Bayesian Statistics seminars

Song learning requires birds to interpret sensory evidence, assign credit to changes in behaviour, and reproduce remembered vocal targets. This lecture compares auditory-feedback adaptation, reinforcement learning and imitation as parts of a possible common learning architecture. Incomplete compensation for pitch-shifted feedback is examined through Bayesian causal inference: internal pitch predictions are combined with auditory evidence while feedback unlikely to be self-generated is discounted. Nonlinear pitch trajectories during conditioning motivate an extension of classical policy-gradient learning. The model separates an exploratory component updated by reward from other components of motor output that need not be updated on each trial. For imitation, vocal syllables can be learned separately from their order. An intrinsic reward based on a sum–max rule combines each target syllable’s best pitch match, with a light-tailed similarity function limiting the contribution of large mismatches. The lecture then considers how these complementary mechanisms might form a unified, testable account of birdsong learning, including initial attempts to use AI to develop the synthesis.

Raymundo Arróyave discusses alloy discovery guided by both metallurgical knowledge and Bayesian optimization. The approach combines physical models, high-throughput CALPHAD calculations, microstructural information and experimental feedback to search chemical and processing spaces that are difficult to explore through data alone. Examples involving high-entropy and refractory alloys address multiple objectives and constraints, including feasibility, correlated properties, uncertainty and microstructural sensitivity. The seminar then connects these decision methods to the Autonomous Robotic Metallurgist under development at his university. This platform links modular synthesis, characterization and testing with digital twins, human–robot collaboration and AI agents. The aim is a closed experimental loop in which scientific judgment and physical understanding guide automated execution.

NOAA's Mussel Watch records are examined as a unified framework for coastal contamination. The study combines sediment chemistry, toxicity, benthic condition and tissue measurements, using AMBI and M-AMBI scores at 732 national assessment sites and 33 Hudson–Raritan stations. Random-forest and Bayesian models associate urbanization with benthic condition in the New York region (ρ=0.62), but not nationally (ρ=0.05). A Delft3D estuary model reproduces observed tides and predicts increased deep-channel bed shear under sea-level rise. The work asks whether sediment contaminants mediate urbanization impacts and whether legacy cleanup remains effective as sea level changes. It was conducted through a NOAA NERTO graduate internship with Kimani Kimbrough and Erik Davenport at NCCOS.

Beth Gardner introduces spatial capture-recapture models for estimating wildlife population dynamics and movement. The seminar considers observations from camera traps and genetic identification using hair or scat, showing how the modeling framework can accommodate different sampling methods, time scales and movement processes. Gardner develops the Bayesian formulation through worked examples in R with NIMBLE, then discusses extensions and audience questions. The methods support estimates of demographic rates, spatial distributions and habitat relationships for conservation and management. The organizer explicitly schedules this occurrence at 15:00 Eastern time, rather than the series’ usual time.

Quantum versions of Bayesian updating should reproduce classical behaviour while respecting genuinely quantum transformations. This talk reviews existing proposals, then examines repeated-evidence limits and updating beliefs about transformations themselves. The Petz recovery map and Leifer–Spekkens conditional states supply these structures and connect the second kind of update to Schrödinger bridges in optimal transport.

Regional-scale (>500 km2) landslide risk reduction models often suffer from their reliance on difficult-to-obtain data, such as inventories of past landslide locations or geomechanical properties of the hillslopes. However, over regional scales, these data are often sparse, inconsistent, and nonrepresentative, which can lead to biased model outputs. In this talk, I will present two recent studies that help overcome these challenges. First, I will share a method of assessing shallow landslide susceptibility based on a morphometric analysis of the landscape’s topography. Despite having no knowledge of past landslide locations, the morphometric approach can better characterize landslide potential over contrasting data-driven models that are generally used for assessing regional-scale landslide susceptibility. Second, I will present a Bayesian statistical comparison of common metrics used to predict rainfall-triggered landsliding across disparate regions of the United States. I will show that parsimonious leaky-bucket models, whose only inputs are a drainage constant and estimates of precipitation, can better distinguish landslide-triggering rainfall from non-landslide-triggering rainfall compared to traditional rainfall metrics or more complex models. The leaky-bucket model had the best performance across vastly different environments within the United States, suggesting that it may be used universally to enhance regional-scale landslide risk reduction efforts.

