Statistical Modeling in Nonlinear Systems

Abstract The use of linear statistical methods in building climate prediction models is examined, particularly the use of anomalies. The author’s perspective is that the climate system is a nonlinear interacting system, so the impact of modeling using anomalies rather than observed data directly is considered. With reference to the Lorenz system and a simple model for regime dependence, it is shown that anomalies impair our ability to reconstruct nonlinear dynamics. Some alternative approaches in the literature that offer an attractive way forward are explored, focusing on Bayesian hierarchical methods to construct so-called physical–statistical models. The author’s view is that anomalies should be reserved in most cases as a tool for enhancing graphical representations of climate data. The exceptions are when the implicit assumptions underlying the use of anomalies are met or when an anomaly representation is physically motivated.

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A Spatiotemporal Prediction Model for Regional Scheduling of Shared Bicycles Based on the INLA Method

Journal of Advanced Transportation ◽

10.1155/2021/4959504 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Zhuoran Yu ◽

Yimeng Duan ◽

Shen Zhang ◽

Xin Liu ◽

Kui Li

Keyword(s):

Prediction Models ◽

Bayesian Hierarchical ◽

Demand Prediction ◽

Point Of Interest ◽

Modeling Process ◽

Proposed Model ◽

Bayesian Hierarchical Method ◽

Spatial Entities ◽

Operation Results ◽

The Impact

Dock-less bicycle-sharing programs have been widely accepted as an efficient mode to benefit health and reduce congestions. And modeling and prediction has always been a core proposition in the field of transportation. Most of the existing demand prediction models for shared bikes take regions as research objects; therefore, a POI-based method can be a beneficial complement to existing research, including zone-level, OD-level, and station-level techniques. Point of interest (POI) is the location description of spatial entities, which can reflect the cycling route characteristics for both commuting and noncommuting trips to a certain extent, and is also the main generating point and attraction point of shared-bike travel flow. In this study, we make an effort to model a POI-level cycling demand with a Bayesian hierarchical method. The proposed model combines the integrated nested Laplace approximation (INLA) and random partial differential equation (SPDE) to cope with the huge computation in the modeling process. In particular, we have adopted the dock-less bicycle-sharing rental records of Mobike as a case study to validate our method; the study area was one of the fastest growing urban districts in Shanghai in August 2016. The operation results show that the method can help better understand, measure, and characterize spatiotemporal patterns of bike-share ridership at the POI level and quantify the impact of the spatiotemporal effect on bicycle-sharing use.

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Prediction Models for Early Childhood Obesity: Applicability and Existing Issues

Hormone Research in Paediatrics ◽

10.1159/000496563 ◽

2018 ◽

Vol 90 (6) ◽

pp. 358-367 ◽

Cited By ~ 9

Author(s):

Éadaoin M. Butler ◽

José G.B. Derraik ◽

Rachael W. Taylor ◽

Wayne S. Cutfield

Keyword(s):

Risk Factors ◽

Early Childhood ◽

Childhood Obesity ◽

Statistical Models ◽

Prediction Models ◽

False Negative ◽

Targeted Interventions ◽

Wide Range ◽

Early Childhood Obesity ◽

The Impact

Statistical models have been developed for the prediction or diagnosis of a wide range of outcomes. However, to our knowledge, only 7 published studies have reported models to specifically predict overweight and/or obesity in early childhood. These models were developed using known risk factors and vary greatly in terms of their discrimination and predictive capacities. There are currently no established guidelines on what constitutes an acceptable level of risk (i.e., risk threshold) for childhood obesity prediction models, but these should be set following consideration of the consequences of false-positive and false-negative predictions, as well as any relevant clinical guidelines. To date, no studies have examined the impact of using early childhood obesity prediction models as intervention tools. While these are potentially valuable to inform targeted interventions, the heterogeneity of the existing models and the lack of consensus on adequate thresholds limit their usefulness in practice.

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Synchronization of Quadratic Chaotic Systems Based on Simultaneous Estimation of Nonlinear Dynamics

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4040459 ◽

2018 ◽

Vol 13 (8) ◽

Cited By ~ 1

Author(s):

Amin Zarei ◽

Saeed Tavakoli

Keyword(s):

Nonlinear Dynamics ◽

Chaotic Systems ◽

Lorenz System ◽

Simultaneous Estimation ◽

Control Law ◽

Adaptive Mechanism ◽

Lyapunov Theorem ◽

Unknown Parameters ◽

The Lorenz System ◽

Synchronization Scheme

To synchronize quadratic chaotic systems, a synchronization scheme based on simultaneous estimation of nonlinear dynamics (SEND) is presented in this paper. To estimate quadratic terms, a compensator including Jacobian matrices in the proposed master–slave schematic is considered. According to the proposed control law and Lyapunov theorem, the asymptotic convergence of synchronization error to zero is proved. To identify unknown parameters, an adaptive mechanism is also used. Finally, a number of numerical simulations are provided for the Lorenz system and a memristor-based chaotic system to verify the proposed method.

