of corrosion defects on energy pipelines using imperfect data obtained from multiple high-resolution in-line inspections (ILI). The growth model is formulated by incorporating the general form of the measurement error (including the biases and random scattering error) of the ILI tools as well as the correlations between the random scattering errors of different tools. The temporal variability of the corrosion growth is captured by allowing the average growth rate between two successive inspections to vary with time. The Markov Chain Monte Carlo simulation is employed to carry out the Bayesian updating of the growth model and evaluate the posterior distributions of the model parameters. An example involving real ILI data collected from an in-service natural gas pipeline is employed to illustrate and validate the growth model. The analysis results show that the defect depths predicted by the proposed model agree well with the actual depths and are more accurate than those predicted by the Gamma process-based growth models reported in the literature.
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Omishore, Abayomi. "Stochastic modelling of fatigue crack growth." In The 13th international scientific conference “Modern Building Materials, Structures and Techniques”. Vilnius Gediminas Technical University, 2019. http://dx.doi.org/10.3846/mbmst.2019.075.

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The article deals with the influence of the skewness of quasi-constant stress range on the fatigue resistance of a steel bridge member subjected to multiple repeated loading. It is shown that it is necessary to know the statistical characteristics and type of probability density function relatively accurately in the case of quasi-constant stress range, otherwise the estimation of the fatigue resistance may be inaccurate. The fatigue resistance is studied using linear fracture mechanics. The random characteristics of the steel member are simulated using the Latin Hypercube Sampling method. The results of experimental research on calibration functions used in linear fracture mechanics are applied in this study. The calibration function for pure bending, which is presented on an extended domain of relative crack length, is applied. Non-parametric rank-order correlation identifies a strong influence of the quasi-constant stress range on the fatigue resistance. A detailed comparison of three variants of fatigue resistance as output random variables is performed. The results show that the probabilistic assessment of reliability may be burdened with greater or lesser epistemic uncertainty, which can distort the estimates of the remaining service life of the load bearing bridge member.
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Al-Amin, M., S. Kariyawasam, S. Zhang, and W. Zhou. "Non-Linear Corrosion Growth: A More Appropriate and Accurate Model for Predicting Corrosion Growth Rate." In 2016 11th International Pipeline Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/ipc2016-64435.

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External metal-loss corrosion is one of the major contributing factors for pipeline failures in North America. Corrosion growth rate plays a crucial role in managing corrosion hazard for gas and liquid pipelines. Quantifying the growth of corrosion over time is critically important for the risk and reliability analysis of pipelines, planning for corrosion mitigation and repair, and determination of time intervals for corrosion inspections. Conservatism in predicting the growth rate has significant engineering implication as non-conservatism can lead to critical anomalies being missed by mitigation actions and may cause pipeline failure; whereas, over conservatism can lead to unnecessary inspections and anomaly mitigations that may result in significant unnecessary cost to pipeline operators. As more and more pipelines are now being inspected by in-line inspection (ILI) tools on a regular basis, the ILI data from multiple inspections provide valuable information about the growth of corrosion anomalies on the pipeline. Although the application of linear growth rate calculated by comparing depths from two successive ILI is a common practice in the pipeline industry, research has shown that the growth of corrosion anomaly is non-linear and anomaly-specific. The authors of this paper have previously developed anomaly-specific non-linear corrosion growth model based on multiple ILI data. The objectives of this paper are to demonstrate the appropriateness of anomaly-specific non-linear corrosion growth model, and to illustrate the advantages of using non-linear corrosion growth model in the integrity management program. Two case studies were performed to illustrate the application of non-linear growth model by incorporating the measurement errors associated with the ILI tools, which include both the bias (constant and non-constant) and random scattering error. The findings of these case studies are presented in this paper.
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Khan, Rizwan A., and Suhail Ahmad. "Probabilistic Fatigue Safety Analysis of Oil and Gas Risers Under Random Loads." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20464.