Bayesian cognitive models incorporate prior knowledge explicitly but often impose restrictive assumptions, whereas neural networks are flexible but make such knowledge difficult to specify. Brenden Lake presents Behaviorally-Informed Meta-Learning, which distils Bayesian priors into Transformer networks before fine-tuning them on behavioural observations. This combination can model behaviour with little experimental data. Initial studies of human concept learning obtain better fits by capturing heuristics and biases that simple Bayesian models miss. The talk also examines the challenge of interpreting these hybrid models and understanding which learned mechanisms account for their predictions.

In our rapidly evolving digital world, there is increasing concern about the impact of digital technologies and social media on the mental health of young people. Policymakers and the public are nervous. Psychologists are facing mounting pressures to deliver evidence that can inform policies and practices to safeguard both young people and society at large. However, research progress is slow while technological change is accelerating.My talk will reflect on this, both as a question of psychological science and metascience. Digital companies have designed highly popular environments that differ in important ways from traditional offline spaces. By revisiting the foundations of psychology (e.g. development and cognition) and considering digital changes' impact on theories and findings, we gain deeper insights into questions such as the following. (1) How do digital environments exacerbate developmental vulnerabilities that predispose young people to mental health conditions? (2) How do digital designs interact with cognitive and learning processes, formalised through computational approaches such as reinforcement learning or Bayesian modelling?However, we also need to face deeper questions about what it means to do science about new technologies and the challenge of keeping pace with technological advancements. Therefore, I discuss the concept of ‘fast science’, where, during crises, scientists might lower their standards of evidence to come to conclusions quicker. Might psychologists want to take this approach in the face of technological change and looming concerns? The talk concludes with a discussion of such strategies for 21st-century psychology research in the era of digitalization.

This webinar addressed computational perspectives on how animals and humans make decisions, spanning normative, descriptive, and mechanistic models. Sam Gershman (Harvard) presented a capacity-limited reinforcement learning framework in which policies are compressed under an information bottleneck constraint. This approach predicts pervasive perseveration, stimulus‐independent “default” actions, and trade-offs between complexity and reward. Such policy compression reconciles observed action stochasticity and response time patterns with an optimal balance between learning capacity and performance. Jonathan Pillow (Princeton) discussed flexible descriptive models for tracking time-varying policies in animals. He introduced dynamic Generalized Linear Models (Sidetrack) and hidden Markov models (GLM-HMMs) that capture day-to-day and trial-to-trial fluctuations in choice behavior, including abrupt switches between “engaged” and “disengaged” states. These models provide new insights into how animals’ strategies evolve under learning. Finally, Kenji Doya (OIST) highlighted the importance of unifying reinforcement learning with Bayesian inference, exploring how cortical-basal ganglia networks might implement model-based and model-free strategies. He also described Japan’s Brain/MINDS 2.0 and Digital Brain initiatives, aiming to integrate multimodal data and computational principles into cohesive “digital brains.”

Animals and humans rapidly adapt their behavior to dynamic environmental changes, such as predator threats or fluctuating food resources, often without immediate rewards. Existing literature posits that animals rely on internal representations of the environment, termed “beliefs”, for their decision policy. However, previous work ties belief updates to external reward signals, which does not explain adaptation in scenarios where trial-and-error approaches are inefficient or potentially perilous. In this work, we propose that the brain utilize dynamic representations that continuously infer the state of the environment, allowing it to update behavior rapidly. I will present a Bayesian theory for state inference in a partially observed Markov Decision Process with multiple interacting latent variables. Optimal behavior requires knowledge of hidden interactions between latent states. I will show that recurrent neural networks trained through reinforcement solve the task by learning the hidden interaction between latent states, and their activity encodes the dynamics of the optimal Bayesian estimators. The behavior of rodents trained on an identical task aligns with our theoretical model and neural network simulations, suggesting that the brain utilizes dynamic internal state representation and inference. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-01-31. Recording duration: 00:51:21.

