The value of probabilistic forecasting in emergency medical resource planning under uncertainty

PurposeMost epidemic transmission forecasting methods can only provide deterministic outputs. This study aims to show that probabilistic forecasting, in contrast, is suitable for stochastic demand modeling and emergency medical resource planning under uncertainty.Design/methodology/approachTwo probabilistic forecasting methods, i.e. quantile regression convolutional neural network and kernel density estimation, are combined to provide the conditional quantiles and conditional densities of infected populations. The value of probabilistic forecasting in improving decision performances and controlling decision risks is investigated by an empirical study on the emergency medical resource planning for the COVID-19 pandemic.FindingsThe managerial implications obtained from the empirical results include (1) the optimization models using the conditional quantile or the point forecasting result obtain better results than those using the conditional density; (2) for sufficient resources, decision-makers' risk preferences can be incorporated to make tradeoffs between the possible surpluses and shortages of resources in the emergency medical resource planning at different quantile levels; and (3) for scarce resources, the differences in emergency medical resource planning at different quantile levels greatly decrease or disappear because of the existing of forecasting errors and supply quantity constraints.Originality/valueVery few studies concern probabilistic epidemic transmission forecasting methods, and this is the first attempt to incorporate deep learning methods into a two-phase framework for data-driven emergency medical resource planning under uncertainty. Moreover, the findings from the empirical results are valuable to select a suitable forecasting method and design an efficient emergency medical resource plan.

The State Space Subdivision Filter for Estimation on SE(2)

The SE(2) domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle. We present a novel filter that involves splitting up the joint density into a (marginalized) density for the periodic part and a conditional density for the linear part. We subdivide the state space along the periodic dimension and describe each part of the state space using the parameters of a Gaussian and a grid value, which is the function value of the marginalized density for the periodic part at the center of the respective area. By using the grid values as weighting factors for the Gaussians along the linear dimensions, we can approximate functions on the SE(2) domain with correlated position and orientation. Based on this representation, we interweave a grid filter with a Kalman filter to obtain a filter that can take different numbers of parameters and is in the same complexity class as a grid filter for circular domains. We thoroughly compared the filters with other state-of-the-art filters in a simulated tracking scenario. With only little run time, our filter outperformed an unscented Kalman filter for manifolds and a progressive filter based on dual quaternions. Our filter also yielded more accurate results than a particle filter using one million particles while being faster by over an order of magnitude.

Flood routing via a copula-based approach

Floods are among the most common natural disasters that if not controlled may cause severe damage and high costs. Flood control and management can be done using structural measures that should be designed based on the flood design studies. The simulation of outflow hydrograph using inflow hydrograph can provide useful information. In this study, a copula-based approach was applied to simulate the outflow hydrograph of various floods, including the Wilson River flood, the River Wye flood and the Karun River flood. In this regard, two-dimensional copula functions and their conditional density were used. The results of evaluating the dependence structure of the studied variables (inflow and outflow hydrographs) using Kendall's tau confirmed the applicability of copula functions for bivariate modeling of inflow and outflow hydrographs. The simulation results were evaluated using the root-mean-square error, the sum of squared errors and the Nash–Sutcliffe efficiency coefficient (NSE). The results showed that the copula-based approach has high performance. In general, the copula-based approach has been able to simulate the peak flow and the rising and falling limbs of the outflow hydrographs well. Also, all simulated data are at the 95% confidence interval. The NSE values for the copula-based approach are 0.99 for all three case studies. According to NSE values and violin plots, it can be seen that the performance of the copula-based approach in simulating the outflow hydrograph in all three case studies is acceptable and shows a good performance.

Variational inference for Markovian queueing networks

Queueing networks are stochastic systems formed by interconnected resources routing and serving jobs. They induce jump processes with distinctive properties, and find widespread use in inferential tasks. Here, service rates for jobs and potential bottlenecks in the routing mechanism must be estimated from a reduced set of observations. However, this calls for the derivation of complex conditional density representations, over both the stochastic network trajectories and the rates, which is considered an intractable problem. Numerical simulation procedures designed for this purpose do not scale, because of high computational costs; furthermore, variational approaches relying on approximating measures and full independence assumptions are unsuitable. In this paper, we offer a probabilistic interpretation of variational methods applied to inference tasks with queueing networks, and show that approximating measure choices routinely used with jump processes yield ill-defined optimization problems. Yet we demonstrate that it is still possible to enable a variational inferential task, by considering a novel space expansion treatment over an analogous counting process for job transitions. We present and compare exemplary use cases with practical queueing networks, showing that our framework offers an efficient and improved alternative where existing variational or numerically intensive solutions fail.