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Marine riser is an important component of oil and gas drilling and production system. It is essentially a slender pipe conveying fluid between well-head and floating production unit. They are formed out of three basic types of configuration namely, free hanging, “lazy-wave (SWLR)” riser. Risers are subjected to varied static, quasi-static and dynamic forces. For the safety of design, the behavior of the riser under these forces is thoroughly investigated. 3D Nonlinear dynamic analysis of riser is obtained in the time domain using finite element software package ABAQUS/Aqua. The response histories so obtained are employed for the study of fatigue reliability analyses of riser. It is based on a bi-linear relationship to model fatigue crack growth and incorporates a failure criterion to describe the interaction between fracture and plastic collapse. Uncertainty modeling, especially of fatigue crack growth parameters, is undertaken using bi-linear crack growth relationship. Results pertaining to fatigue reliability and fatigue crack size evolution are presented using Monte Carlo Simulation. The bi-linear crack growth models are found to lead to higher fatigue life estimation. Sensitivity behavior pertinent to limit state adopted has been thoroughly investigated. These findings implicate inspection schemes for components of the marine structures to ensure minimization of the surprises due to wide scatter of the fatigue phenomenon in marine environment.
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Khan, Rizwan A., and Suhail Ahmad. "Probabilistic Fracture Mechanics Assessment of Welded Joints of Offshore Structure Using a Bilinear Crack Growth Law." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57356.

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Design of welded structures for fatigue limit state is normally carried out by means of either linear or bilinear S-N curves approaches. To properly assess the effects of design, fabrication, inspection and repair strategy for structures degradation due to crack growth, Fracture mechanics (FM) models need to be applied. This paper deals with the application of a probabilistic fracture mechanics approach to predict the fatigue life of welded steel structure in the presence of cracks under random spectral loading. It is based on a BS7910 [1] proposed bi-linear relationship to model fatigue crack growth and incorporates a failure criterion to describe the interaction between fracture and plastic collapse. Uncertainty modeling, especially of fatigue crack growth parameters, is undertaken with the aid of recently published data in support of the bi-linear crack growth relationship. Results pertaining to fatigue reliability and fatigue crack size evolution are presented using the Monte Carlo Simulation technique, and emphasis is placed on a comparison between linear and bi-linear crack growth models. The bi-linear crack growth model is found to lead to higher fatigue life estimates and shows sensitivity to many other parameters in addition to the state of stress of the component. This leads to implications on inspection schemes for components of the marine structures and to ensure minimization of the surprises due to wide scatter of the fatigue phenomenon in marine environment. Variations in the system configuration, service life and coefficients of crack growth laws have been studied on the parametric basis.
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Khan, Rizwan A., and Suhail Ahmad. "Effect of Bi-Linear S-N Curve and Crack Growth Law on the Safety Analyses of Welded Joints of an Offshore Structure." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59442.

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Design of welded structures for fatigue limit state is normally carried out by means of either linear or bilinear S-N curves which have been found adequate to predict crack initiation only. To properly assess the effects of design, fabrication, inspection and repair strategy for structure degradation due to crack growth, Fracture mechanics (FM) models need to be applied. In this paper, alternative S-N and FM formulations of fatigue are investigated. Probabilistic fracture mechanics approach predicts the fatigue life of welded steel structure in the presence of cracks under random spectrum loading. It is based on a recently proposed bi-linear relationship to model fatigue crack growth and incorporates a failure criterion to describe the interaction between fracture and plastic collapse. Uncertainty modeling, especially on fatigue crack growth parameters, is undertaken with the aid of recently published data in support of the bilinear crack growth relationship. Results pertaining to fatigue reliability and fatigue crack size evolution are presented using the Monte Carlo Simulation Technique, and emphasis is placed on a comparison between linear and bi-linear crack growth models. The bi-linear S-N curve and crack growth model are found to lead to higher fatigue life estimates and shows sensitivity to many other parameters in addition to the stress state of the component. These findings implicate inspection schemes for components of the marine structures to ensure minimization of the surprises due to wide scatter of the fatigue phenomenon in marine environment. Variations in system configuration, service life and coefficients of crack growth laws have been studied on the parametric basis.
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Zhao, Zhengwei Jack, and Irewole Wally Orisamolu. "Probabilistic Fatigue Damage Assessment for Small Crack Growth." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2647.

