Methodology (stat.ME)

Abstract: It is well known that it is impossible to construct useful confidence intervals (CIs) about the mean or median of a response $Y$ conditional on features $X = x$ without making strong assumptions about the joint distribution of $X$ and $Y$. This paper introduces a new framework for reasoning about problems of this kind by casting the conditional problem at different levels of resolution, ranging from coarse to fine localization. In each of these problems, we consider local quantiles defined as the marginal quantiles of $Y$ when $(X,Y)$ is resampled in such a way that samples $X$ near $x$ are up-weighted while the conditional distribution $Y \mid X$ does not change. We then introduce the Weighted Quantile method, which asymptotically produces the uniformly most accurate confidence intervals for these local quantiles no matter the (unknown) underlying distribution. Another method, namely, the Quantile Rejection method, achieves finite sample validity under no assumption whatsoever. We conduct extensive numerical studies demonstrating that both of these methods are valid. In particular, we show that the Weighted Quantile procedure achieves nominal coverage as soon as the effective sample size is in the range of 10 to 20.

Abstract: The validation of global climate models plays a crucial role in ensuring the accuracy of climatological predictions. However, existing statistical methods for evaluating differences between climate fields often overlook time misalignment and therefore fail to distinguish between sources of variability. To more comprehensively measure differences between climate fields, we introduce a new vector-valued metric, the sliced elastic distance. This new metric simultaneously accounts for spatial and temporal variability while decomposing the total distance into shape differences (amplitude), timing variability (phase), and bias (translation). We compare the sliced elastic distance against a classical metric and a newly developed Wasserstein-based approach through a simulation study. Our results demonstrate that the sliced elastic distance outperforms previous methods by capturing a broader range of features. We then apply our metric to evaluate the historical model outputs of the Coupled Model Intercomparison Project (CMIP) members, focusing on monthly average surface temperatures and monthly total precipitation. By comparing these model outputs with quasi-observational ERA5 Reanalysis data products, we rank the CMIP models and assess their performance. Additionally, we investigate the progression from CMIP phase 5 to phase 6 and find modest improvements in the phase 6 models regarding their ability to produce realistic climate dynamics.

Abstract: This article explains the usage of R package CausalModels, which is publicly available on the Comprehensive R Archive Network. While packages are available for sufficiently estimating causal effects, there lacks a package that provides a collection of structural models using the conventional statistical approach developed by Hern\'an and Robins (2020). CausalModels addresses this deficiency of software in R concerning causal inference by offering tools for methods that account for biases in observational data without requiring extensive statistical knowledge. These methods should not be ignored and may be more appropriate or efficient in solving particular problems. While implementations of these statistical models are distributed among a number of causal packages, CausalModels introduces a simple and accessible framework for a consistent modeling pipeline among a variety of statistical methods for estimating causal effects in a single R package. It consists of common methods including standardization, IP weighting, G-estimation, outcome regression, instrumental variables and propensity matching.