Bayesian model averaging over tree-based dependence structures for multivariate extremes

Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical dependence structure of the max-stable nested logistic distribution and that identifies possible clusters of extreme variables using reversible jump Markov chain Monte Carlo techniques. Parsimonious representations are achieved when clusters of extreme variables are found to be completely independent. Moreover, we significantly decrease the computational complexity of full likelihood inference by deriving a recursive formula for the nested logistic model likelihood. The algorithm performance is verified through extensive simulation experiments which also compare different likelihood procedures. The new methodology is used to investigate the dependence relationships between extreme concentration of multiple pollutants in California and how these pollutants are related to extreme weather conditions. Overall, we show that our approach allows for the representation of complex extremal dependence structures and has valid applications in multivariate data analysis, such as air pollution monitoring, where it can guide policymaking

Discrete- and Continuous-Time Probabilistic Models and Algorithms for Inferring Neuronal UP and DOWN States

UP and DOWN states, the periodic fluctuations between increased and decreased spiking activity of a neuronal population, are a fundamental feature of cortical circuits. Understanding UP-DOWN state dynamics is important for understanding how these circuits represent and transmit information in the brain. To date, limited work has been done on characterizing the stochastic properties of UP-DOWN state dynamics. We present a set of Markov and semi-Markov discrete- and continuous-time probability models for estimating UP and DOWN states from multiunit neural spiking activity. We model multiunit neural spiking activity as a stochastic point process, modulated by the hidden (UP and DOWN) states and the ensemble spiking history. We estimate jointly the hidden states and the model parameters by maximum likelihood using an expectation-maximization (EM) algorithm and a Monte Carlo EM algorithm that uses reversible-jump Markov chain Monte Carlo sampling in the E-step. We apply our models and algorithms in the analysis of both simulated multiunit spiking activity and actual multi- unit spiking activity recorded from primary somatosensory cortex in a behaving rat during slow-wave sleep. Our approach provides a statistical characterization of UP-DOWN state dynamics that can serve as a basis for verifying and refining mechanistic descriptions of this process.National Institutes of Health (U.S.) (Grant R01-DA015644)National Institutes of Health (U.S.) (Director Pioneer Award DP1- OD003646)National Institutes of Health (U.S.) (NIH/NHLBI grant R01-HL084502)National Institutes of Health (U.S.) (NIH institutional NRSA grant T32 HL07901

Motor unit number estimation via sequential Monte Carlo

A change in the number of motor units that operate a particular muscle is an important indicator for the progress of a neuromuscular disease and the efficacy of a therapy. Inference for realistic statistical models of the typical data produced when testing muscle function is difficult, and estimating the number of motor units is an ongoing statistical challenge. We consider a set of models for the data, each with a different number of working motor units, and present a novel method for Bayesian inference based on sequential Monte Carlo. This provides estimates of the marginal likelihood and, hence, a posterior probability for each model. Implementing this approach in practice requires a sequential Monte Carlo method that has excellent computational and Monte Carlo properties. We achieve this by benefiting from the model's conditional independence structure, where, given knowledge of which motor units fired as a result of a particular stimulus, parameters that specify the size of each unit's response are independent of the parameters defining the probability that a unit will respond at all. The scalability of our methodology relies on the natural conjugacy structure that we create for the former and an enforced, approximate, conjugate structure for the latter. A simulation study demonstrates the accuracy of our method, and inferences are consistent across two different datasets arising from the same rat tibial muscle

From here to infinity - sparse finite versus Dirichlet process mixtures in model-based clustering

In model-based-clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al (2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with $K$ components is chosen in such a way that a priori the number of clusters in the data is random and is allowed to be smaller than $K$ with high probability. The number of cluster is then inferred a posteriori from the data. The present paper makes the following contributions in the context of sparse finite mixture modelling. First, it is illustrated that the concept of sparse finite mixture is very generic and easily extended to cluster various types of non-Gaussian data, in particular discrete data and continuous multivariate data arising from non-Gaussian clusters. Second, sparse finite mixtures are compared to Dirichlet process mixtures with respect to their ability to identify the number of clusters. For both model classes, a random hyper prior is considered for the parameters determining the weight distribution. By suitable matching of these priors, it is shown that the choice of this hyper prior is far more influential on the cluster solution than whether a sparse finite mixture or a Dirichlet process mixture is taken into consideration.Comment: Accepted versio

Bayesian Multi--Dipole Modeling of a Single Topography in MEG by Adaptive Sequential Monte Carlo Samplers

In the present paper, we develop a novel Bayesian approach to the problem of estimating neural currents in the brain from a fixed distribution of magnetic field (called \emph{topography}), measured by magnetoencephalography. Differently from recent studies that describe inversion techniques, such as spatio-temporal regularization/filtering, in which neural dynamics always plays a role, we face here a purely static inverse problem. Neural currents are modelled as an unknown number of current dipoles, whose state space is described in terms of a variable--dimension model. Within the resulting Bayesian framework, we set up a sequential Monte Carlo sampler to explore the posterior distribution. An adaptation technique is employed in order to effectively balance the computational cost and the quality of the sample approximation. Then, both the number and the parameters of the unknown current dipoles are simultaneously estimated. The performance of the method is assessed by means of synthetic data, generated by source configurations containing up to four dipoles. Eventually, we describe the results obtained by analyzing data from a real experiment, involving somatosensory evoked fields, and compare them to those provided by three other methods.Comment: 20 pages, 4 figure

Bayesian exploratory factor analysis

This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates from a high dimensional set of psychological measurements. (authors' abstract