Systematic Resampling Research Articles

How variable are the classic ERP effects during sentence processing? A systematic resampling analysis of the N400 and P600 effects

Although event-related potential (ERP) research on language processing has capitalized on key, theoretically influential components such as the N400 and P600, their measurement properties—especially the variability in their temporal and spatial parameters—have rarely been examined. The current study examined the measurement properties of the N400 and P600 effects elicited by semantic and syntactic anomalies, respectively, during sentence processing. We used a bootstrap resampling procedure to randomly draw many thousands of resamples varying in sample size and stimulus count from a larger sample of 187 participants and 40 stimulus sentences of each type per condition. Our resampling investigation focused on three issues: (a) statistical power; (b) variability in the magnitudes of the effects; and (c) variability in the temporal and spatial profiles of the effects. At the level of grand averages, the N400 and P600 effects were both robust and substantial. However, across resamples, there was a high degree of variability in effect magnitudes, onset times, and scalp distributions, which may be greater than is currently appreciated in the literature, especially for the P600 effects. These results provide a useful basis for designing future studies using these two well-established ERP components. At the same time, the results also highlight challenges that need to be addressed in future research (e.g., how best to analyze the ERP data without engaging in such questionable research practices as p-hacking).

Can Short-Term Online-Monitoring Improve the Current WFD Water Quality Assessment Regime? Systematic Resampling of High-Resolution Data from Four Saxon Catchments

The European Union Water Framework Directive (2000/60/EC; WFD) aims to achieve a good ecological and chemical status of all bodies of surface water by 2027. The development of integrated guidance on surface water chemical monitoring (e.g., WFD Guidance Document No. 7/19) has been transferred into national German law (Ordinance for the Protection of Surface Waters, OGewV). For the majority of compounds, this act requires monthly sampling to assess the chemical quality status of a body of surface water. To evaluate the representativeness of the sampling strategy under the OGewV, high-frequency online monitoring data are investigated under different sampling scenarios and compared with current, monthly grab sampling data. About 23 million data points were analyzed for this study. Three chemical parameters (dissolved oxygen, nitrate-nitrogen, and chloride concentration) and discharge data were selected from four catchments of different sizes, ranging from 51,391 km2 to 84 km2 (Elbe, Vereinigte Mulde, Neiße and two stations at Lockwitzbach). In this paper, we propose short-term online-monitoring (STOM) as a sampling alternative. STOM considers the placement of online sensors over a limited duration and return interval. In general, we: (I) compare the results of conventional grab sampling with STOM, (II) investigate the different performance of STOM and grab sampling using discharge data as a proxy for analyzing event-mobilized pollutants, and (III) investigate the related uncertainties and costs of both sampling methods. Results show that STOM outperforms grab sampling for parameters where minimum/maximum concentrations are required by law, as the probability of catching a single extreme value is higher with STOM. Furthermore, parameters showing a pronounced diurnal pattern, such as dissolved oxygen, are also captured considerably better. The performance of STOM showed no substantial improvements for parameters with small concentration variability, such as nitrogen-nitrate or chloride. The analysis of discharge events as a proxy parameter for event-mobilized pollutants proves that the probability of capturing samples during events is significantly increased by STOM.

Understanding the impact of along-transect resolution on acoustic surveys

Resolution can be defined as the minimum distance between two consecutive sampling points taken by an instrument. In acoustic surveys, the main parameter determining the resolution of sampling along a transect is the distance between successive echosounder transmissions or “pings”. An increase in either the time interval between pings or the speed of the vessel increases the inter-ping distance, hence decreasing the effective sampling resolution. This study investigated whether a loss in along-transect resolution affects the mean backscattered acoustic energy, leading to uncertainty and/or bias in abundance estimates. To this end, a real acoustic survey was echo-integrated, followed by the application of a systematic resampling scheme to simulate a decrease in pinging resolution. For each transect, the mean backscattered acoustic energy calculated at each resolution was compared with that at the original resolution. Transects were characterised according to their heterogeneity and spatial autocorrelation to investigate their effect on the relationship between abundance error and sampling resolution. Uncertainty was seen to increase with decreasing resolution, with higher heterogeneity and lower spatial autocorrelation accelerating the rise in imprecision. Although the mean bias across replicates was zero, the asymmetry of the bias distributions increased with decreasing resolution, leading to an increasing probability and magnitude of underestimation (https://aztigps.shinyapps.io/PingRateStudio/).

