A deep learning method for comparing Bayesian hierarchical models.

Bayesian model comparison (BMC) offers a principled approach to assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then showcase our method by comparing four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. Additionally, we demonstrate how transfer learning can be leveraged to enhance training efficiency. We provide reproducible code for all analyses and an open-source implementation of our method. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Effects of Transcranial Direct Current Stimulation on Social Attention Patterns and Emotion Recognition Ability in Male Adolescents with Autism Spectrum Disorder.

Autism Spectrum Disorder (ASD) is characterized by impairments in social cognition including emotion recognition (ER) abilities. Common symptoms include unusual patterns of visual social attention, which are investigated as early developmental biomarkers for ASD. Transcranial Direct Current Stimulation (tDCS) has shown promising results in influencing social functioning in individuals with ASD. However, the effects of tDCS on social attention patterns and ER ability in adolescents with ASD remain unclear. This double-blind, sham-controlled, randomized clinical trial examined the effects of repeated sessions of tDCS on gaze behavior and ER ability in 22 male adolescents diagnosed with ASD. Participants received either 20 min of 2 mA active tDCS or sham stimulation for 10 days and an intra-stimulation training. Social allocation patterns were assessed using eye-tracking paradigms, including ER tasks. Our results indicated no tDCS-specific effects. Both groups showed improvements in ER and more frequent, faster, and longer fixations on the eyes than the mouth, and on social than nonsocial areas. In tasks with low social content, fixating the mouth seemed to increase ER accuracy. Understanding the effects of tDCS on social functioning in adolescents with ASD holds promise for the development of targeted interventions to improve their social cognition abilities.

Neural superstatistics for Bayesian estimation of dynamic cognitive models.

Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension and estimate the resulting dynamics from a superstatistics perspective. Such a model entails a hierarchy between a low-level observation model and a high-level transition model. The observation model describes the local behavior of a system, and the transition model specifies how the parameters of the observation model evolve over time. To overcome the estimation challenges resulting from the complexity of superstatistical models, we develop and validate a simulation-based deep learning method for Bayesian inference, which can recover both time-varying and time-invariant parameters. We first benchmark our method against two existing frameworks capable of estimating time-varying parameters. We then apply our method to fit a dynamic version of the diffusion decision model to long time series of human response times data. Our results show that the deep learning approach is very efficient in capturing the temporal dynamics of the model. Furthermore, we show that the erroneous assumption of static or homogeneous parameters will hide important temporal information.

Age-Related Differences in Decision-Making: Evidence Accumulation is More Gradual in Older Age.

Older adults tend to exhibit longer response times than younger adults in choice tasks across cognitive domains, such as perception, attention, and memory. The diffusion model has emerged as a standard model for analyzing age differences in choice behavior. Applications of the diffusion model to choice data from younger and older adults indicate that age-related slowing is driven by a more cautious response style and slower non-decisional processes, rather than by age differences in the rate of information accumulation. The Lévy flight model, a new evidence accumulation model that extends the diffusion model, was recently developed to account for differences in response times for correct and error responses. In the Lévy flight model, larger jumps in evidence accumulation can be accommodated compared to the diffusion model. It is currently unknown whether younger and older adults differ with respect to the jumpiness of evidence accumulation. In the current study, younger and older adults (N = 40 per age group) completed a letter-number-discrimination task. Results indicate that older adults show a more gradual (less "jumpy") pattern of evidence accumulation compared to younger adults. Implications for research on cognitive aging are discussed.

Amortized Bayesian Model Comparison With Evidential Deep Learning.

