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Satellite images using multiple wavelength channels provide crucial measurements over large areas, aiding the understanding of pollution generation and transport. However, these images often contain missing data due to cloud cover and algorithm limitations. In this paper, we introduce a novel method for interpolating missing values in satellite images by incorporating pollution transport dynamics influenced by wind patterns. Our approach utilizes a fundamental physics equation to structure the covariance of missing data, improving accuracy by considering pollution transport dynamics. To address computational challenges associated with large datasets, we implement a gradient ascent algorithm. We demonstrate the effectiveness of our method through a case study, showcasing its potential for accurate interpolation in high-resolution, spatio-temporal air pollution datasets. 

Understanding the oscillating behaviors that govern organisms’ internal biological processes requires interdisciplinary efforts combining both biological and computer experiments, as the latter can complement the former by simulating perturbed conditions with higher resolution. Harmonizing the two types of experiment, however, poses significant statistical challenges due to identifiability issues, numerical instability, and ill behavior in high dimension. This article devises a new Bayesian calibration framework for oscillating biochemical models. The proposed Bayesian model is estimated relying on an advanced Markov chain Monte Carlo (MCMC) technique which can efficiently infer the parameter values that match the simulated and observed oscillatory processes. Also proposed is an approach to sensitivity analysis based on the intervention posterior. This approach measures the influence of individual parameters on the target process by using the obtained MCMC samples as a computational tool. The proposed framework is illustrated with circadian oscillations observed in a filamentous fungus, Neurospora crassa.