In the current virtual journal club Dr Di Luca will present findings from a series of psychophysical investigations where he measured sensitivity and bias in the perception of the timing of stimuli. He will present how improved detection with longer sequences and biases in reporting isochrony can be accounted for by optimal statistical predictions. Among his findings was also that the timing of stimuli that occasionally deviate from a regularly paced sequence is perceptually distorted to appear more regular. Such change depends on whether the context these sequences are presented is also regular. Dr Di Luca will present a Bayesian model for the combination of dynamically updated expectations, in the form of a priori probability, with incoming sensory information. These findings contribute to the understanding of how the brain processes temporal information to shape perceptual experiences.

Psychology and neuroscience are increasingly looking to fine-grained analyses of decision-making behaviour, seeking to characterise not just the variation between subjects but also a subject's variability across time. When analysing the behaviour of each subject in a choice task, we ideally want to know not only when the subject has learnt the correct choice rule but also what the subject tried while learning. I introduce a simple but effective Bayesian approach to inferring the probability of different choice strategies at trial resolution. This can be used both for inferring when subjects learn, by tracking the probability of the strategy matching the target rule, and for inferring subjects use of exploratory strategies during learning. Applied to data from rodent and human decision tasks, we find learning occurs earlier and more often than estimated using classical approaches. Around both learning and changes in the rewarded rules the exploratory strategies of win-stay and lose-shift, often considered complementary, are consistently used independently. Indeed, we find the use of lose-shift is strong evidence that animals have latently learnt the salient features of a new rewarded rule. Our approach can be extended to any discrete choice strategy, and its low computational cost is ideally suited for real-time analysis and closed-loop control.

Over the past decade we have demonstrated that the fusion of subject-specific structural information of the human brain with mathematical dynamic models allows building biologically realistic brain network models, which have a predictive value, beyond the explanatory power of each approach independently. The network nodes hold neural population models, which are derived using mean field techniques from statistical physics expressing ensemble activity via collective variables. Our hybrid approach fuses data-driven with forward-modeling-based techniques and has been successfully applied to explain healthy brain function and clinical translation including aging, stroke and epilepsy. Here we illustrate the workflow along the example of epilepsy: we reconstruct personalized connectivity matrices of human epileptic patients using Diffusion Tensor weighted Imaging (DTI). Subsets of brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other healthy brain regions and propagate activity through large brain networks. The identification of the EZ is crucial for the success of neurosurgery and presents one of the historically difficult questions in clinical neuroscience. The application of latest techniques in Bayesian inference and model inversion, in particular Hamiltonian Monte Carlo, allows the estimation of the EZ, including estimates of confidence and diagnostics of performance of the inference. The example of epilepsy nicely underwrites the predictive value of personalized large-scale brain network models. The workflow of end-to-end modeling is an integral part of the European neuroinformatics platform EBRAINS and enables neuroscientists worldwide to build and estimate personalized virtual brains. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-12-06. Recording duration: 00:50:07.

Over the past decade we have demonstrated that the fusion of subject-specific structural information of the human brain with mathematical dynamic models allows building biologically realistic brain network models, which have a predictive value, beyond the explanatory power of each approach independently. The network nodes hold neural population models, which are derived using mean field techniques from statistical physics expressing ensemble activity via collective variables. Our hybrid approach fuses data-driven with forward-modeling-based techniques and has been successfully applied to explain healthy brain function and clinical translation including aging, stroke and epilepsy. Here we illustrate the workflow along the example of epilepsy: we reconstruct personalized connectivity matrices of human epileptic patients using Diffusion Tensor weighted Imaging (DTI). Subsets of brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other healthy brain regions and propagate activity through large brain networks. The identification of the EZ is crucial for the success of neurosurgery and presents one of the historically difficult questions in clinical neuroscience. The application of latest techniques in Bayesian inference and model inversion, in particular Hamiltonian Monte Carlo, allows the estimation of the EZ, including estimates of confidence and diagnostics of performance of the inference. The example of epilepsy nicely underwrites the predictive value of personalized large-scale brain network models. The workflow of end-to-end modeling is an integral part of the European neuroinformatics platform EBRAINS and enables neuroscientists worldwide to build and estimate personalized virtual brains.

