scholarly journals Multi-scale properties of random walk models of animal movement: lessons from statistical inference

2012 ◽  
Vol 468 (2141) ◽  
pp. 1428-1451 ◽  
Author(s):  
Reiichiro Kawai ◽  
Sergei Petrovskii
Keyword(s):  
Random Walk ◽  
Statistical Inference ◽  
Target Location ◽  
Animal Movement ◽  
Random Search ◽  
Human Motion ◽  
Joint Estimation ◽  
Model Parameters ◽  
Search Problem ◽  
Gaussian Random Walk

The random search problem has long attracted continuous interest owing to its broad interdisciplinary range of applications, including animal foraging, facilitated target location in biological systems and human motion. In this paper, we address the issue of statistical inference for ordinary Gaussian, Pareto, tempered Pareto and fractional Gaussian random walk models, which are among the most studied random walk models proposed as the best strategy in the random search problem. Based on rigorous analysis of the local asymptotic normality property and the Fisher information, we discuss some issues in unbiased joint estimation of the model parameters, in particular, the maximum-likelihood estimation. We present that there exist both theoretical and practical difficulties in more realistic tempered Pareto and fractional Gaussian random walk models from a statistical standpoint. We discuss our findings in the context of individual animal movement and show how our results may be used to facilitate the analysis of movement data and to improve the understanding of the underlying stochastic process.

scholarly journals LÉVY PROCESSES IN ANIMAL MOVEMENT: AN EVOLUTIONARY HYPOTHESIS

Fractals ◽  
2007 ◽  
Vol 15 (02) ◽  
pp. 151-162 ◽  
Author(s):  
FREDERIC BARTUMEUS
Keyword(s):  
Lévy Processes ◽  
Animal Movement ◽  
Fundamental Problem ◽  
Random Search ◽  
Levy Processes ◽  
Search Problem ◽  
Animal Movements ◽  
Adaptive Mechanisms ◽  
Wide Range ◽  
Fractal Patterns

The origin of fractal patterns is a fundamental problem in many areas of science. In ecological systems, fractal patterns show up in many subtle ways and have been interpreted as emergent phenomena related to some universal principles of complex systems. Recently, Lévy-type processes have been pointed out as relevant in large-scale animal movements. The existence of Lévy probability distributions in the behavior of relevant variables of movement, introduces new potential diffusive properties and optimization mechanisms in animal foraging processes. In particular, it has been shown that Lévy processes can optimize the success of random encounters in a wide range of search scenarios, representing robust solutions to the general search problem. These results set the scene for an evolutionary explanation for the widespread observed scale-invariant properties of animal movements. Here, it is suggested that scale-free reorientations of the movement could be the basis for a stochastic organization of the search whenever strongly reduced perceptual capacities come into play. Such a proposal represents two new evolutionary insights. First, adaptive mechanisms are explicitly proposed to work on the basis of stochastic laws. And second, though acting at the individual-level, these adaptive mechanisms could have straightforward effects at higher levels of ecosystem organization and dynamics (e.g. macroscopic diffusive properties of motion, population-level encounter rates). Thus, I suggest that for the case of animal movement, fractality may not be representing an emergent property but instead adaptive random search strategies. So far, in the context of animal movement, scale-invariance, intermittence, and chance have been studied in isolation but not synthesized into a coherent ecological and evolutionary framework. Further research is needed to track the possible evolutionary footprint of Lévy processes in animal movement.

A point-based Bayesian hierarchical model to predict the outcome of tennis matches

2019 ◽  
Vol 15 (4) ◽  
pp. 313-325 ◽  
Author(s):  
Martin Ingram
Keyword(s):  
Random Walk ◽  
Hierarchical Model ◽  
Bayesian Hierarchical Model ◽  
Bayesian Hierarchical ◽  
Gaussian Random Walk ◽  
Over Time ◽  
Modelling Approach ◽  
Independent And Identically Distributed

Abstract A well-established assumption in tennis is that point outcomes on each player’s serve in a match are independent and identically distributed (iid). With this assumption, it is enough to specify the serve probabilities for both players to derive a wide variety of event distributions, such as the expected winner and number of sets, and number of games. However, models using this assumption, which we will refer to as “point-based”, have typically performed worse than other models in the literature at predicting the match winner. This paper presents a point-based Bayesian hierarchical model for predicting the outcome of tennis matches. The model predicts the probability of winning a point on serve given surface, tournament and match date. Each player is given a serve and return skill which is assumed to follow a Gaussian random walk over time. In addition, each player’s skill varies by surface, and tournaments are given tournament-specific intercepts. When evaluated on the ATP’s 2014 season, the model outperforms other point-based models, predicting match outcomes with greater accuracy (68.8% vs. 66.3%) and lower log loss (0.592 vs. 0.641). The results are competitive with approaches modelling the match outcome directly, demonstrating the forecasting potential of the point-based modelling approach.