Comparing competing mathematical models of complex processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for guiding decisions. However, many interesting models are intractable with standard Bayesian methods, as they lack a closed-form likelihood function or the likelihood is computationally too expensive to evaluate. In this work, we propose a novel method for performing Bayesian model comparison using specialized deep learning architectures. Our method is purely simulation-based and circumvents the step of explicitly fitting all alternative models under consideration to each observed dataset. Moreover, it requires no hand-crafted summary statistics of the data and is designed to amortize the cost of simulation over multiple models, datasets, and dataset sizes. This makes the method especially effective in scenarios where model fit needs to be assessed for a large number of datasets, so that case-based inference is practically infeasible. Finally, we propose a novel way to measure epistemic uncertainty in model comparison problems. We demonstrate the utility of our method on toy examples and simulated data from nontrivial models from cognitive science and single-cell neuroscience. We show that our method achieves excellent results in terms of accuracy, calibration, and efficiency across the examples considered in this work. We argue that our framework can enhance and enrich model-based analysis and inference in many fields dealing with computational models of natural processes. We further argue that the proposed measure of epistemic uncertainty provides a unique proxy to quantify absolute evidence even in a framework which assumes that the true data-generating model is within a finite set of candidate models.

Evaluation of Neurofeedback Learning in Patients with ADHD: A Systematic Review.

NFB has a clear potential as a recognised treatment option for ADHD, but suffers from a lack of clarity about its efficacy, still unresolved after multiple controlled trials. Comparing learners and non-learners based on the evolution of patient-level indicators during the trial serves as a 'natural' control, and can help elucidate the mechanisms of NFB. We present a systematic review motivated by the need to establish the state of the art of patient learning during NFB treatment in current clinical literature. One particularly striking question we would like to answer here is whether existing NFB papers study learning variability, since only individual performance differences can give us information about mechanisms of learning. The results show that very few clinical trial reports have dealt with the heterogeneity of NFB learning, nor analysed whether NFB efficacy is dependent on NFB learning, even though NFB is believed to be a treatment based on learning to perform. In this systematic review we examine not only what has been reported, but also provide a critical analysis of possible flaws or gaps in existing studies, and discuss why no generalized conclusions about NFB efficacy have yet been made. Future research should focus on finding reliable ways of identifying the performers and studying participants' individual learning trajectories as it might enhance prognosis and the allocation of clinical resources.

Impulsivity Moderates the Effect of Neurofeedback Training on the Contingent Negative Variation in Autism Spectrum Disorder.

Background: The contingent negative variation (CNV) is a well-studied indicator of attention- and expectancy-related processes in the human brain. An abnormal CNV amplitude has been found in diverse neurodevelopmental psychiatric disorders. However, its role as a potential biomarker of successful clinical interventions in autism spectrum disorder (ASD) remains unclear. Methods: In this randomized controlled trial, we investigated how the CNV changes following an intensive neurofeedback training. Therefore, twenty-one adolescents with ASD underwent 24 sessions of slow cortical potential (SCP) neurofeedback training. Twenty additional adolescents with ASD formed a control group and received treatment as usual. CNV waveforms were obtained from a continuous performance test (CPT), which all adolescents performed before and after the corresponding 3-month long training period. In order to utilize all available neural time series, trial-based area under the curve values for all four electroencephalogram (EEG) channels were analyzed with a hierarchical Bayesian model. In addition, the model included impulsivity, inattention, and hyperactivity as potential moderators of change in CNV. Results: Our model implies that impulsivity moderates the effects of neurofeedback training on CNV depending on group. In the control group, the average CNV amplitude decreased or did not change after treatment as usual. In the experimental group, the CNV changed depending on the severity of comorbid impulsivity symptoms. The average CNV amplitude of participants with low impulsivity scores decreased markedly, whereas the average CNV amplitude of participants with high impulsivity increased. Conclusion: The degree of impulsivity seems to play a crucial role in the changeability of the CNV following an intensive neurofeedback training. Therefore, comorbid symptomatology should be recorded and analyzed in future EEG-based brain training interventions. Clinical Trial Registration: https://www.drks.de, identifier DRKS00012339.

Mental speed is high until age 60 as revealed by analysis of over a million participants.

Response speeds in simple decision-making tasks begin to decline from early and middle adulthood. However, response times are not pure measures of mental speed but instead represent the sum of multiple processes. Here we apply a Bayesian diffusion model to extract interpretable cognitive components from raw response time data. We apply our model to cross-sectional data from 1.2 million participants to examine age differences in cognitive parameters. To efficiently parse this large dataset, we apply a Bayesian inference method for efficient parameter estimation using specialized neural networks. Our results indicate that response time slowing begins as early as age 20, but this slowing was attributable to increases in decision caution and to slower non-decisional processes, rather than to differences in mental speed. Slowing of mental speed was observed only after approximately age 60. Our research thus challenges widespread beliefs about the relationship between age and mental speed.