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Abstract Fatigue and fracture are typical random phenomena due to various uncertainty sources, including material property, initial flaw and crack shape, structural configuration and geometry around crack tip, load fluctuation, and other environmental factors. As contrast to the most commonly used probabilistic fatigue growth models, which are built based on simplified fatigue crack growth law, a framework of probabilistic fracture mechanics based fatigue damage assessment methodology for small crack propagation is presented here. The proposed modeling is developed based on a comprehensive fatigue crack growth model, which accounts the effect of crack aspect ratio, stress ratio, and crack closure and retardation. Due to the complicated nature of the fatigue damage modeling adopted, a high non-linear limit state function with discontinuity resulted from physical domain jumping and overlapping are encountered. The advanced fast probability integration techniques in conjunction with response surface methodology and Monte Carlo simulation are used and the accuracy of the analysis is verified. The interface between probabilistic analysis package and the deterministic fracture mechanics analysis program is developed for the purpose of uncertainty propagation. The probability of failure of fatigue damage is computed first. The statistical characteristics of estimated fatigue life and critical crack size are obtained and presented through CDF/PDF curves. The sensitivity analysis is also performed, which provides an indication of the order of importance for the random variables considered. The results of the study have shown robustness and efficiency of the probabilistic analysis to deal with the real world challenge of uncertainty modelling, propagation, and quantification. Currently, possibility to combine the subject probabilistic damage assessment methodology with reliability updating techniques is under the investigation. The successfulness of the presented research activity will address an important issue of quantitative risk analysis for aging structures subjected to accumulative material damage.
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Reports on the topic "Linear random growth models"

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Parkins and Leis. L51654 Spatial Densities of Stress-Corrosion Cracks in Line-Pipe Steels. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), April 1992. http://dx.doi.org/10.55274/r0010367.

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There was a need to define the spatial density of stress-corrosion crack arrays that develop in operating gas-transmission pipelines and in laboratory test specimens of line-pipe steel, to improve understanding of the factors that control the density and provide data to test models of pipeline cracking. Within the broad definition of crack density are included the locations, numbers, lengths, depths, and degree of linkage of cracks. An analysis has been conducted of location, numbers, lengths, depths, and degree of linkage of stress-corrosion crack colonies in samples from the field and from laboratory tests. This has provided data to test any model of the cracking of pipelines. Thus, it is shown that crack densities are of the order of 5 cracks/mm of distance normal to the crack length direction and that the depths and lengths of cracks are distributed according to log normal and Weibull functions. During the growth stage of cracks in a colony, their spatial distribution is not random, because of the interaction of their associated stress fields. That interaction also results in the coalescence of cracks, an extremely important part of the overall growth process, and that interaction is defined quantitatively to provide further information to which modeling must aspire.
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Zhang, Zhen. Longitudinal SEM in Mplus: Latent Growth and Cross-Lagged Models. Instats Inc., 2022. http://dx.doi.org/10.61700/shmr7uf60jtgi469.

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This seminar introduces longitudinal panel data models in Mplus using SEM, including latent growth models (i.e., latent curve or latent trajectory models) and cross-lagged panel models (i.e., panel vector autoregression) with random and fixed effects, including the random intercept cross-lagged panel model (RI-CLPM) to assess time-varying and stable relationships. Short-run and long-run effects will be covered and methods for assessing them provided. An official Instats certificate of completion is provided at the conclusion of the seminar.
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Zyphur, Michael. Longitudinal SEM in Mplus: Latent Growth and Cross-Lagged Panel Models. Instats Inc., 2022. http://dx.doi.org/10.61700/zvz8cn20pod2l469.

