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An atmospheric release of hazardous material, whether accidental or intentional, can be catastrophic for those in the path of the plume. Predicting the path of a plume based on characteristics of the release (location, amount, and duration) and meteorological conditions is an active research area highly relevant for emergency and long-term response to these releases. As a result, researchers have developed particle dispersion simulators to provide plume path predictions that incorporate release characteristics and meteorological conditions. However, since release characteristics and meteorological conditions are often unknown, the inverse problem is of great interest, that is, based on all the observations of the plume so far, what can be inferred about the release characteristics? This is the question we seek to answer using plume observations from a controlled release at the Diablo Canyon Nuclear Power Plant in Central California. With access to a large number of evaluations of a computationally expensive particle dispersion simulator that includes continuous and categorical inputs and spatio-temporal output, building a fast statistical surrogate model (or emulator) presents many statistical challenges, but is an essential tool for inverse modeling and sensitivity analysis. We achieve accurate emulation using Bayesian adaptive splines to model weights on empirical orthogonal functions. We use this emulator as well as appropriately identifiable simulator discrepancy and observational error models to calibrate the simulator, thus finding a posterior distribution of characteristics of the release. Since the release was controlled, these characteristics are known, making it possible to compare our findings to the truth. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

An atmospheric release of hazardous material, whether accidental or intentional, can be catastrophic for those in the path of the plume. Predicting the path of a plume based on characteristics of the release (location, amount and duration) and meteorological conditions is an active research area highly relevant for emergency and long-term response to these releases. As a result, researchers have developed particle dispersion simulators to provide plume path predictions that incorporate release characteristics and meteorological conditions. However, since release characteristics and meteorological conditions are often unknown, the inverse problem is of great interest, that is, based on all the observations of the plume so far, what can be inferred about the release characteristics? This is the question we seek to answer using plume observations from a controlled release at the Diablo Canyon Nuclear Power Plant in Central California. With access to a large number of evaluations of a computationally expensive particle dispersion simulator that includes continuous and categorical inputs and spatio-temporal output, building a fast statistical surrogate model (or emulator) presents many statistical challenges, but is an essential tool for inverse modeling and sensitivity analysis. We achieve accurate emulation using Bayesian adaptive splines to model weights on empirical orthogonal functions. Here, we use this emulator as well as appropriately identifiable simulator discrepancy and observational error models to calibrate the simulator, thus finding a posterior distribution of characteristics of the release. Since the release was controlled, these characteristics are known, making it possible to compare our findings to the truth.

Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between the fields might also differ substantially. Extending a recently proposed Bayesian approach to describe the distribution of a nonstationary univariate spatial field using a triangular transport map, we cast the inference problem for a multivariate spatial field for a small number of replicates into a series of independent Gaussian process (GP) regression tasks with Gaussian errors. Due to the potential nonlinearity in the conditional means, the joint distribution modeled can be non-Gaussian. The resulting nonparametric Bayesian methodology scales well to high-dimensional spatial fields. It is especially useful when only a few training samples are available, because it employs regularization priors and quantifies uncertainty. Inference is conducted in an empirical Bayes setting by a highly scalable stochastic gradient approach. The implementation benefits from mini-batching and could be accelerated with parallel computing. We illustrate the extended transport-map model by studying hydrological variables from non-Gaussian climate-model output.

I discuss recent research advances in Bayesian state-space modeling of multivariate time series. A main focus is on the “decouple/recouple” concept that enables application of state-space models to increasingly large-scale data, applying to continuous or discrete time series outcomes. Applied motivations come from areas such as financial and commercial forecasting and dynamic network studies. Explicit forecasting and decision goals are often paramount and should factor into model assessment and comparison, a perspective that is highlighted. The Akaike Memorial Lecture is a context to reflect on the contributions of Hirotugu Akaike and to promote new areas of research. In this spirit, this paper aims to promote new research on foundations of statistics and decision analysis, as well as on further modeling, algorithmic and computational innovation in dynamic models for increasingly complex and challenging problems in multivariate time series analysis and forecasting.

Present study evaluates the usability of compaction simulation-based mechanical models as a material-sparing approach to predict tablet capping under processing compression conditions using Acetaminophen (APAP) and Ibuprofen (IBU). Measured mechanical properties were evaluated using principal component analysis (PCA) and principal component regression (PCR) models. PCR models were then utilized to predict the capping score (CS) from compression pressure (CP). APAP formulations displayed a quadratic correlation between CS and CP, with CS rank order following CP of 200MPa < 300MPa < 100MPa, indicating threshold compression pressure (TCP) limit between 200 and 300 MPa, resulting in higher CS at 300 than 200 MPa regardless of increased CP. IBU formulations displayed a linear correlation between CS and CP, with CS rank order following CP of 100MPa < 200MPa < 300MPa, indicating TCP limit between 100 and 200 MPa, resulting in higher CS at 200 and 300 than 100 MPa regardless of increased CP. Molecular models were developed as validation methods to predict capping from CP. Measured XRPD patterns of compressed tablets were linked with calculated Eatt and d-spacing of slip planes and analyzed using variable component least square methods to predict TCP triggering cleavage in slip planes and leading to capping. In APAP and IBU, TCP values were predicted at 245 and 175 MPa, meaning capped tablets above these TCP limits regardless of increased CP. A similar trend was observed in CS predictions from mechanical assessment, confirming that compaction simulation-based mechanical models can predict capping risk under desired compression conditions rapidly and accurately. Graphical Abstract