BayesFlow: Learning Complex Stochastic Models With Invertible Neural Networks.

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit likelihood function is not available. With this work, we propose a novel method for globally amortized Bayesian inference based on invertible neural networks that we call BayesFlow. The method uses simulations to learn a global estimator for the probabilistic mapping from observed data to underlying model parameters. A neural network pretrained in this way can then, without additional training or optimization, infer full posteriors on arbitrarily many real data sets involving the same model family. In addition, our method incorporates a summary network trained to embed the observed data into maximally informative summary statistics. Learning summary statistics from data makes the method applicable to modeling scenarios where standard inference techniques with handcrafted summary statistics fail. We demonstrate the utility of BayesFlow on challenging intractable models from population dynamics, epidemiology, cognitive science, and ecology. We argue that BayesFlow provides a general framework for building amortized Bayesian parameter estimation machines for any forward model from which data can be simulated.

OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany.

Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and interventional measures during an ongoing outbreak. However, reliably inferring the epidemical dynamics by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address this problem with a novel combination of epidemiological modeling with specialized neural networks. Our approach entails two computational phases: In an initial training phase, a mathematical model describing the epidemic is used as a coach for a neural network, which acquires global knowledge about the full range of possible disease dynamics. In the subsequent inference phase, the trained neural network processes the observed data of an actual outbreak and infers the parameters of the model in order to realistically reproduce the observed dynamics and reliably predict future progression. With its flexible framework, our simulation-based approach is applicable to a variety of epidemiological models. Moreover, since our method is fully Bayesian, it is designed to incorporate all available prior knowledge about plausible parameter values and returns complete joint posterior distributions over these parameters. Application of our method to the early Covid-19 outbreak phase in Germany demonstrates that we are able to obtain reliable probabilistic estimates for important disease characteristics, such as generation time, fraction of undetected infections, likelihood of transmission before symptom onset, and reporting delays using a very moderate amount of real-world observations.

Repeated Sessions of Transcranial Direct Current Stimulation on Adolescents With Autism Spectrum Disorder: Study Protocol for a Randomized, Double-Blind, and Sham-Controlled Clinical Trial.

Background: Social-emotional difficulties are a core symptom of autism spectrum disorder (ASD). Accordingly, individuals with ASD have problems with social cognition such as recognizing emotions from other peoples' faces. Various results from functional magnetic resonance imaging and electroencephalography studies as well as eye-tracking data reveal a neurophysiological basis of these deficits by linking them to abnormal brain activity. Thus, an intervention targeting the neural origin of ASD impairments seems warranted. A safe method able to influence neural activity is transcranial direct current stimulation (tDCS). This non-invasive brain stimulation method has already demonstrated promising results in several neuropsychiatric disorders in adults and children. The aim of this project is to investigate the effects of tDCS on ASD symptoms and their neural correlates in children and adolescents with ASD. Method: This study is designed as a double-blind, randomized, and sham-controlled trial with a target sample size of 20 male participants (aged 12-17 years) diagnosed with ASD. Before randomization, the participants will be stratified into comorbid depression, comorbid ADHS/conduct disorder, or no-comorbidity groups. The intervention phase comprises 10 sessions of anodal or sham tDCS applied over the left prefrontal cortex within 2 consecutive weeks. To engage the targeted brain regions, participants will perform a social cognition training during the stimulation. TDCS-induced effects on ASD symptoms and involved neural circuits will be investigated through psychological, neurophysiological, imaging, and behavioral data at pre- and post-measurements. Tolerability will be evaluated using a standardized questionnaire. Follow-up assessments 1 and 6 months after the intervention will examine long-lasting effects. Discussion: The results of this study will provide insights into the changeability of social impairments in ASD by investigating social and emotional abilities on different modalities following repeated sessions of anodal tDCS with an intra-simulation training. Furthermore, this trial will elucidate the tolerability and the potential of tDCS as a new treatment approach for ASD in adolescents. Clinical Trial Registration: The study is ongoing and has been registered in the German Registry of Clinical Trials (DRKS00017505) on 02/07/2019.

