A Conceptual Introduction to Bayesian Model Averaging Hinne, Max; Gronau, Quentin F.; van den Bergh, Don ...
Advances in methods and practices in psychological science,
06/2020, Letnik:
3, Številka:
2
Journal Article
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Many statistical scenarios initially involve several candidate models that describe the data-generating process. Analysis often proceeds by first selecting the best model according to some criterion ...and then learning about the parameters of this selected model. Crucially, however, in this approach the parameter estimates are conditioned on the selected model, and any uncertainty about the model-selection process is ignored. An alternative is to learn the parameters for all candidate models and then combine the estimates according to the posterior probabilities of the associated models. This approach is known as Bayesian model averaging (BMA). BMA has several important advantages over all-or-none selection methods, but has been used only sparingly in the social sciences. In this conceptual introduction, we explain the principles of BMA, describe its advantages over all-or-none model selection, and showcase its utility in three examples: analysis of covariance, meta-analysis, and network analysis.
Despite the increasing popularity of Bayesian inference in empirical research, few practical guidelines provide detailed recommendations for how to apply Bayesian procedures and interpret the ...results. Here we offer specific guidelines for four different stages of Bayesian statistical reasoning in a research setting:
planning
the analysis,
executing
the analysis,
interpreting
the results, and
reporting
the results. The guidelines for each stage are illustrated with a running example. Although the guidelines are geared towards analyses performed with the open-source statistical software JASP, most guidelines extend to Bayesian inference in general.
The network approach to psychological phenomena advances our understanding of the interrelations between autism and well-being. We use the Perceived Causal Relations methodology in order to (i) ...identify perceived causal pathways in the well-being system, (ii) validate networks based on self-report data, and (iii) quantify and integrate clinical expertise in autism research. Trained clinicians served as raters (N = 29) completing 374 cause-effects ratings of 34 variables on well-being and symptomatology. A subgroup (N = 16) of raters chose intervention targets in the resulting network which we found to match the respective centrality of nodes. Clinicians' perception of causal relations was similar to the interrelatedness found in self-reported client data (N = 323). We present a useful tool for translating clinical expertise into quantitative information enabling future research to integrate this in scientific studies.
Quasi-experimental research designs, such as regression discontinuity and interrupted time series, allow for causal inference in the absence of a randomized controlled trial, at the cost of ...additional assumptions. In this paper, we provide a framework for discontinuity-based designs using Bayesian model averaging and Gaussian process regression, which we refer to as ‘Bayesian nonparametric discontinuity design’, or BNDD for short. BNDD addresses the two major shortcomings in most implementations of such designs: overconfidence due to implicit conditioning on the alleged effect, and model misspecification due to reliance on overly simplistic regression models. With the appropriate Gaussian process covariance function, our approach can detect discontinuities of any order, and in spectral features. We demonstrate the usage of BNDD in simulations, and apply the framework to determine the effect of running for political positions on longevity, of the effect of an alleged historical phantom border in the Netherlands on Dutch voting behaviour, and of Kundalini Yoga meditation on heart rate.
Evaluation of the structural connectivity (SC) of the brain based on tractography has mainly focused on the choice of diffusion model, tractography algorithm, and their respective parameter settings. ...Here, we systematically validate SC derived from a post mortem monkey brain, while varying key acquisition parameters such as the b-value, gradient angular resolution and image resolution. As gold standard we use the connectivity matrix obtained invasively with histological tracers by Markov et al. (2014). As performance metric, we use cross entropy as a measure that enables comparison of the relative tracer labeled neuron counts to the streamline counts from tractography. We find that high angular resolution and high signal-to-noise ratio are important to estimate SC, and that SC derived from low image resolution (1.03 mm3) are in better agreement with the tracer network, than those derived from high image resolution (0.53 mm3) or at an even lower image resolution (2.03 mm3). In contradiction, sensitivity and specificity analyses suggest that if the angular resolution is sufficient, the balanced compromise in which sensitivity and specificity are identical remains 60–64% regardless of the other scanning parameters. Interestingly, the tracer graph is assumed to be the gold standard but by thresholding, the balanced compromise increases to 70–75%. Hence, by using performance metrics based on binarized tracer graphs, one risks losing important information, changing the performance of SC graphs derived by tractography and their dependence of different scanning parameters.
