Daniel Shen

Daniel Shen, Marija Ilic, John Parsons

Energy storage shifts energy from off-peak periods to on-peak periods. Unlike conventional generation, storage is duration-limited: the stored energy capacity constrains the duration over which it can supply power. To understand how these constraints affect optimal pricing and investment decisions, we extend the classic two-period peak-load pricing model to include duration-limited storage. By adopting assumptions typical of solar-dominated systems, we link on- and off-peak prices to storage investment costs, round-trip efficiency, and the duration of the peak period. The bulk of the scarcity premium from on-peak prices is associated with the fixed costs of storage as opposed to variable costs stemming from round-trip efficiency losses. Unlike conventional generators, the binding duration constraints lead storage to recover energy capacity costs on a per-peak-event basis instead of amortizing these costs over total peak hours. A numerical example illustrates the implications for equilibrium prices and capacity investment.

Nikita Dhawan, Daniel Shen, Leonardo Cotta et al.

Causal inference, especially in observational studies, relies on untestable assumptions about the true data-generating process. Sensitivity analysis helps us determine how robust our conclusions are when we alter these underlying assumptions. Existing frameworks for sensitivity analysis are concerned with worst-case changes in assumptions. In this work, we argue that using such pessimistic criteria can often become uninformative or lead to conclusions contradicting our prior knowledge about the world. To demonstrate this claim, we generalize the recent s-value framework (Gupta & Rothenhäusler, 2023) to estimate the sensitivity of three different common assumptions in causal inference. Empirically, we find that, indeed, worst-case conclusions about sensitivity can rely on unrealistic changes in the data-generating process. To overcome this, we extend the s-value framework with a new sensitivity analysis criterion: Bayesian Sensitivity Value (BSV), which computes the expected sensitivity of an estimate to assumption violations under priors constructed from real-world evidence. We use Monte Carlo approximations to estimate this quantity and illustrate its applicability in an observational study on the effect of diabetes treatments on weight loss.

Daniel Shen, Min Chi

Dynamic time warping (DTW) plays an important role in analytics on time series. Despite the large body of research on speeding up univariate DTW, the method for multivariate DTW has not been improved much in the last two decades. The most popular algorithm used today is still the one developed seventeen years ago. This paper presents a solution that, as far as we know, for the first time consistently outperforms the classic multivariate DTW algorithm across dataset sizes, series lengths, data dimensions, temporal window sizes, and machines. The new solution, named TC-DTW, introduces Triangle Inequality and Point Clustering into the algorithm design on lower bound calculations for multivariate DTW. In experiments on DTW-based nearest neighbor finding, the new solution avoids as much as 98% (60% average) DTW distance calculations and yields as much as 25X (7.5X average) speedups.