The evolution of epidemiological parameters, such as instantaneous reproduction number Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often face problems such as lagging observations, averaging inference, and improper quantification of uncertainties. To address these problems, we propose a Bayesian data assimilation framework for time-varying parameter estimation. Specifically, this framework is applied to Rt estimation, resulting in the state-of-the-art DARt system. With DARt, time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and Rt; the drawback of averaging is overcome by instantaneously updating upon new observations and developing a model selection mechanism that captures abrupt changes; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DARt and demonstrate its power in revealing the transmission dynamics of COVID-19. The proposed approach provides a promising solution for accurate and timely estimating transmission dynamics from reported data.
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Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic. In this paper, we propose an extension of the SUIHTER model, first introduced in [Parolini et al, Proc R. Soc. A., 2021] to analyse the COVID-19 spreading in Italy, which accounts for the vaccination campaign and the presence of new variants when they become dominant. In particular, the specific features of the variants (e.g. their increased transmission rate) and vaccines (e.g. their efficacy to prevent transmission, hospitalization and death) are modeled, based on clinical evidence. The new model is validated comparing its near-future forecast capabilities with other epidemiological models and exploring different scenario analyses.
Targets are essential in problems such as object tracking in cluttered or textureless environments, camera (and multi-sensor) calibration tasks, and simultaneous localization and mapping (SLAM). Target shapes for these tasks typically are symmetric (square, rectangular, or circular) and work well for structured, dense sensor data such as pixel arrays (i.e., image). However, symmetric shapes lead to pose ambiguity when using sparse sensor data such as LiDAR point clouds and suffer from the quantization uncertainty of the LiDAR. This paper introduces the concept of optimizing target shape to remove pose ambiguity for LiDAR point clouds. A target is designed to induce large gradients at edge points under rotation and translation relative to the LiDAR to ameliorate the quantization uncertainty associated with point cloud sparseness. Moreover, given a target shape, we present a means that leverages the target's geometry to estimate the target's vertices while globally estimating the pose. Both the simulation and the experimental results (verified by a motion capture system) confirm that by using the optimal shape and the global solver, we achieve centimeter error in translation and a few degrees in rotation even when a partially illuminated target is placed 30 meters away. All the implementations and datasets are available at //github.com/UMich-BipedLab/optimal_shape_global_pose_estimation.
The fast transmission rate of COVID-19 worldwide has made this virus the most important challenge of year 2020. Many mitigation policies have been imposed by the governments at different regional levels (country, state, county, and city) to stop the spread of this virus. Quantifying the effect of such mitigation strategies on the transmission and recovery rates, and predicting the rate of new daily cases are two crucial tasks. In this paper, we propose a hybrid modeling framework which not only accounts for such policies but also utilizes the spatial and temporal information to characterize the pattern of COVID-19 progression. Specifically, a piecewise susceptible-infected-recovered (SIR) model is developed while the dates at which the transmission/recover rates change significantly are defined as "break points" in this model. A novel and data-driven algorithm is designed to locate the break points using ideas from fused lasso and thresholding. In order to enhance the forecasting power and to describe additional temporal dependence among the daily number of cases, this model is further coupled with spatial smoothing covariates and vector auto-regressive (VAR) model. The proposed model is applied to several U.S. states and counties, and the results confirm the effect of "stay-at-home orders" and some states' early "re-openings" by detecting break points close to such events. Further, the model provided satisfactory short-term forecasts of the number of new daily cases at regional levels by utilizing the estimated spatio-temporal covariance structures. They were also better or on par with other proposed models in the literature, including flexible deep learning ones. Finally, selected theoretical results and empirical performance of the proposed methodology on synthetic data are reported which justify the good performance of the proposed method.
We develop a new method to estimate an ARMA model in the presence of big time series data. Using the concept of a rolling average, we develop a new efficient algorithm, called Rollage, to estimate the order of an AR model and subsequently fit the model. When used in conjunction with an existing methodology, specifically Durbin's algorithm, we show that our proposed method can be used as a criterion to optimally fit ARMA models. Empirical results on large-scale synthetic time series data support the theoretical results and reveal the efficacy of this new approach, especially when compared to existing methodology.
A central obstacle in the objective assessment of treatment effect (TE) estimators in randomized control trials (RCTs) is the lack of ground truth (or validation set) to test their performance. In this paper, we provide a novel cross-validation-like methodology to address this challenge. The key insight of our procedure is that the noisy (but unbiased) difference-of-means estimate can be used as a ground truth "label" on a portion of the RCT, to test the performance of an estimator trained on the other portion. We combine this insight with an aggregation scheme, which borrows statistical strength across a large collection of RCTs, to present an end-to-end methodology for judging an estimator's ability to recover the underlying treatment effect. We evaluate our methodology across 709 RCTs implemented in the Amazon supply chain. In the corpus of AB tests at Amazon, we highlight the unique difficulties associated with recovering the treatment effect due to the heavy-tailed nature of the response variables. In this heavy-tailed setting, our methodology suggests that procedures that aggressively downweight or truncate large values, while introducing bias, lower the variance enough to ensure that the treatment effect is more accurately estimated.