Mobile organisms must be capable of deciding both where and when to move in order to keep up with a changing environment; therefore, a strong sense of time is necessary, otherwise, we would fail in many of our movement goals. Despite this intrinsic link between movement and timing, only recently has research begun to investigate the interaction. Two primary effects that have been observed include: movements biasing time estimates (i.e., affecting accuracy) as well as making time estimates more precise. The goal of this presentation is to review this literature, discuss a Bayesian cue combination framework to explain these effects, and discuss the experiments I have conducted to test the framework. The experiments herein include: a motor timing task comparing the effects of movement vs non-movement with and without feedback (Exp. 1A & 1B), a transcranial magnetic stimulation (TMS) study on the role of the supplementary motor area (SMA) in transforming temporal information (Exp. 2), and a perceptual timing task investigating the effect of noisy movement on time perception with both visual and auditory modalities (Exp. 3A & 3B). Together, the results of these studies support the Bayesian cue combination framework, in that: movement improves the precision of time perception not only in perceptual timing tasks but also motor timing tasks (Exp. 1A & 1B), stimulating the SMA appears to disrupt the transformation of temporal information (Exp. 2), and when movement becomes unreliable or noisy there is no longer an improvement in precision of time perception (Exp. 3A & 3B). Although there is support for the proposed framework, more studies (i.e., fMRI, TMS, EEG, etc.) need to be conducted in order to better understand where and how this may be instantiated in the brain; however, this work provides a starting point to better understanding the intrinsic connection between time and movement

Humans constantly make perceptual decisions on human faces and voices. These regularly come with the challenge of receiving only uncertain sensory evidence, resulting from noisy input and noisy neural processes. Efficiently adapting one’s internal decision system including prior expectations and subsequent metacognitive assessments to these challenges is crucial in everyday life. However, the exact decision mechanisms and whether these represent modifiable states remain unknown in the general population and clinical patients with psychosis. Using data from a laboratory-based sample of healthy controls and patients with psychosis as well as a complementary, large online sample of healthy controls, I will demonstrate how a combination of perceptual face and voice recognition decision fidelity, metacognitive ratings, and Bayesian computational modelling may be used as indicators to differentiate between non-clinical and clinical states in the future.

Efficient navigation requires animals to track their position, velocity and heading direction (HD). Some animals’ behavior suggests that they also track uncertainties about these navigational variables, and make strategic use of these uncertainties, in line with a Bayesian computation. Ring-attractor networks have been proposed to estimate and track these navigational variables, for instance in the HD system of the fruit fly Drosophila. However, such networks are not designed to incorporate a notion of uncertainty, and therefore seem unsuited to implement dynamic Bayesian inference. Here, we close this gap by showing that specifically tuned ring-attractor networks can track both a HD estimate and its associated uncertainty, thereby approximating a circular Kalman filter. We identified the network motifs required to integrate angular velocity observations, e.g., through self-initiated turns, and absolute HD observations, e.g., visual landmark inputs, according to their respective reliabilities, and show that these network motifs are present in the connectome of the Drosophila HD system. Specifically, our network encodes uncertainty in the amplitude of a localized bump of neural activity, thereby generalizing standard ring attractor models. In contrast to such standard attractors, however, proper Bayesian inference requires the network dynamics to operate in a regime away from the attractor state. More generally, we show that near-Bayesian integration is inherent in generic ring attractor networks, and that their amplitude dynamics can account for close-to-optimal reliability weighting of external evidence for a wide range of network parameters. This only holds, however, if their connection strengths allow the network to sufficiently deviate from the attractor state. Overall, our work offers a novel interpretation of ring attractor networks as implementing dynamic Bayesian integrators. We further provide a principled theoretical foundation for the suggestion that the Drosophila HD system may implement Bayesian HD tracking via ring attractor dynamics.

Fate decisions in developing tissues involve cells transitioning between a set of discrete cell states. Geometric models, often referred to as Waddington landscapes, are an appealing way to describe differentiation dynamics and developmental decisions. We consider the differentiation of neural and mesodermal cells from pluripotent mouse embryonic stem cells exposed to different combinations and durations of signalling factors. We developed a principled statistical approach using flow cytometry data to quantify differentiating cell states. Then, using a framework based on Catastrophe Theory and approximate Bayesian computation, we constructed the corresponding dynamical landscape. The result was a quantitative model that accurately predicted the proportions of neural and mesodermal cells differentiating in response to specific signalling regimes. Taken together, the approach we describe is broadly applicable for the quantitative analysis of differentiation dynamics and for determining the logic of developmental cell fate decisions.