Conditional Particle Filters with Bridge Backward Sampling

Conditional particle filters (CPFs) with backward/ancestor sampling are powerful methods for sampling from the posterior distribution of the latent states of a dynamic model such as a hidden Markov model. However, the performance of these methods deteriorates with models involving weakly informative observations and/or slowly mixing dynamics. Both of these complications arise when sampling finely time-discretized continuous-time path integral models, but can occur with hidden Markov models too. Multinomial resampling, which is commonly employed with CPFs, resamples excessively for weakly informative observations and thereby introduces extra variance. Furthermore, slowly mixing dynamics render the backward/ancestor sampling steps ineffective, leading to degeneracy issues. We detail two conditional resampling strategies suitable for the weakly informative regime: the so-called “killing” resampling and the systematic resampling with mean partial order. To avoid the degeneracy issues, we introduce a generalization of the CPF with backward sampling that involves auxiliary “bridging” CPF steps that are parameterized by a blocking sequence. We present practical tuning strategies for choosing an appropriate blocking. Our experiments demonstrate that the CPF with a suitable resampling and the developed “bridge backward sampling” can lead to substantial efficiency gains in the weakly informative and slow mixing regime. Supplementary materials for this article are available online.

A hybrid particle-stochastic map filter

Filtering in nonlinear state-space models is known to be a challenging task due to the posterior distribution being either intractable or expressed in a complex form. One of the most successful methods, particle filtering (PF), although generally outperforming traditional filters, suffers from sample degeneracy. Drawing from optimal transport theory, the stochastic map filter (SMF) accommodates a solution to this problem, but its performance is influenced by the limited flexibility of nonlinear map parameterisation. To alleviate these drawbacks, we propose a hybrid filter which combines the PF and SMF, and hence call it PSMF. Specifically, the PSMF splits the likelihood into two parts, which are then updated by PF and SMF, respectively. The proposed approach adopts systematic resampling and smoothing to break the particle degeneracy caused by the PF. To investigate the influence of the nonlinearity of transport maps, we introduce two variants of the proposed filter, the PSMF-L and PSMF-NL, which are based on linear and nonlinear maps, respectively. The PSMF is tested on various nonlinear state-space models and a nonlinear non-Gaussian target tracking model. The proposed linear PSMF-L outperforms all the reference models for medium-to-large numbers of particles, whilst the PSMF-NL shows better resilience to parameter changes.

On resampling schemes for particle filters with weakly informative observations

We consider particle filters with weakly informative observations (or ‘potentials’) relative to the latent state dynamics. The particular focus of this work is on particle filters to approximate time-discretisations of continuous-time Feynman–Kac path integral models—a scenario that naturally arises when addressing filtering and smoothing problems in continuous time—but our findings are indicative about weakly informative settings beyond this context too. We study the performance of different resampling schemes, such as systematic resampling, SSP (Srinivasan sampling process) and stratified resampling, as the time-discretisation becomes finer and also identify their continuous-time limit, which is expressed as a suitably defined ‘infinitesimal generator.’ By contrasting these generators, we find that (certain modifications of) systematic and SSP resampling ‘dominate’ stratified and independent ‘killing’ resampling in terms of their limiting overall resampling rate. The reduced intensity of resampling manifests itself in lower variance in our numerical experiment. This efficiency result, through an ordering of the resampling rate, is new to the literature. The second major contribution of this work concerns the analysis of the limiting behaviour of the entire population of particles of the particle filter as the time discretisation becomes finer. We provide the first proof, under general conditions, that the particle approximation of the discretised continuous-time Feynman–Kac path integral models converges to a (uniformly weighted) continuous-time particle system.

