Analysis of High dimensional Gibbs samplers and Bayesian modeling of climate data
Abstract
This project has two interconnected themes: (i) Analysis of high dimensional Gibbs samplers occurring in the context of Bayesian statistics and models from statistical physics, (ii) Developing Bayesian methodology for analyzing climate data, including bias correction, and design of novel Markov ChainMonte Carlo algorithms for statistical inference for these complex data.The first part of my proposed research will develop new tools in probability theory with the primary goal of answering foundational questions in mathematical physics and computational statistics that have a similar mathematical structure.The second part of the proposal deals with the following problem. Long, high-quality records of temperature provide an important basis for our understanding of climate variability and change. Historically, there has been a focus on monthly-average temperature records, which are sufficient for certain analyses, such as quantifying long-term changes in temperature. As our knowledge of climate change expands, however, there is increasing interest in understanding changes in temperature on shorter timescales, with a particular focus on extreme events. To do so, it is necessary to utilize higher-resolutiontemperature data. Recent work has led to the development of the Global Historical Climatology Network- Daily (GHCND) database, which contains, among other variables, daily maximum and minimum temperaturesfrom weather stations around the globe. The database draws from a range of different sources, and the data within it undergoes basic quality control to remove erroneous values.The current quality control methodology, however, does not account for so-called ???inhomogeneities???. Inhomogeneities result from changes in measurement practices that impact the recorded temperatures.While this may be sufficient for monthly data, it is known that certain changes in measurement practices affect different percentiles of daily temperature in different ways. To address this issue, some homogenization methods have also employed percentile matching techniques, wherein the adjustment to atimeseries after a breakpoint is a function of percentile. In this proposal, we detail a radically different approach based on constrained Markov Chain Monte Carlo methods and missing data.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 27, 2018
- Source ID
- N000141812730
Entities
People
- Natesh Pillai
Organizations
- Office of Naval Research
- President and Fellows of Harvard College
- United States Navy