Motor imagery (MI) is the mental rehearsal of a motor first person action-representation. There is interest in using MI to access the motor network after stroke. Conventional fMRI modeling has shown that MI and executed movement (EM) activate similar cortical areas but it remains unknown whether they share cortical networks. Proving this is central to using MI to access the motor network and as a form of motor training. Here we use multivariate analysis (tensor independent component analysis-TICA) to map the array of neural networks involved during MI and EM. Fifteen right-handed healthy volunteers (mean-age 28.4 years) were recruited and screened for their ability to carry out MI (Chaotic MI Assessment). fMRI consisted of an auditory-paced (1 Hz) right hand finger-thumb opposition sequence (2,3,4,5; 2…) with two separate runs acquired (MI & rest and EM & rest: block design). No distinction was made between MI and EM until the final stage of processing. This allowed TICA to identify independent-components (IC) that are common or distinct to both tasks with no prior assumptions. TICA defined 52 ICs. Non-significant ICs and those representing artifact were excluded. Components in which the subject scores were significantly different to zero (for either EM or MI) were included. Seven IC remained. There were IC's shared between EM and MI involving the contralateral BA4, PMd, parietal areas and SMA. IC's exclusive to EM involved the contralateral BA4, S1 and ipsilateral cerebellum whereas the IC related exclusively to MI involved ipsilateral BA4 and PMd. In addition to networks specific to each task indicating a degree of independence, we formally demonstrate here for the first time that MI and EM share cortical networks. This significantly strengthens the rationale for using MI to access the motor networks, but the results also highlight important differences.

In brain-computer interfacing (BCI), motor imagery is used to provide a gateway to an effector action or behavior. However, in contrast to the main functional role of the primary motor cortex (M1) in motor execution, the M1's involvement in motor imagery has been debated, while the roles of secondary motor areas such as the premotor cortex (PMC) and supplementary motor area (SMA) in motor imagery have been proposed. We examined which motor cortical region had the greatest predictive ability for imagined movement among the primary and secondary motor areas. For two modes of motor performance, executed movement and imagined movement, in 12 healthy subjects who performed two types of motor task, hand grasping and hand rotation, we used the multivariate Bayes method to compare predictive ability between the primary and secondary motor areas (M1, PMC, and SMA) contralateral to the moved hand. With the distributed representation of activation, executed movement was best predicted from the M1 while imagined movement from the SMA, among the three motor cortical regions, in both types of motor task. In addition, the most predictive information about the distinction between executed movement and imagined movement was contained in the M1. The greater predictive ability of the SMA for imagined movement suggests its functional role that could be applied to motor imagery-based BCI. •Bayesian decoding enabled to compare predictive ability of motor cortical regions.•Cortical regions exhibited distributed patterns of activation in motor performance.•Executed movement was best predicted from the M1 and imagined movement from the SMA.•Predictive ability of the SMA for imagined movement suggests implications for BCI.

A crucial issue in the current global warming debate is the effect of vegetation and soils on carbon dioxide (CO₂) concentrations in the atmosphere. Vegetation can extract CO₂ through photosynthesis, but respiration, decay of soil organic matter and disturbance effects such as fire return it to the atmosphere. The balance of these processes is the net carbon flux. To estimate the biospheric carbon flux for England and Wales, we address the statistical problem of inference for the sum of multiple outputs from a complex deterministic computer code whose input parameters are uncertain. The code is a process model which simulates the carbon dynamics of vegetation and soils, including the amount of carbon that is stored as a result of photosynthesis and the amount that is returned to the atmosphere through respiration. The aggregation of outputs corresponding to multiple sites and types of vegetation in a region gives an estimate of the total carbon flux for that region over a period of time. Expert prior opinions are elicited for marginal uncertainty about the relevant input parameters and for correlations of inputs between sites. A Gaussian process model is used to build emulators of the multiple code outputs and Bayesian uncertainty analysis is then used to propagate uncertainty in the input parameters through to uncertainty on the aggregated output. Numerical results are presented for England and Wales in the year 2000. It is estimated that vegetation and soils in England and Wales constituted a net sink of 7.55 Mt C (1 Mt C = 10¹² g of carbon) in 2000, with standard deviation 0.56 Mt C resulting from the sources of uncertainty that are considered.