Orchestration tools to support the teacher during student collaboration: a\xa0review

Technological advances have steadily increased the detail of animal tracking datasets, yet fundamental data limitations exist for many species that cause substantial biases in home‐range estimation. Specifically, the effective sample size of a range estimate is proportional to the number of observed range crossings, not the number of sampled locations. Currently, the most accurate home‐range estimators condition on an autocorrelation model, for which the standard estimation frame‐works are based on likelihood functions, even though these methods are known to underestimate variance—and therefore ranging area—when effective sample sizes are small.Residual maximum likelihood (REML) is a widely used method for reducing bias in maximum‐likelihood (ML) variance estimation at small sample sizes. Unfortunately, we find that REML is too unstable for practical application to continuous‐time movement models. When the effective sample sizeNis decreased toN ≤ (10), which is common in tracking applications, REML undergoes a sudden divergence in variance estimation. To avoid this issue, while retaining REML’s first‐order bias correction, we derive a family of estimators that leverage REML to make a perturbative correction to ML. We also derive AIC values for REML and our estimators, including cases where model structures differ, which is not generally understood to be possible.Using both simulated data and GPS data from lowland tapir (Tapirus terrestris), we show how our perturbative estimators are more accurate than traditional ML and REML methods. Specifically, when(5) home‐range crossings are observed, REML is unreliable by orders of magnitude, ML home ranges are ~30% underestimated, and our perturbative estimators yield home ranges that are only ~10% underestimated. A parametric bootstrap can then reduce the ML and perturbative home‐range underestimation to ~10% and ~3%, respectively.Home‐range estimation is one of the primary reasons for collecting animal tracking data, and small effective sample sizes are a more common problem than is currently realized. The methods introduced here allow for more accurate movement‐model and home‐range estimation at small effective sample sizes, and thus fill an important role for animal movement analysis. Given REML’s widespread use, our methods may also be useful in other contexts where effective sample sizes are small.

Several methods for reliability analysis have been established and applied to engineering fields bearing in mind uncertainties as a major contributing factor. Small sample size based reliability analysis can be very beneficial when rising uncertainty from statistics of interest such as mean and standard deviation are considered. Model selection and evaluation methods like Akaike Information Criteria (AIC) have demonstrated efficient output for reliability analysis. However, information criterion based on maximum likelihood can provide better model selection and evaluation in small sample size scenario by considering the well-known measure of bootstrapping for curtailing uncertainty with resampling. Our purpose is to utilize the capabilities of bootstrap resampling in information criterion based reliability analysis to check for uncertainty arising from statistics of interest for small sample size problems. In this study, therefore, a unique and efficient simulation scheme is proposed which contemplates the best model selection frequency devised from information criterion to be combined with reliability analysis. It is also beneficial to compute the spread of reliability values as against solitary fixed values with desirable statistics of interest under replication based approach. The proposed simulation scheme is verified using a number of small and moderate sample size focused mathematical example with AIC based reliability analysis for comparison and Monte Carlo simulation (MCS) for accuracy. The results show that the proposed simulation scheme favors the statistics of interest by reducing the spread and hence the uncertainty in small sample size based reliability analysis when compared with conventional methods whereas moderate sample size based reliability analysis did not show any considerable favor.

In the present paper, we implemented the Bayesian regularization (BR) backpropagation algorithm for calibrating an artificial neural network (ANN) as an accident prediction model (APM) to be used on Italian four-lane divided roads. We chose the BR-ANN since it efficiently allows for dealing with small sample size and avoiding overfitting issues by adding a regularization term in the objective function to be minimized during training. Moreover, BR-ANNs are sparsely employed in road safety analyses, and their peculiarities deserve to be emphasized. In our work, the BR-ANN aims to predict the number of fatal and injury (FI) crashes across 236 road elements, for a total length of 78 km. The input features are road element length, horizontal and vertical alignment, cross-section geometry, operating speed, traffic flow, sight distance, and road area type (i.e., a categorical predictor accounting for the potential influence of merge and diverge influence areas). Training and test phases of the BR-ANN have been evaluated by determination coefficient ( R2), root mean square error (RMSE), overfitting ratio (OR), scatterplots, residuals analysis, and by the same ANN architecture trained with the gradient descent (GD) with momentum and adaptive learning rate backpropagation algorithm (GD-ANN). Results demonstrate that the BR-ANN markedly outperforms the GD-ANN, which suffers severe overfitting issues. Furthermore, BR-ANN does not overfit data (OR close to the unity), reports a satisfactory R2 (0.726), and shows a Gaussian residual distribution with zero mean. Therefore, road authorities could consider regularized ANNs for performing appropriate safety analyses, especially when dealing with small road sample sizes.

