Bayesian model selection with fractional Brownian motion

Krog, Jens; Jacobsen, Lars Hervig; Lund, Frederik Wendelboe; Wüstner, Daniel; Lomholt, Michael A.

doi:10.1088/1742-5468/aadb0e

Cited by 30 publications

(47 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Methods were classified based on the type of approach (as machine learning (ML), or classical statistics (Stat)); their input data (as raw/lightly preprocessed trajectories (Traj), or features (Feat)); and their training procedure (as length-specific ( L -specific, Yes), or not (No)). Label Team name Method Class Input Tasks L -specific A Anomalous Unicorns Ensemble of CNN and RNN 45 , 76 ML Traj T1(1D), T2(1D) No B BIT Bayesian inference 77 , 78 Stat Traj All No C DecBayComp Graph neural networks 79 ML Traj + Feat T1, T2(1D, 2D) No D DeepSPT ResNet + XGBoost 80 , 81 ML Traj + Feat T1(1D), T2(1D) No E eduN RNN + Dense NN 82 ML Traj All Yes F Erasmus MC bi-LSTM + Dense NN 31 ML Feat T1, T2 Yes G HNU LSTM 83 ML Traj T1 Yes H NOA CNN + bi-LSTM 84 ML Traj T1(1D) No I QUBI ELM 85 ML Feat T1(1D), T2(1D) …”

Section: Resultsmentioning

confidence: 99%

Objective comparison of methods to decode anomalous diffusion

et al. 2021

View full text Add to dashboard Cite

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

show abstract

Section: Resultsmentioning

confidence: 99%

Objective comparison of methods to decode anomalous diffusion

et al. 2021

View full text Add to dashboard Cite

show abstract

“…For the case of fractional Brownian motion, techniques to infer both the anomalous diffusion coefficient (α) and the generalized diffusion coefficient (D α ) have been proposed. The former approach [71] takes into account noise (localization error) and drift, and uses Bayesian inference. The latter [72] relies on squared displacements and uses least squares to estimate D α .…”

Section: Inferring Anomalous Diffusionmentioning

confidence: 99%

Anomalous Subdiffusion in Living Cells: Bridging the Gap Between Experiments and Realistic Models Through Collaborative Challenges

et al. 2020

View full text Add to dashboard Cite

The life of a cell is governed by highly dynamical microscopic processes. Two notable examples are the diffusion of membrane receptors and the kinetics of transcription factors governing the rates of gene expression. Different fluorescence imaging techniques have emerged to study molecular dynamics. Among them, fluorescence correlation spectroscopy (FCS) and singleparticle tracking (SPT) have proven to be instrumental to our understanding of cell dynamics and function. The analysis of SPT and FCS is an ongoing effort, and despite decades of work, much progress remains to be done. In this paper, we give a quick overview of the existing techniques used to analyze anomalous diffusion in cells and propose a collaborative challenge to foster the development of state-of-the-art analysis algorithms. We propose to provide labelled (training) and unlabelled (evaluation) simulated data to competitors all over the world in an open and fair challenge. The goal is to offer unified data benchmarks based on biologically-relevant metrics in order to compare the diffusion analysis software available for the community. Diffusion in cells | continuous-time random walks | fractional Brownian Motion | fluorescence correlation spectroscopy | single-particle tracking.

show abstract

“…We have demonstrated that hierarchical copulas offer a straightforward method in the study of meta-analysis of diagnostic tests, where the accuracy of the tests depends on thresholds, while also taking into account the stochastic relationship of sensitivity and specificity [47,48].…”

Section: Conclusion and Remarksmentioning

confidence: 99%

Hierarchical Modeling for Diagnostic Test Accuracy Using Multivariate Probability Distribution Functions

et al. 2021

View full text Add to dashboard Cite

Models implemented in statistical software for the precision analysis of diagnostic tests include random-effects modeling (bivariate model) and hierarchical regression (hierarchical summary receiver operating characteristic). However, these models do not provide an overall mean, but calculate the mean of a central study when the random effect is equal to zero; hence, it is difficult to calculate the covariance between sensitivity and specificity when the number of studies in the meta-analysis is small. Furthermore, the estimation of the correlation between specificity and sensitivity is affected by the number of studies included in the meta-analysis, or the variability among the analyzed studies. To model the relationship of diagnostic test results, a binary covariance matrix is assumed. Here we used copulas as an alternative to capture the dependence between sensitivity and specificity. The posterior values were estimated using methods that consider sampling algorithms from a probability distribution (Markov chain Monte Carlo), and estimates were compared with the results of the bivariate model, which assumes statistical independence in the test results. To illustrate the applicability of the models and their respective comparisons, data from 14 published studies reporting estimates of the accuracy of the Alcohol Use Disorder Identification Test were used. Using simulations, we investigated the performance of four copula models that incorporate scenarios designed to replicate realistic situations for meta-analyses of diagnostic accuracy of the tests. The models’ performances were evaluated based on p-values using the Cramér–von Mises goodness-of-fit test. Our results indicated that copula models are valid when the assumptions of the bivariate model are not fulfilled.

show abstract

Bayesian model selection with fractional Brownian motion

Cited by 30 publications

References 38 publications

Objective comparison of methods to decode anomalous diffusion

Objective comparison of methods to decode anomalous diffusion

Anomalous Subdiffusion in Living Cells: Bridging the Gap Between Experiments and Realistic Models Through Collaborative Challenges

Hierarchical Modeling for Diagnostic Test Accuracy Using Multivariate Probability Distribution Functions

Contact Info

Product

Resources

About