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This seminar introduces longitudinal panel data models in Mplus using SEM, including latent growth models (i.e., latent curve or latent trajectory models) and cross-lagged panel models (i.e., panel vector autoregression) with random and fixed effects, including the random intercept cross-lagged panel model (RI-CLPM) to assess time-varying and stable relationships. Short-run and long-run effects will be covered and methods for assessing them provided. An official Instats certificate of completion is provided at the conclusion of the seminar. For European PhD students, the seminar offers 2 ECTS Equivalent point.
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Zhang, Zhen. Longitudinal SEM in Mplus: Latent Growth and Cross-Lagged Panel Models. Instats Inc., 2022. http://dx.doi.org/10.61700/k7ip0jnkhqk0z469.

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This seminar introduces longitudinal panel data models in Mplus using SEM, including latent growth models (i.e., latent curve or latent trajectory models) and cross-lagged panel models (i.e., panel vector autoregression) with random and fixed effects, including the random intercept cross-lagged panel model (RI-CLPM) to assess time-varying and stable relationships. Short-run and long-run effects will be covered and methods for assessing them provided. An official Instats certificate of completion is provided at the conclusion of the seminar. For European PhD students, the seminar offers 2 ECTS Equivalent point.
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Zyphur, Michael. Longitudinal SEM in R: Latent Growth and Cross-Lagged Panel Models. Instats Inc., 2022. http://dx.doi.org/10.61700/0cgexcmkbt2w4469.

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This seminar introduces longitudinal panel data models in Lavaan using SEM, including latent growth models (i.e., latent curve or latent trajectory models) and cross-lagged panel models (i.e., panel vector autoregression) with random and fixed effects, including the random intercept cross-lagged panel model (RI-CLPM) to assess time-varying and stable relationships. Short-run and long-run effects will be covered and methods for assessing them provided. An official Instats certificate of completion is provided at the conclusion of the seminar. For European PhD students, the seminar offers 2 ECTS Equivalent point.
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Grimm, Kevin, and Nilam Ram. Growth Modeling with SEM. Instats Inc., 2024. http://dx.doi.org/10.61700/scobgclr2wfd61424.

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This comprehensive seminar on Growth Modeling with SEM, led by professors Kevin Grimm (ASU) and Nilam Ram (Stanford University), provides essential training for analyzing longitudinal data in various disciplines, including Psychology, Sociology, and Public Health. Participants will gain practical skills in applying linear and nonlinear growth models using Mplus and R, enhancing their ability to conduct sophisticated longitudinal research.
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Kottke, Albert, Norman Abrahamson, David Boore, Yousef Bozorgnia, Christine Goulet, Justin Hollenback, Tadahiro Kishida, et al. Selection of Random Vibration Procedures for the NGA-East Project. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, November 2018. http://dx.doi.org/10.55461/ltmu9309.

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Pseudo-spectral acceleration (PSA) is the most commonly used intensity measure in earthquake engineering as it serves as a simple approximate predictor of structural response for many types of systems. Therefore, most ground-motion models (GMMs, aka GMPEs) provide median and standard deviation PSA using a suite of input parameters characterizing the source, path, and site effects. Unfortunately, PSA is a complex metric: the PSA for a single oscillator frequency depends on the Fourier amplitudes across a range of frequencies. The Fourier amplitude spectrum (FAS) is an appealing alternative because its simple linear superposition allows effects to be modeled as transfer functions. For this reason, most seismological models, i.e., the source spectrum, are developed for the FAS. Using FAS in conjunction with random-vibration theory (RVT) allows GMM developers to superimpose seismological models directly, computing PSA only at the end of the process. The FAS-RVT-PSA approach was first used by the Hollenback et al. team in their development of GMMs for the Next Generation Attenuation Relationships for Central & Eastern North-America (NGA-East) project (see Chapter 11 of PEER Report No. 2015/04). As part of the NGA-East project to support the Hollenback et al. team and similar efforts, the current report summarizes a systematic processing algorithm for FAS that minimizes computational requirements and bias that results from the RVT approximation for median GMM development.
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Zhang, Zhen. Longitudinal SEM in Mplus (Free with Course Purchase). Instats Inc., 2023. http://dx.doi.org/10.61700/qbnb0rzkq0afl469.