Stability and Change in Diffusion Model Parameters over Two Years.

In recent years, mathematical models of decision making, such as the diffusion model, have been endorsed in individual differences research. These models can disentangle different components of the decision process, like processing speed, speed-accuracy trade-offs, and duration of non-decisional processes. The diffusion model estimates individual parameters of cognitive process components, thus allowing the study of individual differences. These parameters are often assumed to show trait-like properties, that is, within-person stability across tasks and time. However, the assumption of temporal stability has so far been insufficiently investigated. With this work, we explore stability and change in diffusion model parameters by following over 270 participants across a time period of two years. We analysed four different aspects of stability and change: rank-order stability, mean-level change, individual differences in change, and profile stability. Diffusion model parameters showed strong rank-order stability and mean-level changes in processing speed and speed-accuracy trade-offs that could be attributed to practice effects. At the same time, people differed little in these patterns across time. In addition, profiles of individual diffusion model parameters proved to be stable over time. We discuss implications of these findings for the use of the diffusion model in individual differences research.

Balancing the brain of offenders with psychopathy? Resting state EEG and electrodermal activity after a pilot study of brain self-regulation training.

Although investigation of the brains of criminals began quite early in the history of psychophysiological research, little is known about brain plasticity of offenders with psychopathy. Building on our preliminary study reporting successful brain self-regulation using slow cortical potential (SCP) neurofeedback in offenders with psychopathy, we investigated the central nervous and autonomic peripheral changes occurring after brain self-regulation in a group of severe male offenders with psychopathy. Regarding the central nervous system, an overall suppression of the psychopathic overrepresentation of slow frequency bands was found, such as delta and theta band activity, after EEG neurofeedback. In addition, an increase in alpha band activity could be observed after the SCP self-regulation training. Electrodermal activity adaptively changed according to the regulation task, and this flexibility improved over training time. The results of this study point towards a constructive learning process and plasticity in neural and peripheral measures of offenders with psychopathy.

Gamma Band Oscillations Reflect Sensory and Affective Dimensions of Pain.

Pain is a multidimensional process, which can be modulated by emotions; however, the mechanisms underlying this modulation are unknown. We used pictures with different emotional valence (negative, positive, and neutral) as primes and applied electrical painful stimuli as targets to healthy participants. We assessed pain intensity and unpleasantness ratings and recorded electroencephalograms (EEGs). We found that pain unpleasantness and not pain intensity ratings were modulated by emotion, with increased ratings for negative and decreased ratings for positive pictures. We also found two consecutive gamma band oscillations (GBOs) related to pain processing from time frequency analyses of the EEG signals. The early GBO had a cortical distribution contralateral to the painful stimulus and its amplitude was positively correlated with intensity and unpleasantness ratings, but not with prime valence. The late GBO had a centroparietal distribution and its amplitude was larger for negative compared to neutral and positive pictures. The emotional modulation effect (negative vs. positive) of the late GBO amplitude was positively correlated with pain unpleasantness. The early GBO might reflect the overall pain perception, possibly involving the thalamocortical circuit, while the late GBO might be related to the affective dimension of pain and top-down-related processes.

A Bayesian brain model of adaptive behavior: an application to the Wisconsin Card Sorting Task.

