Browsing by Author "Tang, Tao"

Previously, we usually analyze climate responses to all the climate drivers combined. However, the climate responses to individual climate drivers are far from well-known, as it is nearly impossible to separate the climate responses to individual climate drivers from the pure observational records. In this dissertation, I analyzed the responses of effective radiative forcing (ERF), precipitation and clouds to five individual climate drivers by using the model output from the Precipitation and Driver Response Model Inter-comparison Project (PDRMIP, consisting of five core experiments: CO2x2, CH4x3, Solar+2%, BCx10, and SO4x5). Firstly, I compared the ERF values estimated by six different methods and demonstrated that the values estimated using fixed sea-surface temperature and linear regression methods are fairly consistent for most climate drivers. For each individual driver, multi-model mean ERF values vary by 10-50% with different methods, and this difference may reach 70-100% for BC. Then, I analyzed the dynamical responses of precipitation in Mediterranean to well-mixed greenhouse gases (WMGHGs) and aerosols and found that precipitation in Mediterranean is more sensitive to BC forcing. When scaled to historical forcing level, WMGHG contributed roughly two-thirds to the Mediterranean drying during the past century and BC aerosol contributed the remaining one-third by causing a northward shift of the jet streams and storm tracks. Lastly, I explored the responses of shortwave cloud radiative effect (SWCRE) to CO2 and the two aerosol species and found that CO2 causes positive SWCRE changes over most of the Northern Hemisphere during boreal summer, and BC causes similar positive responses over North America, Europe and East China but negative SWCRE over India and tropical Africa. When normalized by global ERF, the change of SWCRE from BC forcing is roughly 3-5 times larger than that from CO2. SWCRE change is mainly due to cloud cover changes resulting from the changes in relative humidity, and to a lesser extent, changes in circulation and stability. The SWCRE response to sulfate aerosols, however, is negligible compared to that from CO2 and BC, because the radiation scattered by clouds under all-sky conditions will also be scattered by aerosols under clear-sky conditions. As SW is in effect only during daytime, positive (negative) SWCRE could amplify (dampen) daily maximum temperature (Tmax). Using a multi-linear regression model, I found that Tmax increases by 0.15 K and 0.13 K given unit increase in local SWCRE under the CO2 and BC experiments, respectively. When domain-averaged, SWCRE changes contributed to summer mean Tmax changes by 10-30% under CO2 forcing and by 30-50% under BC forcing, varying by regions, which can have important implications extreme climatic events and socio-economic activities.

This dissertation propels the frontier of Bayesian inference, particularly for structurally diverse data, by developing innovative methodologies and robust theories, delineated into three distinct segments, each tackling Dynamical systems, continuous time Markov Chains, and data with low-dimensional structures.

The initial part presents the Hierarchical Shrinkage Gaussian Process (HierGP), a novel model adept at detecting structured sparse features within limited data from response surfaces. Incorporating the principles of effect sparsity, heredity, and hierarchy into a Gaussian process framework, HierGP demonstrates superior performance compared to its contemporaries. This superiority is backed by a range of numerical experiments and its successful application to dynamical system recovery.

The dissertation's second segment introduces the Bayesian Approximation Spectral Inference (BASI) method. Inspired by the necessity for pragmatic inference techniques for continuous-time Markov chains, BASI innovatively employs probabilistic matrix factorization to estimate a continuous-time Markov chain generator's low-rank representation. This approach effectively circumvents the computational challenges of assessing implicit likelihood functions inherent in previous methods, with our theoretical support for BASI showcased via the asymptotic properties of the posterior distribution.

In its final part, the dissertation delves into posterior contraction rates for Gaussian process regression in the context of data with low-dimensional structures. The conditions established enable adaptivity to any intrinsic dimension, thereby giving the optimal posterior contraction rate. This exploration is further enriched by an innovative empirical Bayes prior of bandwidth, dispensing with the necessity for prior knowledge of the intrinsic dimension.

Cumulatively, these three essays enhance Bayesian statistics for data with varying and intricate structures. The dissertation seamlessly intertwines theoretical contributions with practical numerical experiments, lending empirical weight to our innovative propositions.