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This seminar introduces longitudinal panel data models in Mplus using SEM, including latent growth models (i.e., latent curve or latent trajectory models) and cross-lagged panel models (i.e., panel vector autoregression) with random and fixed effects, including the random intercept cross-lagged panel model (RI-CLPM) to assess time-varying and stable relationships. Short-run and long-run effects will be covered and methods for assessing them provided. An official Instats certificate of completion is provided at the conclusion of the seminar. For European PhD students, the seminar offers 2 ECTS Equivalent point.
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Nasr, Elhami, Tariq Shehab, Nigel Blampied, and Vinit Kanani. Estimating Models for Engineering Costs on the State Highway Operation and Protection Program (SHOPP) Portfolio of Projects. Mineta Transportation Institute, November 2024. http://dx.doi.org/10.31979/mti.2024.2365.

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The State Highway Operation and Protection Program (SHOPP) is crucial for maintaining California’s 15,000-mile state highway system, which includes projects like pavement rehabilitation, bridge repair, safety enhancements, and traffic management systems. Administered by Caltrans, SHOPP aims to preserve highway efficiency and safety, supporting economic growth and public safety. This research aimed to develop robust cost-estimating models to improve budgeting and financial planning, aiding Caltrans, the California Transportation Commission (CTC), and the Legislature. The research team collected and refined comprehensive data from Caltrans project expenditures from 1983 to 2021, ensuring a high-quality dataset. Subject matter experts validated the data, enhancing its reliability. Two models were developed: a statistical model using exponential regression to account for non-linear cost growth, and an AI model employing neural networks to handle complex relationships in the data. Model performance was evaluated based on accuracy and reliability through repeated testing and validation. Key findings indicated that the new models significantly improved the precision of cost forecasts, reducing the variance between predicted and actual project costs. This advancement minimizes budget overruns and enhances resource allocation efficiency. Additionally, leveraging historical data with current market trends refined the models’ predictive power, boosting stakeholder confidence in project budgeting and financial planning. The study’s innovative approach, integrating machine learning and big data analytics, transforms traditional estimation practices and serves as a reference for other state highway programs. Continuous improvement and broader application of these models are recommended to further enhance cost estimation accuracy and support informed decision-making in transportation infrastructure management.
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Huang, Lei, Meng Song, Hui Shen, Huixiao Hong, Ping Gong, Deng Hong-Wen, and Zhang Chaoyang. Deep learning methods for omics data imputation. Engineer Research and Development Center (U.S.), February 2024. http://dx.doi.org/10.21079/11681/48221.

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One common problem in omics data analysis is missing values, which can arise due to various reasons, such as poor tissue quality and insufficient sample volumes. Instead of discarding missing values and related data, imputation approaches offer an alternative means of handling missing data. However, the imputation of missing omics data is a non-trivial task. Difficulties mainly come from high dimensionality, non-linear or nonmonotonic relationships within features, technical variations introduced by sampling methods, sample heterogeneity, and the non-random missingness mechanism. Several advanced imputation methods, including deep learning-based methods, have been proposed to address these challenges. Due to its capability of modeling complex patterns and relationships in large and high-dimensional datasets, many researchers have adopted deep learning models to impute missing omics data. This review provides a comprehensive overview of the currently available deep learning-based methods for omics imputation from the perspective of deep generative model architectures such as autoencoder, variational autoencoder, generative adversarial networks, and Transformer, with an emphasis on multi-omics data imputation. In addition, this review also discusses the opportunities that deep learning brings and the challenges that it might face in this field.
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