Multidimensional projection filters via automatic differentiation and sparse-grid integration

The projection filter is a technique for approximating the solutions of optimal filtering problems. In projection filters, the Kushner–Stratonovich stochastic partial differential equation that governs the propagation of the optimal filtering density is projected to a manifold of parametric densities, resulting in a finite-dimensional stochastic differential equation. Despite the fact that projection filters are capable of representing complicated probability densities, their current implementations are limited to Gaussian family or unidimensional filtering applications. This work considers a combination of numerical integration and automatic differentiation to construct projection filter algorithms for more generic problems. Specifically, we provide a detailed exposition of this combination for the manifold of the exponential family, and show how to apply the projection filter to multidimensional cases. We demonstrate numerically that based on comparison to a finite-difference solution to the Kushner–Stratonovich equation and a bootstrap particle filter with systematic resampling, the proposed algorithm retains an accurate approximation of the filtering density while requiring a comparatively low number of quadrature points. Due to the sparse-grid integration and automatic differentiation used to calculate the expected values of the natural statistics and the Fisher metric, the proposed filtering algorithms are highly scalable. They therefore are suitable to many applications in which the number of dimensions exceeds the practical limit of particle filters, but where the Gaussian-approximations are deemed unsatisfactory.

A Framework for Solving the Source Localization of the EEG Measurements with the Application of Particle Filtering with Branching Resampling

Inverse algorithms are used to assess EEG source parameters. This involves identifying unknown voxels in hundreds of different regions, giving an incomplete picture of the brain. There are no uniform solutions since the same sensor output may come from many source configurations. To overcome the lack of uniqueness, one must consider previous information and parameters inherent in the source. Our goal is to predict the location of brain sources from the recorded EEG signal without any prior knowledge of sources. We applied a particle filter to locate the brain sources in this article. The degeneracy of particle weights limits the particle filter’s performance. Various resampling techniques are suggested to address this problem. The performance of the branching resampling approach is compared to a systematic resampling method for brain source localization. To perform assessment and comparison studies, both simulated and real EEG data are used.

Ensemble kalman filter and particle filter-based state estimation on electrical power systems

In this article, a referential study of the sequential importance sampling particle filter with a systematic resampling and the ensemble Kalman filter is provided to estimate the dynamic states of several synchronous machines connected to a modified 14-bus test case, when a balanced three-phase fault is applied at a bus bar near one of the generators. Both are supported by Monte Carlo simulations with practical noise and model uncertainty considerations. Such simulations were carried out in MATLAB by the Power System Toolbox, whereas the evaluation of the Particle Filter and the Ensemble Kalman Filter by script files developed inside the toolbox. The results obtained show that the particle filter has higher accuracy and more robustness to measurement and model noise than the ensemble Kalman filter, which helps support the feasibility of the method for dynamic state estimation applications.

The broken window: An algorithm for quantifying and characterizing misleading trajectories in ecological processes

A core issue in temporal ecology is the concept of trajectory—that is, when can ecologists have reasonable assurance that they know where a system is going? In this paper, we describe a non-random resampling method to directly address the temporal aspects of scaling ecological observations by leveraging existing data. Findings from long-term research sites have been hugely influential in ecology because of their unprecedented longitudinal perspective, yet short-term studies more consistent with typical grant cycles and graduate programs are still the norm. We use long-term insights to create ‘broken windows,’ that is, reanalyze long-term studies from short-term observational perspectives to examine discontinuities in trends at differing temporal scales.The broken window algorithm connects our observations between the short-term and the long-term with an automated, systematic resampling approach: in short, we repeatedly ‘sample’ moving windows of data from existing long-term time series, and analyze these sampled data as if they represented the entire dataset. We then compile typical statistics used to describe the relationship in the sampled data, through repeated samplings, and then use these derived data to gain insights to the questions: 1) how often are the trends observed in short-term data misleading, and 2) can characteristics of these trends be used to predict our likelihood of being misled? We develop a systematic resampling approach, the ‘broken_window algorithm, and illustrate its utility with a case study of firefly observations produced at the Kellogg Biological Station Long-Term Ecological Research Site (KBS LTER). Through a variety of visualizations, summary statistics, and downstream analyses, we provide a standardized approach to evaluating the trajectory of a system, the amount of observation required to find a meaningful trajectory in similar systems, and a means of evaluating our confidence in our conclusions.

