Umberto Villa

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (∼ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

Background : Extreme heat may discourage physical activity of children while shade may provide thermal comfort. The authors determined the associations between ambient temperature, shade, and moderate to vigorous physical activity (MVPA) of children during school recess. Methods : Children aged 8–10 (n = 213) wore accelerometers and global positioning system monitors during recess at 3 school parks in Austin, Texas (September–November 2019). Weather data originated from 10 sensors per park. The authors calculated shade from imagery using a geographic information system (GIS) and time-matched physical activity, location, temperature, and shade data. The authors specified piecewise multilevel regression to assess relations between average temperature and percentage of recess time in MVPA and shade. Results : Temperature ranged 11 °C to 35 °C. Each 1 °C higher temperature was associated with a 0.7 percentage point lower time spent in MVPA, until 33 °C (91 °F) when the association changed to a 1.5 lower time ( P < .01). Each 1 °C higher temperature was associated with a 0.3 percentage point higher time spent under shade, until 33 °C when the association changed to a 3.4 higher time ( P < .001). At 33 °C or above, the direct association between shade and MVPA weakened ( P < .05), with no interaction effect above 33 °C ( P > .05). Children at the park with the most tree canopy spent 6.0 percentage points more time in MVPA ( P < .01). Conclusions : Children engage in less MVPA and seek shade during extreme heat and engage in more MVPA in green schoolyards. With climate change, schools should consider interventions (eg, organizing shaded play, tree planting) to promote heat safe MVPA.