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The Use of Bayesian Hierarchical Methods to Assess Selection and Observer Bias in Observational Health Outcome Studies

SSRN Electronic Journal ◽

10.2139/ssrn.944483 ◽

2006 ◽

Author(s):

Mark Ratcliffe ◽

Josep Maria Haro ◽

Stathis Kontodimas ◽

Miguel Angel Negrin ◽

David Suarez ◽

...

Keyword(s):

Health Outcome ◽

Outcome Studies ◽

Observer Bias ◽

Bayesian Hierarchical ◽

Bayesian Hierarchical Methods

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Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419501979 ◽

2019 ◽

Vol 29 (14) ◽

pp. 1950197 ◽

Cited By ~ 2

Author(s):

P. D. Kamdem Kuate ◽

Qiang Lai ◽

Hilaire Fotsin

Keyword(s):

Chaotic System ◽

Chaotic Systems ◽

Lorenz System ◽

Chaotic Behavior ◽

Piecewise Linear ◽

Period Doubling ◽

Adaptive Synchronization ◽

The Novel ◽

Algebraic Equations ◽

The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

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Bayesian hierarchical methods for modeling electrical grid component failures

Electric Power Systems Research ◽

10.1016/j.epsr.2020.106789 ◽

2020 ◽

Vol 189 ◽

pp. 106789

Author(s):

Laurel N. Dunn ◽

Ioanna Kavvada ◽

Mathilde D. Badoual ◽

Scott J. Moura

Keyword(s):

Bayesian Hierarchical ◽

Electrical Grid ◽

Bayesian Hierarchical Methods ◽

Component Failures

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Measuring spatial allocative efficiency in basketball

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2019-0126 ◽

2020 ◽

Vol 16 (4) ◽

pp. 271-289

Author(s):

Nathan Sandholtz ◽

Jacob Mortensen ◽

Luke Bornn

Keyword(s):

Spatial Distribution ◽

Hierarchical Model ◽

Opportunity Cost ◽

Allocative Efficiency ◽

Bayesian Hierarchical Model ◽

National Basketball Association ◽

Spatial Context ◽

Bayesian Hierarchical ◽

The Impact

AbstractEvery shot in basketball has an opportunity cost; one player’s shot eliminates all potential opportunities from their teammates for that play. For this reason, player-shot efficiency should ultimately be considered relative to the lineup. This aspect of efficiency—the optimal way to allocate shots within a lineup—is the focus of our paper. Allocative efficiency should be considered in a spatial context since the distribution of shot attempts within a lineup is highly dependent on court location. We propose a new metric for spatial allocative efficiency by comparing a player’s field goal percentage (FG%) to their field goal attempt (FGA) rate in context of both their four teammates on the court and the spatial distribution of their shots. Leveraging publicly available data provided by the National Basketball Association (NBA), we estimate player FG% at every location in the offensive half court using a Bayesian hierarchical model. Then, by ordering a lineup’s estimated FG%s and pairing these rankings with the lineup’s empirical FGA rate rankings, we detect areas where the lineup exhibits inefficient shot allocation. Lastly, we analyze the impact that sub-optimal shot allocation has on a team’s overall offensive potential, demonstrating that inefficient shot allocation correlates with reduced scoring.

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Models for predicting treatment efficacy of antiepileptic drugs and prognosis of treatment withdrawal in epilepsy patients

Acta Epileptologica ◽

10.1186/s42494-020-00035-9 ◽

2021 ◽

Vol 3 (1) ◽

Author(s):

Shijun Yang ◽

Bin Wang ◽

Xiong Han

Keyword(s):

Antiepileptic Drugs ◽

Statistical Models ◽

Prediction Models ◽

External Validation ◽

Machine Learning Algorithms ◽

Treatment Withdrawal ◽

Patient Treatment ◽

Recent Developments ◽

Progression Of Disease ◽

Patients With Epilepsy

AbstractAlthough antiepileptic drugs (AEDs) are the most effective treatment for epilepsy, 30–40% of patients with epilepsy would develop drug-refractory epilepsy. An accurate, preliminary prediction of the efficacy of AEDs has great clinical significance for patient treatment and prognosis. Some studies have developed statistical models and machine-learning algorithms (MLAs) to predict the efficacy of AEDs treatment and the progression of disease after treatment withdrawal, in order to provide assistance for making clinical decisions in the aim of precise, personalized treatment. The field of prediction models with statistical models and MLAs is attracting growing interest and is developing rapidly. What’s more, more and more studies focus on the external validation of the existing model. In this review, we will give a brief overview of recent developments in this discipline.