Enhanced Localization with Adaptive Normal Distribution Transform Monte Carlo Localization for Map Based Navigation Robot

Map-based navigation is the common navigation method used among the mobile robotic application. The localization plays an important role in the navigation where it estimates the robot position in an environment. Monte Carlo Localization (MCL) is found as the widely used estimation algorithm due to it non-linear characteristic. There are classifications of MCL such as Adaptive MCL (AMCL), Normal Distribution Transform MCL (NDT-MCL) which can perform better than the MCL. However, AMCL is adaptive to particles but the position estimation accuracy is not optimized. NDT-MCL has good position estimation but it requires higher number of particles which results in higher computational effort. The objective of the research is to design and develop a localization algorithm which can achieve better performance in term of position estimation and computational effort. The new MCL algorithm which is named as Adaptive Normal Distribution Transform Monte Carlo Localization (ANDT-MCL) is then designed and developed. It integrates Kullback–Leibler divergence, Normal Distribution Transform and Systematic Resampling into the algorithm. Three experiments are conducted to evaluate the performance of proposed ANDT-MCL in simulated environment. These experiments include evaluating the performance of ANDT-MCL with different path shape, distance and velocity. In the end of the research work, the proposed ANDT-MCL is successfully developed. It is adaptive to the number of particles used, higher position estimation and lower computational effort than existing algorithms. The algorithm can produce better position estimation with less computational effort in any kind paths and is consistent in long journey as well as can outperform in high speed navigation.

Effect of Resampling on the Performance and Execution Speed of Adaptive Marginalized Particle Filter

One of the major factors that affects the performance of adaptive filters like Particle Filter (PF), Marginalized Particle Filter (MPF) and Adaptive Marginalized Particle Filter (AMPF) is sample degeneracy. Sample degeneracy occurs when the weights associated with particles converges to zero making them useless in state estimation. Resampling is the most common method used to avoid sample degeneracy problem, in which a new set of particles are generated and weights are assigned. Performance and execution time of these filter depends a lot on what type of resampling technique is employed. AMPF is the modified version of MPF which is typically faster than PF and MPF. The main aim of this paper is to find the effect of different types of resampling on the performance and execution time of AMPF. For this, a typical target tracking problem is simulated using MATLAB. AMPF with different types of resampling techniques is used for state estimation for the above-mentioned problem and the best in terms of performance and execution speed will be found out. From the simulation, it will be clear that AMPF with systematic resampling is found to be best in terms of execution speed and performance i.e. minimum Root Mean Square Error.

Negative association, ordering and convergence of resampling methods

We study convergence and convergence rates for resampling schemes. Our first main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost sure weak convergence of measures output from Kitagawa’s [J. Comput. Graph. Statist. 5 (1996) 1–25] stratified resampling method. Carpenter, Ckiffird and Fearnhead’s [IEE Proc. Radar Sonar Navig. 146 (1999) 2–7] systematic resampling method is similar in structure but can fail to converge depending on the order of the input samples. We introduce a new resampling algorithm based on a stochastic rounding technique of [In 42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001) (2001) 588–597 IEEE Computer Soc.], which shares some attractive properties of systematic resampling, but which exhibits negative association and, therefore, converges irrespective of the order of the input samples. We confirm a conjecture made by [J. Comput. Graph. Statist. 5 (1996) 1–25] that ordering input samples by their states in $\mathbb{R}$ yields a faster rate of convergence; we establish that when particles are ordered using the Hilbert curve in $\mathbb{R}^{d}$, the variance of the resampling error is ${\scriptstyle\mathcal{O}}(N^{-(1+1/d)})$ under mild conditions, where $N$ is the number of particles. We use these results to establish asymptotic properties of particle algorithms based on resampling schemes that differ from multinomial resampling.

Repeated sampling adds to the genetic diversity of Lepidochelys olivacea (Eschscholtz 1829) olive ridley sea turtle

ABSTRACTFirst sampled in the late 1990s, Campamento Tortuguero La Gloria, in Jalisco, Mexico, was resampled for olive ridley sea turtle (Lepidochyles olivacea Eschscholtz) diversity 10 years later. A comparison with all previously reported mitochondrial sequences revealed that these new samples added to the known genetic diversity for this species, and revealed unexpectedly high genetic diversity among turtles nesting on this beach. The results highlight the importance of systematic resampling in known nesting rookeries to verify the genetic diversity of study populations. Three new olive ridley haplotypes are reported, all more closely related to Baja Californian haplotypes than to Australian haplotypes. Significant genetic divergence is reported within populations, within ocean basins (Atlantic, Pacific, Indian and Indo-Pacific), and between ocean basins. Furthermore, this is the first study that integrates satellite tagging data to demonstrate diverse post-nesting migration patterns of turtles with identical haplotypes, and it demonstrates flexibility in post-nesting migratory behaviour for olive ridley sea turtles of the same genetic provenance.