Considerations of sample size in medical research

294 Background: Economic evaluations in oncology aim to assess the value of new therapies in the long term based on clinical trial data that often have restricted follow-up times (< 5 years) and small sample sizes (< 500 patients). This requires the use of extrapolation assumptions on long-term survival that go beyond the observed data. In this analysis, differences in survival extrapolation methods are tested in samples of sizes and follow-up reflecting typical clinical trials against a background of known survival in prostate cancer from a US based cancer registry. Methods: Data from the National Cancer Institute's Surveillance Epidemiology and End Results (SEER) registry on long-term survival in patients with stage IV prostate cancer were employed. The data set comprised those patients diagnosed between 1988 and 2003, with follow-up data available until 2012. Additional survival for those who received surgery (compared to those who did not), was estimated based on extrapolations using standard parametric statistical models (exponential, Weibull, log-logistic, log-normal, Gamma) fitted to the observed data. Survival analyses were run for 5 sample size scenarios (n = 27,670, 1000, 500, 200, 50) and 6 follow-up scenarios (follow-up years = 25, 20, 10, 5, 2, 1) yielding 30 combination scenarios. Performance of the methods was tested relative to the maximum follow-up, maximum sample size scenario (i.e. reference case) from the SEER registry. Results: Log-logistic and log-normal models were associated with flat tails which led to inflated survival estimations. For scenarios with smaller sizes, gamma models often did not converge. Exponential models were the most frequently reported as best model fit (in approximately 50% of scenarios). Also, gains in OS were consistent when exponential models were selected, and closely matched gain in OS from the reference case. Conclusions: Since clinical trials in oncology are often associated with small patient sample sizes and restricted follow-up, selecting an exponential model may lead to the most consistent and stable results based on the experiment constructed here. Further research should confirm these results for other types of cancer.

Two Dimensional Linear Discriminant Analyses for Hyperspectral Data

The performance on small and medium‐size samples of several techniques to solve the classification problem in discriminant analysis is investigated. The techniques considered are two widely used parametric statistical techniques (Fisher's linear discriminant function and Smith's quadratic function), and a class of recently proposed nonparametric estimation techniques based on mathematical programming (linear and mixed‐integer programming). A simulation study is performed, analyzing the relative performance of the above techniques in the two‐group case, for various small sample sizes, moderate group overlap and across six different data conditions. Training samples as well as validation samples are used to assess the classificatory performance of the techniques. The degree of group overlap and sample sizes selected for analysis in this paper are of interest in practice because they closely reflect conditions of many real data sets. The results of the experiment show that Smith's nonlinear quadratic function tends to be superior on the training samples and validation samples when the variances–covariances across groups are heterogeneous, while the mixed‐integer technique performs best on the training samples when the variances–covariances are equal, and on validation samples with equal variances and discrete uniform independent variables. The mixed‐integer technique and the quadratic discriminant function are also found to be more sensitive than the other techniques to the sample size, giving disproportionally inaccurate results on small samples.

Probabilistic-based random maximum defect estimation and defect-related fatigue life prediction for laser direct deposited 316L parts

Aberrant changes to interactions among cellular components have been conjectured to be potential causes of abnormalities in cellular functions. By systematic analysis of high-throughput-omics data, researchers hope to detect potential associations among measured variables for better biomarker identification and phenotype prediction. In this paper, we focus on the methods to measure pairwise interactive effects among continuous random variables, representing molecular expressions, with respect to a given categorical outcome. Together with a comprehensive review on the existing measures, we further propose new measures that better estimate interactive effects, especially in small sample size scenarios. We first evaluate the performance of the existing and new methods for both small and large sample sizes based on simulated datasets that shows our proposed methods outperform previous methods in general. The best performing method for small sample size scenarios suggested by simulation experiments is then implemented to estimate interactive effects among genes with respect to the metastasis outcome in two breast cancer studies based on micro-array gene expression datasets. Our results further demonstrate that integrating detected interactive effects together with individual effects can help in finding more accurate biomarkers for breast cancer metastasis, which are indeed involved in important pathways related to cancer metastasis based on gene set enrichment analysis.

