Bayesian inference for partial orders from random linear extensions: power relations from 12th Century Royal Acta

We give a new class of models for time series data in which actors are listed in order of precedence. We model the lists as a realisation of a queue in which queue-position is constrained by an underlying social hierarchy. We model the hierarchy as a partial order so that the lists are random linear extensions. We account for noise via a random queue-jumping process. We give a marginally consistent prior for the stochastic process of partial orders based on a latent variable representation for the partial order. This allows us to introduce a parameter controlling partial order depth and incorporate actor-covariates informing the position of actors in the hierarchy. We fit the model to witness lists from Royal Acta from England, Wales and Normandy in the eleventh and twelfth centuries. Witnesses are listed in order of social rank, with any bishops present listed as a group. Do changes in the order in which the bishops appear reflect changes in their personal authority? The underlying social order which constrains the positions of bishops within lists need not be a complete order and so we model the evolving social order as an evolving partial order. The status of an Anglo-Norman bishop was at the time partly determined by the length of time they had been in office. This enters our model as a time-dependent covariate. We fit the model, estimate partial orders and find evidence for changes in status over time. We interpret our results in terms of court politics. Simpler models, based on bucket orders and vertex-series-parallel orders, are rejected. We compare our results with a stochastic process extension of the Plackett-Luce model.Comment: 70 pages, 38 figures and 2 tables including appendix and supplemen

osl-dynamics, a toolbox for modeling fast dynamic brain activity

Neural activity contains rich spatiotemporal structure that corresponds to cognition. This includes oscillatory bursting and dynamic activity that span across networks of brain regions, all of which can occur on timescales of tens of milliseconds. While these processes can be accessed through brain recordings and imaging, modeling them presents methodological challenges due to their fast and transient nature. Furthermore, the exact timing and duration of interesting cognitive events are often a priori unknown. Here, we present the OHBA Software Library Dynamics Toolbox (osl-dynamics), a Python-based package that can identify and describe recurrent dynamics in functional neuroimaging data on timescales as fast as tens of milliseconds. At its core are machine learning generative models that are able to adapt to the data and learn the timing, as well as the spatial and spectral characteristics, of brain activity with few assumptions. osl-dynamics incorporates state-of-the-art approaches that can be, and have been, used to elucidate brain dynamics in a wide range of data types, including magneto/electroencephalography, functional magnetic resonance imaging, invasive local field potential recordings, and electrocorticography. It also provides novel summary measures of brain dynamics that can be used to inform our understanding of cognition, behavior, and disease. We hope osl-dynamics will further our understanding of brain function, through its ability to enhance the modeling of fast dynamic processes