arXiv subjects

Peter Zeidman

Publications and source records attributed to Peter Zeidman.

At least 19 recordsLinked to original sources

arXiv2025

Variational Representational Similarity Analysis (vRSA) for M/EEG

This paper introduces variational representational similarity analysis RSA (vRSA) for electromagnetic recordings of neural responses (e.g., EEG, MEG, ECoG or LFP). Variational RSA is a Bayesian approach for testing whether the similarity of stimuli or experimental conditions is expressed in univariate or multivariate neural recordings. Extending an approach previously introduced in the context of functional MRI, vRSA decomposes the condition-by-condition data covariance matrix into hypothesised effects and observation noise, thereby casting RSA as a covariance component estimation problem. In this context, peristimulus time may be treated as an experimental factor, enabling one to test for the probability that different experimental effects are expressed in data at different times. Variational Bayesian methods are used for model estimation and model comparison, which confer a number of advantages over classical approaches, including statistically efficient hypothesis testing, quantification of uncertainty using Bayesian credible intervals and computational efficiency. After introducing the theory, we provide a worked example using openly available EEG data. Software functions implementing vRSA for the SPM software package accompany this paper, together with exemplar analysis scripts.

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arXiv2025

SPM 25: open source neuroimaging analysis software

Statistical Parametric Mapping (SPM) is an integrated set of methods for testing hypotheses about the brain's structure and function, using data from imaging devices. These methods are implemented in an open source software package, SPM, which has been in continuous development for more than 30 years by an international community of developers. This paper reports the release of SPM 25.01, a major new version of the software that incorporates novel analysis methods, optimisations of existing methods, as well as improved practices for open science and software development.

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arXiv2024

Dynamic Causal Models of Time-Varying Connectivity

This paper introduces a novel approach for modelling time-varying connectivity in neuroimaging data, focusing on the slow fluctuations in synaptic efficacy that mediate neuronal dynamics. Building on the framework of Dynamic Causal Modelling (DCM), we propose a method that incorporates temporal basis functions into neural models, allowing for the explicit representation of slow parameter changes. This approach balances expressivity and computational efficiency by modelling these fluctuations as a Gaussian process, offering a middle ground between existing methods that either strongly constrain or excessively relax parameter fluctuations. We validate the ensuing model through simulations and real data from an auditory roving oddball paradigm, demonstrating its potential to explain key aspects of brain dynamics. This work aims to equip researchers with a robust tool for investigating time-varying connectivity, particularly in the context of synaptic modulation and its role in both healthy and pathological brain function.

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arXiv2024

BSD: a Bayesian framework for parametric models of neural spectra

The analysis of neural power spectra plays a crucial role in understanding brain function and dysfunction. While recent efforts have led to the development of methods for decomposing spectral data, challenges remain in performing statistical analysis and group-level comparisons. Here, we introduce Bayesian Spectral Decomposition (BSD), a Bayesian framework for analysing neural spectral power. BSD allows for the specification, inversion, comparison, and analysis of parametric models of neural spectra, addressing limitations of existing methods. We first establish the face validity of BSD on simulated data and show how it outperforms an established method (\fooof{}) for peak detection on artificial spectral data. We then demonstrate the efficacy of BSD on a group-level study of EEG spectra in 204 healthy subjects from the LEMON dataset. Our results not only highlight the effectiveness of BSD in model selection and parameter estimation, but also illustrate how BSD enables straightforward group-level regression of the effect of continuous covariates such as age. By using Bayesian inference techniques, BSD provides a robust framework for studying neural spectral data and their relationship to brain function and dysfunction.