The structure in cortical microcircuits deviates from what would be expected in a purely random network, which has been seen as evidence of clustering. To address this issue, we sought to reproduce the nonrandom features of cortical circuits by considering several distinct classes of network topology, including clustered networks, networks with distance-dependent connectivity, and those with broad degree distributions. To our surprise, we found that all of these qualitatively distinct topologies could account equally well for all reported nonrandom features despite being easily distinguishable from one another at the network level. This apparent paradox was a consequence of estimating network properties given only small sample sizes. In other words, networks that differ markedly in their global structure can look quite similar locally. This makes inferring network structure from small sample sizes, a necessity given the technical difficulty inherent in simultaneous intracellular recordings, problematic. We found that a network statistic called the sample degree correlation (SDC) overcomes this difficulty. The SDC depends only on parameters that can be estimated reliably given small sample sizes and is an accurate fingerprint of every topological family. We applied the SDC criterion to data from rat visual and somatosensory cortex and discovered that the connectivity was not consistent with any of these main topological classes. However, we were able to fit the experimental data with a more general network class, of which all previous topologies were special cases. The resulting network topology could be interpreted as a combination of physical spatial dependence and nonspatial, hierarchical clustering.SIGNIFICANCE STATEMENT The connectivity of cortical microcircuits exhibits features that are inconsistent with a simple random network. Here, we show that several classes of network models can account for this nonrandom structure despite qualitative differences in their global properties. This apparent paradox is a consequence of the small numbers of simultaneously recorded neurons in experiment: when inferred via small sample sizes, many networks may be indistinguishable despite being globally distinct. We develop a connectivity measure that successfully classifies networks even when estimated locally with a few neurons at a time. We show that data from rat cortex is consistent with a network in which the likelihood of a connection between neurons depends on spatial distance and on nonspatial, asymmetric clustering.

Scholars are increasingly aware that studies-across many disciplines-cannot be replicated by independent researchers. Here, the authors describe how medical education research may be vulnerable to this "replication crisis," explain how researchers can act together to reduce risks, and discuss the positive steps that can increase confidence in research findings. Medical education research contributes to policy and influences practitioner behavior. Findings that cannot be replicated suggest that the original research was not credible. This risk raises the possibility that unhelpful or even harmful changes to medical education have been implemented as a result of research that appeared defensible but was not. By considering these risk factors, researchers can increase the likelihood that studies are generating credible results. The authors discuss and provide examples of 6 factors that may endanger the replicability of medical education research: (1) small sample sizes, (2) small effect sizes, (3) exploratory designs, (4) flexibility in design choices, analysis strategy, and outcome measures, (5) conflicts of interest, and (6) very active fields with many competing research teams. Importantly, medical education researchers can adopt techniques used successfully elsewhere to improve the rigor of their investigations. Researchers can improve their work through better planning in the development stage, carefully considering design choices, and using sensible data analysis. The wider medical education community can help by encouraging higher levels of collaboration among medical educators, by routinely evaluating existing educational innovations, and by raising the prestige of replication and collaborative medical education research. Medical education journals should adopt new approaches to publishing. As medical education research improves, so too will the quality of medical education and patient care.

BackgroundNational or regional population-based HIV prevalence surveys have small sample sizes at district or sub-district levels; this leads to wide confidence intervals when estimating HIV prevalence at district level for programme monitoring and decision making. Health facility programme data, collected during service delivery is widely available, but since people self-select for HIV testing, HIV prevalence estimates based on it, is subject to selection bias. We present a statistical annealing technique, Hybrid Prevalence Estimation (HPE), that combines a small population-based survey sample with a facility-based sample to generate district level HIV prevalence estimates with associated confidence intervals.MethodsWe apply the HPE methodology to combine the 2011 Uganda AIDS indicator survey with the 2011 health facility HIV testing data to obtain HIV prevalence estimates for districts in Uganda. Multilevel logistic regression was used to obtain the propensity of testing for HIV in a health facility, and the propensity to test was used to combine the population survey and health facility HIV testing data to obtain the HPEs. We assessed comparability of the HPEs and survey-based estimates using Bland Altman analysis.ResultsThe estimates ranged from 0.012 to 0.178 and had narrower confidence intervals compared to survey-based estimates. The average difference between HPEs and population survey estimates was 0.00 (95% CI: − 0.04, 0.04). The HPE standard errors were 28.9% (95% CI: 23.4–34.4) reduced, compared to survey-based standard errors. Overall reduction in HPE standard errors compared survey-based standard errors ranged from 5.4 to 95%.ConclusionsFacility data can be combined with population survey data to obtain more accurate HIV prevalence estimates for geographical areas with small population survey sample sizes. We recommend use of the methodology by district level managers to obtain more accurate HIV prevalence estimates to guide decision making without incurring additional data collection costs.