Recursive Particle Filter-Based RBF Network on Time Series Prediction of Measurement Data

Most physical phenomena in nature are chaotic or close to chaos. An irregular time series can be generated or measured with a purely deterministic equation of motion in nonlinear and chaotic systems. This paper presents an adaptive state-space particle filtering (PF)-based trained radial basis function (RBF) network for chaotic and nonstationary observation–prediction. The recursive Bayesian filtering algorithm, which uses the particle representation of density function, is adopted to accomplish nonlinear and non-Gaussian state estimation and achieve improved convergence rate and quality of solution. Four sampling importance resampling approaches, namely, multinomial, systematic, stratified, and residual resampling methods, are considered to resolve weight degeneracy. The effectiveness of our proposed methods is investigated using two chaotic time series and three measurement datasets, including the Mackey–Glass time series, Rossler time series, monthly Lake Erie levels, monthly water usage series, and SML2010 data set. The performances are evaluated through an extensive simulation by computing the average mean square error, mean absolute percentage error, and average relative variance metrics. Simulation results show that the proposed PF-based RBF structure can provide more effective and accurate prediction performances compared with the conventional gradient descent, extended Kalman filter (EKF), and decoupled EKF algorithms (DEKF).

A holistic comparison of the different resampling algorithms for particle filter based prognosis using lithium ion batteries as a case study

Prognostic health management (PHM) is a critical and essential aspect of any robust maintenance program in the manufacturing industry for early failure detection and prediction of the remaining useful life (RUL) for the entire system or for a component (sub-system) whose condition is being monitored in real-time. In recent years, a lot of research has been done on developing better performing prognostic algorithms for RUL prediction with the “particle filter (PF)” framework being the most widely used amongst them. To address the problems of particle degeneracy and particle impoverishment, several adaptations of standard particle filters have been proposed by improvising the resampling strategies. However, the efficacy of these algorithms is assessed only under specific conditions involving relatively clean degradation data (low noise), large training data sets and limited degradation patterns (mostly linear or “almost” linear). The purpose of this study is to make a comparison of four most frequently used resampling strategies: Multinomial resampling, Stratified resampling, Systematic resampling and Residual Systematic resampling for lithium-ion battery RUL prediction. They are similar in terms of operation but differ only in the way the ordered sequence of random numbers is generated for resampling thus enabling a standardized comparison in terms of computational complexity of O(N). The robustness of these resampling techniques is tested by adding 50 dB of noise to the measurement data and by considering three different time instants at different stages of the device lifecycle for prediction with different amount of training data. We use the mean squared deviation (MSD), relative accuracy (RA), execution time and the α – λ plot as the performance metrics for comparing the effectiveness of the different resampling techniques. Our analysis shows that the residual systematic resampling algorithm is the most preferred approach considering the reasonable accuracy and short computational time.

Adaptive particle filter for localization problem in service robotics

In this paper we present a statistical approach to the likelihood computation and adaptive resampling algorithm for particle filters using low cost ultrasonic sensors in the context of service robotics. This increases the efficiency of the particle filter in the Monte Carlo Localization problem by means of preventing sample impoverishment and ensuring it converges towards the most likely particle and simultaneously keeping less likely ones by systematic resampling. Proposed algorithms were developed in the ROS framework, simulation was done in Gazebo environment. Experiments using a differential drive mobile platform with 4 ultrasonic sensors in the office environment show that our approach provides strong improvement over particle filters with fixed sample sizes.