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arXiv2023

Linking fast and slow: the case for generative models

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multi-scale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

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arXiv2020

Dynamic causal modelling of immune heterogeneity

An interesting inference drawn by some Covid-19 epidemiological models is that there exists a proportion of the population who are not susceptible to infection -- even at the start of the current pandemic. This paper introduces a model of the immune response to a virus. This is based upon the same sort of mean-field dynamics as used in epidemiology. However, in place of the location, clinical status, and other attributes of people in an epidemiological model, we consider the state of a virus, B and T-lymphocytes, and the antibodies they generate. Our aim is to formalise some key hypotheses as to the mechanism of resistance. We present a series of simple simulations illustrating changes to the dynamics of the immune response under these hypotheses. These include attenuated viral cell entry, pre-existing cross-reactive humoral (antibody-mediated) immunity, and enhanced T-cell dependent immunity. Finally, we illustrate the potential application of this sort of model by illustrating variational inversion (using simulated data) of this model to illustrate its use in testing hypotheses. In principle, this furnishes a fast and efficient immunological assay--based on sequential serology--that provides a (i) quantitative measure of latent immunological responses and (ii) a Bayes optimal classification of the different kinds of immunological response (c.f., glucose tolerance tests used to test for insulin resistance). This may be especially useful in assessing SARS-CoV-2 vaccines.

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arXiv2020

Parametric dynamic causal modelling

This technical note introduces parametric dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity.

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arXiv2020

Effective immunity and second waves: a dynamic causal modelling study

This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak; namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that speaks to both the consequences of relaxing lockdown and the propensity for a second wave of infections. Using a dynamic causal model of reported cases and deaths from multiple countries, we evaluated the evidence models of progressively longer periods of immunity. The results speak to an effective population immunity of about three months that, under the model, defers any second wave for approximately six months in most countries. This may have implications for the window of opportunity for tracking and tracing, as well as for developing vaccination programmes, and other therapeutic interventions.

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arXiv2020

Tracking and tracing in the UK: a dynamic causal modelling study

By equipping a previously reported dynamic causal model of COVID-19 with an isolation state, we modelled the effects of self-isolation consequent on tracking and tracing. Specifically, we included a quarantine or isolation state occupied by people who believe they might be infected but are asymptomatic, and only leave if they test negative. We recovered maximum posteriori estimates of the model parameters using time series of new cases, daily deaths, and tests for the UK. These parameters were used to simulate the trajectory of the outbreak in the UK over an 18-month period. Several clear-cut conclusions emerged from these simulations. For example, under plausible (graded) relaxations of social distancing, a rebound of infections within weeks is unlikely. The emergence of a later second wave depends almost exclusively on the rate at which we lose immunity, inherited from the first wave. There exists no testing strategy that can attenuate mortality rates, other than by deferring or delaying a second wave. A sufficiently powerful tracking and tracing policy--implemented at the time of writing (10th May 2020)--will defer any second wave beyond a time horizon of 18 months. Crucially, this deferment is within current testing capabilities (requiring an efficacy of tracing and tracking of about 20% of asymptomatic infected cases, with less than 50,000 tests per day). These conclusions are based upon a dynamic causal model for which we provide some construct and face validation, using a comparative analysis of the United Kingdom and Germany, supplemented with recent serological studies.

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arXiv2020

Second waves, social distancing, and the spread of COVID-19 across America

We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several of these (epidemic) models to create a (pandemic) model of viral spread among regions. Our focus is on a second wave of new cases that may result from loss of immunity--and the exchange of people between regions--and how mortality rates can be ameliorated under different strategic responses. In particular, we consider hard or soft social distancing strategies predicated on national (Federal) or regional (State) estimates of the prevalence of infection in the population. The modelling is demonstrated using timeseries of new cases and deaths from the United States to estimate the parameters of a factorial (compartmental) epidemiological model of each State and, crucially, coupling between States. Using Bayesian model reduction, we identify the effective connectivity between States that best explains the initial phases of the outbreak in the United States. Using the ensuing posterior parameter estimates, we then evaluate the likely outcomes of different policies in terms of mortality, working days lost due to lockdown and demands upon critical care. The provisional results of this modelling suggest that social distancing and loss of immunity are the two key factors that underwrite a return to endemic equilibrium.