This paper introduces a simple approach for object tracking using hyperspectral (HS) spectral features. The approach addresses the object tracking problem using a small object sample size. For a particular application, the key challenges are: (i) Offline training cannot be utilized; (ii) motor vehicles of interest (targets) have a small sample size (e.g., less than 9); and (iii) kinematic states of targets cannot be used for tracking, since stationary targets are also of interest. Using HS imagery, this paper introduces a method that exploits the mean and median averages spectra to estimate higher moments of the underlying (and unknown) probability distribution function of spectra; in particular, skew tendency and sign. Tracking HS targets is then possible using this algorithm to test a sequence of HS imagery, given that target spectra are initially cued by the user. The approach was implemented into a commercially off the shelf workstation, featuring the IBM Cell Processor and GA-180 Add in Board. Preliminary results are promising using a challenging HS data cube.

Climate change-induced shifts, such as prolonged growing seasons and milder winters, coupled with land-use alterations like forest management abandonment, are reshaping species composition across European forests. A significant spread of evergreen broad-leaved species (EVEs) was observed in southern European forests, driven by global change dynamics. However, large-scale spatio-temporal analysis of these changes are lacking and emphasizes the necessity of mapping these dynamics. The TRACEVE projects (“Tracing the evergreen broad-leaved species and their spread”) primary goal is therefore tracking  EVEs' cover, spread and diversity on a national-scale in Italy. As part of the project, this study focuses on satellite remote sensing, Deep Learning, and forest mapping, aiming at creating seamless maps quantifying the current degree of EVEs cover within forests in Italy.Challenges arise in the transitional zones between evergreen and deciduous forests, where EVEs initially spread in the understory of a deciduous canopy. Tracking EVEs at the edge of their range, where abundance is rare and in mixed forests is therefore difficult. Leveraging Sentinel-2 remote sensing time series covering the full annual phenological cycle addresses this challenge, utilizing leaf-on and leaf-off canopy conditions. Values of species cover derived from ad-hoc forest plot observations in Italian protected areas across a latitudinal gradient serve as initial training data, although the small sampling size (~1000 plots) poses challenges for the generalizability of time series extrinsic regression models, particularly when employing state-of-the-art Deep Learning architectures.The main aim of the study is therefore the development of a robust, Sentinel-2 based mapping procedure to track EVEs within Italian forests on a national-scale. A remote sensing time series extrinsic regression model based on a Deep Learning architecture for cover degree mapping will be developed. Sentinel-2 annual time series, along with derived indices serve as predictors for the models, while target cover will be derived from the plot observations. The study is built around exploring selected strategies to address the issue of large-scale model generalizability, given a small training sample size, that is recorded within small representative areas scattered across Italy. This entails assessing the efficacy of self-supervised pretraining methodologies applied to remote sensing time series within forested regions, pretraining on a more extensive forest database, and evaluating the viability of training data augmentation techniques.To validate and evaluate results on a national scale, an independent forest vegetation database containing around 17,000 forest plots sampled across Italy is employed. This extensive dataset enhances the understanding of EVEs' distribution within Italy's diverse forest ecosystems and can further enhance understanding of complex model results.In conclusion, the study combines advanced satellite remote sensing technologies, Deep Learning methodologies coupled with vegetation plot datasets to map current distribution of EVEs in Italian forests. The findings contribute to the TRACEVE project's future objectives but also offer insights into the challenges and opportunities of Deep Learning models in large-scale forest mapping applications.AcknowledgementsThis research has been conducted within the project “TRACEVE - Tracing the evergreen broad-leaved species and their spread” (I 6452-B) funded by the Austrian Science Fund (FWF).

Multicollinearity is a case of multiple regression in which the predictor variables are themselves highly correlated. The aim of the study was to investigate the impact of multicollinearity on linear regression estimates. The study was guided by the following specific objectives, (i) to examined the asymptotic properties of estimators and (ii) to compared lasso, ridge, elastic net with ordinary least squares. The study employed Monte-carlo simulation to generate set of highly collinear and induced multicollinearity variables with sample sizes of 25, 50, 100, 150, 200, 250, 1000 as a source of data in this research work and the data was analyzed with lasso, ridge, elastic net and ordinary least squares using statistical package. The study findings revealed that absolute bias of ordinary least squares was consistent at all sample sizes as revealed by past researched on multicollinearity as well while lasso type estimators were fluctuate alternately. Also revealed that, mean square error of ridge regression was outperformed other estimators with minimum variance at small sample size and ordinary least squares was the best at large sample size. The study recommended that ols was asymptotically consistent at a specified sample sizes on this research work and ridge regression was efficient at small and moderate sample size.