Simulated annealing for airborne EM inversion

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. F189-F195 ◽  
Author(s):  
Changchun Yin ◽  
Greg Hodges
Keyword(s):  
Simulated Annealing ◽  
Random Walk ◽  
Boltzmann Distribution ◽  
Model Parameters ◽  
Local Minima ◽  
Model Configuration ◽  
Airborne Electromagnetic ◽  
Starting Model ◽  
Airborne Em ◽  
Cooling Schedule

The traditional algorithms for airborne electromagnetic (EM) inversion, e.g., the Marquardt-Levenberg method, generally run only a downhill search. Consequently, the model solutions are strongly dependent on the starting model and are easily trapped in local minima. Simulated annealing (SA) starts from the Boltzmann distribution and runs both downhill and uphill searches, rendering the searching process to easily jump out of local minima and converge to a global minimum. In the SA process, the calculation of Jacobian derivatives can be avoided because no preferred searching direction is required as in the case of the traditional algorithms. We apply SA technology for airborne EM inversion by comparing the inversion with a thermodynamic process, and we discuss specifically the SA procedure with respect to model configuration, random walk for model updates, objective function, and annealing schedule. We demonstrate the SA flexibility for starting models by allowing the model parameters to vary in a large range (far away from the true model). Further, we choose a temperature-dependent random walk for model updates and an exponential cooling schedule for the SA searching process. The initial temperature for the SA cooling scheme is chosen differently for different model parameters according to their resolvabilities. We examine the effectiveness of the algorithm for airborne EM by inverting both theoretical and survey data and by comparing the results with those from the traditional algorithms.

scholarly journals Joint Estimation of Hydraulic and Biochemical Parameters for Reactive Transport Modelling with a Modified ILUES Algorithm

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2161
Author(s):  
Ruicheng Zhang ◽  
Nianqing Zhou ◽  
Xuemin Xia ◽  
Guoxian Zhao ◽  
Simin Jiang
Keyword(s):  
Reactive Transport ◽  
Biochemical Parameters ◽  
Transport Model ◽  
Joint Estimation ◽  
Model Parameters ◽  
Transport Modelling ◽  
Selection Scheme ◽  
Related Model ◽  
Ensemble Smoother ◽  
Iterative Ensemble Smoother

Multicomponent reactive transport modeling is a powerful tool for the comprehensive analysis of coupled hydraulic and biochemical processes. The performance of the simulation model depends on the accuracy of related model parameters whose values are usually difficult to determine from direct measurements. In this situation, estimates of these uncertain parameters can be obtained by solving inverse problems. In this study, an efficient data assimilation method, the iterative local updating ensemble smoother (ILUES), is employed for the joint estimation of hydraulic parameters, biochemical parameters and contaminant source characteristics in the sequential biodegradation process of tetrachloroethene (PCE). In the framework of the ILUES algorithm, parameter estimation is realized by updating local ensemble with the iterative ensemble smoother (IES). To better explore the parameter space, the original ILUES algorithm is modified by determining the local ensemble partly with a linear ranking selection scheme. Numerical case studies based on the sequential biodegradation of PCE are then used to evaluate the performance of the ILUES algorithm. The results show that the ILUES algorithm is able to achieve an accurate joint estimation of related model parameters in the reactive transport model.

scholarly journals Simultaneous state-parameter estimation of rainfall-induced landslide displacement using data assimilation

2019 ◽  
Author(s):  
Jing Wang ◽  
Guigen Nie ◽  
Shengjun Gao ◽  
Changhu Xue
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Prediction Method ◽  
State Parameter ◽  
Joint Estimation ◽  
Model Parameters ◽  
Displacement Estimation ◽  
Landslide Stability ◽  
Landslide Displacement Prediction ◽  
Using Data

Abstract. Landslide displacement prediction has great practical engineering significance to landslide stability evaluation and early warning. The evolution of landslide is a complex dynamic process, applying classical prediction method will result in significant error. Data assimilation method offers a new way to merge multi-source data with the model. However, data assimilation is still deficient in the ability to meet the demand of dynamic landslide system. In this paper, simultaneous state-parameter estimation (SSPE) using particle filter-based data assimilation is applied to predict displacement of the landslide. Landslide SSPE assimilation strategy can make use of time-series displacements and hydrological information for the joint estimation of landslide displacement and model parameters, which can improve the performance considerably. We select Xishan Village, Sichuan province, China as experiment site to test SSPE assimilation strategy. Based on the comparison of actual monitoring data with prediction values, results strongly suggest the effectiveness and feasibility of SSPE assimilation strategy in short-term landslide displacement estimation.

scholarly journals Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 449 ◽  
Author(s):  
Abdullah M. Almarashi ◽  
Majdah M. Badr ◽  
Mohammed Elgarhy ◽  
Farrukh Jamal ◽  
Christophe Chesneau
Keyword(s):  
Statistical Inference ◽  
Goodness Of Fit ◽  
Stochastic Ordering ◽  
Linear Representation ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Data Sets ◽  
New Model ◽  
Entropy Measures ◽  
Lifetime Studies

The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models.

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