A fundamental assumption in neuroscience is that brain function is constrained by its structural properties. This motivates the idea that the brain can be parcellated into functionally coherent ...regions based on anatomical connectivity patterns that capture how different areas are interconnected. Several studies have successfully implemented this idea in humans using diffusion weighted MRI, allowing parcellation to be conducted in vivo. Two distinct approaches to connectivity-based parcellation can be identified. The first uses the connection profiles of brain regions as a feature vector, and groups brain regions with similar connection profiles together. Alternatively, one may adopt a network perspective that aims to identify clusters of brain regions that show dense within-cluster and sparse between-cluster connectivity. In this paper, we introduce a probabilistic model for connectivity-based parcellation that unifies both approaches. Using the model we are able to obtain a parcellation of the human brain whose clusters may adhere to either interpretation. We find that parts of the connectome consistently cluster as densely connected components, while other parts consistently result in clusters with similar connections. Interestingly, the densely connected components consist predominantly of major cortical areas, while the clusters with similar connection profiles consist of regions that have previously been identified as the 'rich club'; regions known for their integrative role in connectivity. Furthermore, the probabilistic model allows quantification of the uncertainty in cluster assignments. We show that, while most clusters are clearly delineated, some regions are more difficult to assign. These results indicate that care should be taken when interpreting connectivity-based parcellations obtained using alternative deterministic procedures.
Functional connectivity concerns the correlated activity between neuronal populations in spatially segregated regions of the brain, which may be studied using functional magnetic resonance imaging ...(fMRI). This coupled activity is conveniently expressed using covariance, but this measure fails to distinguish between direct and indirect effects. A popular alternative that addresses this issue is partial correlation, which regresses out the signal of potentially confounding variables, resulting in a measure that reveals only direct connections. Importantly, provided the data are normally distributed, if two variables are conditionally independent given all other variables, their respective partial correlation is zero. In this paper, we propose a probabilistic generative model that allows us to estimate functional connectivity in terms of both partial correlations and a graph representing conditional independencies. Simulation results show that this methodology is able to outperform the graphical LASSO, which is the de facto standard for estimating partial correlations. Furthermore, we apply the model to estimate functional connectivity for twenty subjects using resting-state fMRI data. Results show that our model provides a richer representation of functional connectivity as compared to considering partial correlations alone. Finally, we demonstrate how our approach can be extended in several ways, for instance to achieve data fusion by informing the conditional independence graph with data from probabilistic tractography. As our Bayesian formulation of functional connectivity provides access to the posterior distribution instead of only to point estimates, we are able to quantify the uncertainty associated with our results. This reveals that while we are able to infer a clear backbone of connectivity in our empirical results, the data are not accurately described by simply looking at the mode of the distribution over connectivity. The implication of this is that deterministic alternatives may misjudge connectivity results by drawing conclusions from noisy and limited data.
Our understanding of the wiring map of the brain, known as the connectome, has increased greatly in the last decade, mostly due to technological advancements in neuroimaging techniques and ...improvements in computational tools to interpret the vast amount of available data. Despite this, with the exception of the C. elegans roundworm, no definitive connectome has been established for any species. In order to obtain this, tracer studies are particularly appealing, as these have proven highly reliable. The downside of tract tracing is that it is costly to perform, and can only be applied ex vivo. In this paper, we suggest that instead of probing all possible connections, hitherto unknown connections may be predicted from the data that is already available. Our approach uses a 'latent space model' that embeds the connectivity in an abstract physical space. Regions that are close in the latent space have a high chance of being connected, while regions far apart are most likely disconnected in the connectome. After learning the latent embedding from the connections that we did observe, the latent space allows us to predict connections that have not been probed previously. We apply the methodology to two connectivity data sets of the macaque, where we demonstrate that the latent space model is successful in predicting unobserved connectivity, outperforming two baselines and an alternative model in nearly all cases. Furthermore, we show how the latent spatial embedding may be used to integrate multimodal observations (i.e. anterograde and retrograde tracers) for the mouse neocortex. Finally, our probabilistic approach enables us to make explicit which connections are easy to predict and which prove difficult, allowing for informed follow-up studies.
Habituation and dishabituation are the most prevalent measures of infant cognitive functioning, and they have reliably been shown to predict later cognitive outcomes. Yet, the exact mechanisms ...underlying infant habituation and dishabituation are still unclear. To investigate them, we tested 106 8‐month‐old infants on a classic habituation task and a novel visual learning task. We used a hierarchical Bayesian model to identify individual differences in sustained attention, learning performance, processing speed and curiosity from the visual learning task. These factors were then related to habituation and dishabituation. We found that habituation time was related to individual differences in processing speed, while dishabituation was related to curiosity, but only for infants who did not habituate. These results offer novel insights in the mechanisms underlying habituation and serve as proof of concept for hierarchical models as an effective tool to measure individual differences in infant cognitive functioning.
Research Highlights
We used a hierarchical Bayesian model to measure individual differences in infants’ processing speed, learning performance, sustained attention, and curiosity.
Faster processing speed was related to shorter habituation time.
High curiosity was related to stronger dishabituation responses, but only for infants who did not habituate.
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