Adaptive behavior emerges through a dynamic interaction between cognitive agents and changing environmental demands. The investigation of information processing underlying adaptive behavior relies on controlled experimental settings in which individuals are asked to accomplish demanding tasks whereby a hidden regularity or an abstract rule has to be learned dynamically. Although performance in such tasks is considered as a proxy for measuring high-level cognitive processes, the standard approach consists in summarizing observed response patterns by simple heuristic scoring measures. With this work, we propose and validate a new computational Bayesian model accounting for individual performance in the Wisconsin Card Sorting Test (WCST), a renowned clinical tool to measure set-shifting and deficient inhibitory processes on the basis of environmental feedback. We formalize the interaction between the task's structure, the received feedback, and the agent's behavior by building a model of the information processing mechanisms used to infer the hidden rules of the task environment. Furthermore, we embed the new model within the mathematical framework of the Bayesian Brain Theory (BBT), according to which beliefs about hidden environmental states are dynamically updated following the logic of Bayesian inference. Our computational model maps distinct cognitive processes into separable, neurobiologically plausible, information-theoretic constructs underlying observed response patterns. We assess model identification and expressiveness in accounting for meaningful human performance through extensive simulation studies. We then validate the model on real behavioral data in order to highlight the utility of the proposed model in recovering cognitive dynamics at an individual level. We highlight the potentials of our model in decomposing adaptive behavior in the WCST into several information-theoretic metrics revealing the trial-by-trial unfolding of information processing by focusing on two exemplary individuals whose behavior is examined in depth. Finally, we focus on the theoretical implications of our computational model by discussing the mapping between BBT constructs and functional neuroanatomical correlates of task performance. We further discuss the empirical benefit of recovering the assumed dynamics of information processing for both clinical and research practices, such as neurological assessment and model-based neuroscience.

Towards end-to-end likelihood-free inference with convolutional neural networks.

Complex simulator-based models with non-standard sampling distributions require sophisticated design choices for reliable approximate parameter inference. We introduce a fast, end-to-end approach for approximate Bayesian computation (ABC) based on fully convolutional neural networks. The method enables users of ABC to derive simultaneously the posterior mean and variance of multidimensional posterior distributions directly from raw simulated data. Once trained on simulated data, the convolutional neural network is able to map real data samples of variable size to the first two posterior moments of the relevant parameter's distributions. Thus, in contrast to other machine learning approaches to ABC, our approach allows us to generate reusable models that can be applied by different researchers employing the same model. We verify the utility of our method on two common statistical models (i.e., a multivariate normal distribution and a multiple regression scenario), for which the posterior parameter distributions can be derived analytically. We then apply our method to recover the parameters of the leaky competing accumulator (LCA) model and we reference our results to the current state-of-the-art technique, which is the probability density estimation (PDA). Results show that our method exhibits a lower approximation error compared with other machine learning approaches to ABC. It also performs similarly to PDA in recovering the parameters of the LCA model.

ABrox-A user-friendly Python module for approximate Bayesian computation with a focus on model comparison.

We give an overview of the basic principles of approximate Bayesian computation (ABC), a class of stochastic methods that enable flexible and likelihood-free model comparison and parameter estimation. Our new open-source software called ABrox is used to illustrate ABC for model comparison on two prominent statistical tests, the two-sample t-test and the Levene-Test. We further highlight the flexibility of ABC compared to classical Bayesian hypothesis testing by computing an approximate Bayes factor for two multinomial processing tree models. Last but not least, throughout the paper, we introduce ABrox using the accompanied graphical user interface.

Physical-optics approximation of near-critical-angle scattering by spheroidal bubbles.

A first-order approximation is derived for the near-critical-angle scattering of a large spheroidal bubble illuminated by a plane wave propagating along the bubble axis of symmetry. The intensity of the far-field scattering pattern is expressed as a function of the relative refractive index and the two radii of curvature of the spheroidal bubble at the critical impact point.

Superimposed noninterfering probes to extend the capabilities of phase Doppler anemometry.

We propose using multiple superimposed noninterfering probes (SNIPs) of the same wavelength but different beam angles to extend the capabilities of phase Doppler anemometry. When a particle is moving in a SNIP the Doppler signals that are produced exhibit multiple Doppler frequencies and phase shifts. The resolution of the measurements of particle size (i.e., by fringe spacing and Doppler frequency) increases with beam angle. Then, with the solution proposed, even with only two detectors several measurements of size can be obtained for the same particle with increasing resolution if we consider higher frequencies in the signal. Several optical solutions to produce SNIPs as well as a signal-processing algorithm to treat the multiple-frequency Doppler signals are proposed. Experimental validations of the sizing of spherical and cylindrical particles demonstrate the applicability of this technique for particle measurement. We believe that this new technique can be of great interest when high resolution of size, velocity, and even refractive index is required.