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arXiv2020

Dynamic causal modelling of COVID-19

This technical report describes a dynamic causal model of the spread of coronavirus through a population. The model is based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time. The purpose of this model is to quantify the uncertainty that attends predictions of relevant outcomes. By assuming suitable conditional dependencies, one can model the effects of interventions (e.g., social distancing) and differences among populations (e.g., herd immunity) to predict what might happen in different circumstances. Technically, this model leverages state-of-the-art variational (Bayesian) model inversion and comparison procedures, originally developed to characterise the responses of neuronal ensembles to perturbations. Here, this modelling is applied to epidemiological populations to illustrate the kind of inferences that are supported and how the model per se can be optimised given timeseries data. Although the purpose of this paper is to describe a modelling protocol, the results illustrate some interesting perspectives on the current pandemic; for example, the nonlinear effects of herd immunity that speak to a self-organised mitigation process.

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arXiv2019

Bayesian model reduction

This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in their priors. In the setting of variational Bayes this has an analytical solution, which finesses the problem of scoring large model spaces in model comparison or structure learning. In this technical note, we review Bayesian model reduction and provide the relevant equations for several discrete and continuous probability distributions. We provide worked examples in the context of multivariate linear regression, Gaussian mixture models and dynamical systems (dynamic causal modelling). These examples are accompanied by the Matlab scripts necessary to reproduce the results. Finally, we briefly review recent applications in the fields of neuroimaging and neuroscience. Specifically, we consider structure learning and hierarchical or empirical Bayes that can be regarded as a metaphor for neurobiological processes like abductive reasoning.

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arXiv2019

Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of (ie, hypotheses about) network architectures and implicit coupling functions in terms of their Bayesian model evidence. These methods are collectively referred to as dynamical casual modelling (DCM). We focus on a relatively new approach that is proving remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems.

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arXiv2019

Bayesian fusion and multimodal DCM for EEG and fMRI

This paper asks whether integrating multimodal EEG and fMRI data offers a better characterisation of functional brain architectures than either modality alone. This evaluation rests upon a dynamic causal model that generates both EEG and fMRI data from the same neuronal dynamics. We introduce the use of Bayesian fusion to provide informative (empirical) neuronal priors - derived from dynamic causal modelling (DCM) of EEG data - for subsequent DCM of fMRI data. To illustrate this procedure, we generated synthetic EEG and fMRI timeseries for a mismatch negativity (or auditory oddball) paradigm, using biologically plausible model parameters (i.e., posterior expectations from a DCM of empirical, open access, EEG data). Using model inversion, we found that Bayesian fusion provided a substantial improvement in marginal likelihood or model evidence, indicating a more efficient estimation of model parameters, in relation to inverting fMRI data alone. We quantified the benefits of multimodal fusion with the information gain pertaining to neuronal and haemodynamic parameters - as measured by the Kullback-Leibler divergence between their prior and posterior densities. Remarkably, this analysis suggested that EEG data can improve estimates of haemodynamic parameters; thereby furnishing proof-of-principle that Bayesian fusion of EEG and fMRI is necessary to resolve conditional dependencies between neuronal and haemodynamic estimators. These results suggest that Bayesian fusion may offer a useful approach that exploits the complementary temporal (EEG) and spatial (fMRI) precision of different data modalities. We envisage the procedure could be applied to any multimodal dataset that can be explained by a DCM with a common neuronal parameterisation.