Adaptive memory-based single distribution resampling for particle filter

The restrictions that are related to using single distribution resampling for some specific computing devices’ memory gives developers several difficulties as a result of the increased effort and time needed for the development of a particle filter. Thus, one needs a new sequential resampling algorithm that is flexible enough to allow it to be used with various computing devices. Therefore, this paper formulated a new single distribution resampling called the adaptive memory size-based single distribution resampling (AMSSDR). This resampling method integrates traditional variation resampling and traditional resampling in one architecture. The algorithm changes the resampling algorithm using the memory in a computing device. This helps the developer formulate a particle filter without over considering the computing devices’ memory utilisation during the development of different particle filters. At the start of the operational process, it uses the AMSSDR selector to choose an appropriate resampling algorithm (for example, rounding copy resampling or systematic resampling), based on the current computing devices’ physical memory. If one chooses systematic resampling, the resampling will sample every particle for every cycle. On the other hand, if it chooses the rounding copy resampling, the resampling will sample more than one of each cycle’s particle. This illustrates that the method (AMSSDR) being proposed is capable of switching resampling algorithms based on various physical memory requirements. The aim of the authors is to extend this research in the future by applying their proposed method in various emerging applications such as real-time locator systems or medical applications.

Value of Tracking Biopsy in Men Undergoing Active Surveillance of Prostate Cancer.

We compared the upgrading rate obtained by resampling precise spots of prostate cancer (tracking biopsy) vs conventional systematic resampling during followup of men on active surveillance. From 2009 to 2017 in 352 men prostate cancer was Gleason 3 + 3 in 268 and Gleason 3 + 4 in 84 at initial magnetic resonance imaging-ultrasound fusion biopsy. These men subsequently underwent a second fusion biopsy. At the first biopsy session all men underwent 12-core systematic biopsies and, when magnetic resonance imaging visible lesions were present, targeted biopsies. All cancerous sites were recorded electronically. During active surveillance at a second fusion biopsy session 6 to 18 months later tracking and systematic nontracking samples were obtained. The primary outcome measure was an increase in Gleason score (upgrading) at followup sampling, which was stratified by biopsy method. Overall 91 of the 352 men (25.9%) experienced upgrading at the second biopsy during a median 11-month interval. The upgrade rate in the Gleason 3 + 3 and 3 + 4 groups was 26.9% and 22.6%, respectively. The mean number of cores taken at second biopsy was 12.2 ± 3.3 in men with upgrading and 12.4 ± 4.1 in those who remained stable (p not significant). Men with grade 0 to 4 magnetic resonance imaging targets were all upgraded at approximately the same rate of 20% to 30% (p not significant). However, 58.8% of the men with grade 5 magnetic resonance imaging targets were upgraded. Of the 91 upgrades 48 (53%) were detected only by tracking. The tracking function of magnetic resonance imaging-ultrasound fusion biopsy warrants further study. When specific sites are resampled in men undergoing active surveillance of prostate cancer, upgrading is detected more often than by nontracking biopsy.

Assessing sequential data assimilation techniques for integrating GRACE data into a hydrological model

The time-variable terrestrial water storage (TWS) products from the Gravity Recovery And Climate Experiment (GRACE) have been increasingly used in recent years to improve the simulation of hydrological models by applying data assimilation techniques. In this study, for the first time, we assess the performance of the most popular data assimilation sequential techniques for integrating GRACE TWS into the World-Wide Water Resources Assessment (W3RA) model. We implement and test stochastic and deterministic ensemble-based Kalman filters (EnKF), as well as Particle filters (PF) using two different resampling approaches of Multinomial Resampling and Systematic Resampling. These choices provide various opportunities for weighting observations and model simulations during the assimilation and also accounting for error distributions. Particularly, the deterministic EnKF is tested to avoid perturbing observations before assimilation (that is the case in an ordinary EnKF). Gaussian-based random updates in the EnKF approaches likely do not fully represent the statistical properties of the model simulations and TWS observations. Therefore, the fully non-Gaussian PF is also applied to estimate more realistic updates. Monthly GRACE TWS are assimilated into W3RA covering the entire Australia. To evaluate the filters performances and analyze their impact on model simulations, their estimates are validated by independent in-situ measurements. Our results indicate that all implemented filters improve the estimation of water storage simulations of W3RA. The best results are obtained using two versions of deterministic EnKF, i.e. the Square Root Analysis (SQRA) scheme and the Ensemble Square Root Filter (EnSRF), respectively, improving the model groundwater estimations errors by 34% and 31% compared to a model run without assimilation. Applying the PF along with Systematic Resampling successfully decreases the model estimation error by 23%.