The increasing integration of intermittent renewable generation, especially at the distribution level,necessitates advanced planning and optimisation methodologies contingent on the knowledge of thegrid, specifically the admittance matrix capturing the topology and line parameters of an electricnetwork. However, a reliable estimate of the admittance matrix may either be missing or quicklybecome obsolete for temporally varying grids. In this work, we propose a data-driven identificationmethod utilising voltage and current measurements collected from micro-PMUs. More precisely,we first present a maximum likelihood approach and then move towards a Bayesian framework,leveraging the principles of maximum a posteriori estimation. In contrast with most existing con-tributions, our approach not only factors in measurement noise on both voltage and current data,but is also capable of exploiting available a priori information such as sparsity patterns and knownline parameters. Simulations conducted on benchmark cases demonstrate that, compared to otheralgorithms, our method can achieve significantly greater accuracy.
A standing challenge in data privacy is the trade-off between the level of privacy and the efficiency of statistical inference. Here we conduct an in-depth study of this trade-off for parameter estimation in the $\beta$-model (Chatterjee, Diaconis and Sly, 2011) for edge differentially private network data released via jittering (Karwa, Krivitsky and Slavkovi\'c, 2017). Unlike most previous approaches based on maximum likelihood estimation for this network model, we proceed via method of moments. This choice facilitates our exploration of a substantially broader range of privacy levels -- corresponding to stricter privacy -- than has been to date. Over this new range we discover our proposed estimator for the parameters exhibits an interesting phase transition, with both its convergence rate and asymptotic variance following one of three different regimes of behavior depending on the level of privacy. Because identification of the operable regime is difficult to impossible in practice, we devise a novel adaptive bootstrap procedure to construct uniform inference across different phases. In fact, leveraging this bootstrap we are able to provide for simultaneous inference of all parameters in the $\beta$-model (i.e., equal to the number of vertices), which would appear to be the first result of its kind. Numerical experiments confirm the competitive and reliable finite sample performance of the proposed inference methods, next to a comparable maximum likelihood method, as well as significant advantages in terms of computational speed and memory.
When performing visual servoing or object tracking tasks, active sensor planning is essential to keep targets in sight or to relocate them when missing. In particular, when dealing with a known target missing from the sensor's field of view, we propose using prior knowledge related to contextual information to estimate its possible location. To this end, this study proposes a Dynamic Bayesian Network that uses contextual information to effectively search for targets. Monte Carlo particle filtering is employed to approximate the posterior probability of the target's state, from which uncertainty is defined. We define the robot's utility function via information-theoretic formalism as seeking the optimal action which reduces uncertainty of a task, prompting robot agents to investigate the location where the target most likely might exist. Using a context state model, we design the agent's high-level decision framework using a Partially-Observable Markov Decision Process. Based on the estimated belief state of the context via sequential observations, the robot's navigation actions are determined to conduct exploratory and detection tasks. By using this multi-modal context model, our agent can effectively handle basic dynamic events, such as obstruction of targets or their absence from the field of view. We implement and demonstrate these capabilities on a mobile robot in real-time.
Decision making in the face of a disaster requires the consideration of several complex factors. In such cases, Bayesian multi-criteria decision analysis provides a framework for decision making. In this paper, we present how to construct a multi-attribute decision support system for choosing between countermeasure strategies, such as lockdowns, designed to mitigate the effects of COVID-19. Such an analysis can evaluate both the short term and long term efficacy of various candidate countermeasures. The expected utility scores of a countermeasure strategy capture the expected impact of the policies on health outcomes and other measures of population well-being. The broad methodologies we use here have been established for some time. However, this application has many novel elements to it: the pervasive uncertainty of the science; the necessary dynamic shifts between regimes within each candidate suite of countermeasures; and the fast moving stochastic development of the underlying threat all present new challenges to this domain. Our methodology is illustrated by demonstrating in a simplified example how the efficacy of various strategies can be formally compared through balancing impacts of countermeasures, not only on the short term (e.g. COVID-19 deaths) but the medium to long term effects on the population (e.g increased poverty).
ABCpy is a highly modular scientific library for Approximate Bayesian Computation (ABC) written in Python. The main contribution of this paper is to document a software engineering effort that enables domain scientists to easily apply ABC to their research without being ABC experts; using ABCpy they can easily run large parallel simulations without much knowledge about parallelization. Further, ABCpy enables ABC experts to easily develop new inference schemes and evaluate them in a standardized environment and to extend the library with new algorithms. These benefits come mainly from the modularity of ABCpy. We give an overview of the design of ABCpy and provide a performance evaluation concentrating on parallelization. This points us towards the inherent imbalance in some of the ABC algorithms. We develop a dynamic scheduling MPI implementation to mitigate this issue and evaluate the various ABC algorithms according to their adaptability towards high-performance computing.
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