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arXiv2019

Neurovascular coupling: insights from multi-modal dynamic causal modelling of fMRI and MEG

This technical note presents a framework for investigating the underlying mechanisms of neurovascular coupling in the human brain using multi-modal magnetoencephalography (MEG) and functional magnetic resonance (fMRI) neuroimaging data. This amounts to estimating the evidence for several biologically informed models of neurovascular coupling using variational Bayesian methods and selecting the most plausible explanation using Bayesian model comparison. First, fMRI data is used to localise active neuronal sources. The coordinates of neuronal sources are then used as priors in the specification of a DCM for MEG, in order to estimate the underlying generators of the electrophysiological responses. The ensuing estimates of neuronal parameters are used to generate neuronal drive functions, which model the pre or post synaptic responses to each experimental condition in the fMRI paradigm. These functions form the input to a model of neurovascular coupling, the parameters of which are estimated from the fMRI data. This establishes a Bayesian fusion technique that characterises the BOLD response - asking, for example, whether instantaneous or delayed pre or post synaptic signals mediate haemodynamic responses. Bayesian model comparison is used to identify the most plausible hypotheses about the causes of the multimodal data. We illustrate this procedure by comparing a set of models of a single-subject auditory fMRI and MEG dataset. Our exemplar analysis suggests that the origin of the BOLD signal is mediated instantaneously by intrinsic neuronal dynamics and that neurovascular coupling mechanisms are region-specific. The code and example dataset associated with this technical note are available through the statistical parametric mapping (SPM) software package.

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arXiv2019

A tutorial on group effective connectivity analysis, part 1: first level analysis with DCM for fMRI

Dynamic Causal Modelling (DCM) is the predominant method for inferring effective connectivity from neuroimaging data. In the 15 years since its introduction, the neural models and statistical routines in DCM have developed in parallel, driven by the needs of researchers in cognitive and clinical neuroscience. In this tutorial, we step through an exemplar fMRI analysis in detail, reviewing the current implementation of DCM and demonstrating recent developments in group-level connectivity analysis. In the first part of the tutorial (current paper), we focus on issues specific to DCM for fMRI, unpacking the relevant theory and highlighting practical considerations. In particular, we clarify the assumptions (i.e., priors) used in DCM for fMRI and how to interpret the model parameters. This tutorial is accompanied by all the necessary data and instructions to reproduce the analyses using the SPM software. In the second part (in a companion paper), we move from subject-level to group-level modelling using the Parametric Empirical Bayes framework, and illustrate how to test for commonalities and differences in effective connectivity across subjects, based on imaging data from any modality.

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arXiv2019

A tutorial on group effective connectivity analysis, part 2: second level analysis with PEB

This tutorial provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). This involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. We walk through this approach in detail, using data from a published fMRI experiment that characterised individual differences in hemispheric lateralization in a semantic processing task. The preliminary subject specific DCM analysis is covered in detail in a companion paper. This tutorial is accompanied by the example dataset and step-by-step instructions to reproduce the analyses.

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arXiv2018

Optimising data for modelling neuronal responses

In this technical note, we address an unresolved challenge in neuroimaging statistics: how to determine which of several datasets is the best for inferring neuronal responses. Comparisons of this kind are important for experimenters when choosing an imaging protocol - and for developers of new acquisition methods. However, the hypothesis that one dataset is better than another cannot be tested using conventional statistics (based on likelihood ratios), as these require the data to be the same under each hypothesis. Here we present Bayesian data comparison, a principled framework for evaluating the quality of functional imaging data, in terms of the precision with which neuronal connectivity parameters can be estimated and competing models can be disambiguated. For each of several candidate datasets, neuronal responses are inferred using Dynamic Casual Modelling (DCM) - a commonly used Bayesian procedure for modelling neuroimaging data. Next, the parameters from subject-specific models are summarised at the group level using a Bayesian General Linear Model (GLM). A series of measures, which we introduce here, are then used to evaluate each dataset in terms of the precision of (group-level) parameter estimates and the ability of the data to distinguish similar models. To exemplify the approach, we compared four datasets that were acquired in a study evaluating multiband fMRI acquisition schemes. To enable people to reproduce these analyses using their own data and experimental paradigms, we provide general-purpose Matlab code via the SPM software.

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