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GPS Coordinates for Modelling Correlated Herd Effects in Genomic Prediction Models Applied to Hanwoo Beef Cattle

Animals ◽

10.3390/ani11072050 ◽

2021 ◽

Vol 11 (7) ◽

pp. 2050

Author(s):

Beatriz Castro Dias Cuyabano ◽

Gabriel Rovere ◽

Dajeong Lim ◽

Tae Hun Kim ◽

Hak Kyo Lee ◽

...

Keyword(s):

Environmental Factors ◽

Genomic Prediction ◽

Prediction Models ◽

Phenotypic Expression ◽

Genetic Evaluation ◽

Genomic Breeding ◽

Breeding Values ◽

Korean Cattle ◽

Evaluation Programs ◽

The Impact

It is widely known that the environment influences phenotypic expression and that its effects must be accounted for in genetic evaluation programs. The most used method to account for environmental effects is to add herd and contemporary group to the model. Although generally informative, the herd effect treats different farms as independent units. However, if two farms are located physically close to each other, they potentially share correlated environmental factors. We introduce a method to model herd effects that uses the physical distances between farms based on the Global Positioning System (GPS) coordinates as a proxy for the correlation matrix of these effects that aims to account for similarities and differences between farms due to environmental factors. A population of Hanwoo Korean cattle was used to evaluate the impact of modelling herd effects as correlated, in comparison to assuming the farms as completely independent units, on the variance components and genomic prediction. The main result was an increase in the reliabilities of the predicted genomic breeding values compared to reliabilities obtained with traditional models (across four traits evaluated, reliabilities of prediction presented increases that ranged from 0.05 ± 0.01 to 0.33 ± 0.03), suggesting that these models may overestimate heritabilities. Although little to no significant gain was obtained in phenotypic prediction, the increased reliability of the predicted genomic breeding values is of practical relevance for genetic evaluation programs.

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Application of SWAT in Hydrological Simulation of Complex Mountainous River Basin (Part II: Climate Change Impact Assessment)

Water ◽

10.3390/w13111548 ◽

2021 ◽

Vol 13 (11) ◽

pp. 1548

Author(s):

Suresh Marahatta ◽

Deepak Aryal ◽

Laxmi Prasad Devkota ◽

Utsav Bhattarai ◽

Dibesh Shrestha

Keyword(s):

Climate Change ◽

River Basin ◽

Climate Models ◽

Assessment Tool ◽

Swat Model ◽

Global Climate Models ◽

Climate Data ◽

The Future ◽

The Impact ◽

Mountainous River

This study aims at analysing the impact of climate change (CC) on the river hydrology of a complex mountainous river basin—the Budhigandaki River Basin (BRB)—using the Soil and Water Assessment Tool (SWAT) hydrological model that was calibrated and validated in Part I of this research. A relatively new approach of selecting global climate models (GCMs) for each of the two selected RCPs, 4.5 (stabilization scenario) and 8.5 (high emission scenario), representing four extreme cases (warm-wet, cold-wet, warm-dry, and cold-dry conditions), was applied. Future climate data was bias corrected using a quantile mapping method. The bias-corrected GCM data were forced into the SWAT model one at a time to simulate the future flows of BRB for three 30-year time windows: Immediate Future (2021–2050), Mid Future (2046–2075), and Far Future (2070–2099). The projected flows were compared with the corresponding monthly, seasonal, annual, and fractional differences of extreme flows of the simulated baseline period (1983–2012). The results showed that future long-term average annual flows are expected to increase in all climatic conditions for both RCPs compared to the baseline. The range of predicted changes in future monthly, seasonal, and annual flows shows high uncertainty. The comparative frequency analysis of the annual one-day-maximum and -minimum flows shows increased high flows and decreased low flows in the future. These results imply the necessity for design modifications in hydraulic structures as well as the preference of storage over run-of-river water resources development projects in the study basin from the perspective of climate resilience.

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