Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

Car ownership modeling and forecasts for China

A great increase of private car ownership took place in China from 1980 to 2009 with the development of the economy. To explain the relationship between car ownership and economic and social changes, an ordinary least squares linear regression model is developed using car ownership per capita as the dependent variable with GDP, savings deposits and highway mileages per capita as the independent variables. The model is tested and corrected for econometric problems such as spurious correlation and cointegration. Finally, the regression model is used to project oil consumption by the Chinese transportation sector through 2015. The result shows that about 2.0 million barrels of oil will be consumed by private cars in conservative scenario, and about 2.6 million barrels of oil per day in high case scenario in 2015. Both of them are much higher than the consumption level of 2009, which is 1.9 million barrels per day. It also shows that the annual growth rate of oil demand by transportation is 2.7% - 3.1% per year in the conservative scenario, and 6.9% - 7.3% per year in the high case forecast scenario from 2010 to 2015. As a result, actions like increasing oil efficiency need to be taken to deal with challenges of the increasing demand for oil.

Towards greater accuracy in individual-tree mortality regression

Background mortality is an essential component of any forest growth and yield model. Forecasts of mortality contribute largely to the variability and accuracy of model predictions at the tree, stand and forest level. In the present study, I implement and evaluate state-of-the-art techniques to increase the accuracy of individual tree mortality models, similar to those used in many of the current variants of the Forest Vegetation Simulator, using data from North Idaho and Montana. The first technique addresses methods to correct for bias induced by measurement error typically present in competition variables. The second implements survival regression and evaluates its performance against the traditional logistic regression approach. I selected the regression calibration (RC) algorithm as a good candidate for addressing the measurement error problem. Two logistic regression models for each species were fitted, one ignoring the measurement error, which is the “naïve” approach, and the other applying RC. The models fitted with RC outperformed the naïve models in terms of discrimination when the competition variable was found to be statistically significant. The effect of RC was more obvious where measurement error variance was large and for more shade-intolerant species. The process of model fitting and variable selection revealed that past emphasis on DBH as a predictor variable for mortality, while producing models with strong metrics of fit, may make models less generalizable. The evaluation of the error variance estimator developed by Stage and Wykoff (1998), and core to the implementation of RC, in different spatial patterns and diameter distributions, revealed that the Stage and Wykoff estimate notably overestimated the true variance in all simulated stands, but those that are clustered. Results show a systematic bias even when all the assumptions made by the authors are guaranteed. I argue that this is the result of the Poisson-based estimate ignoring the overlapping area of potential plots around a tree. Effects, especially in the application phase, of the variance estimate justify suggested future efforts of improving the accuracy of the variance estimate. The second technique implemented and evaluated is a survival regression model that accounts for the time dependent nature of variables, such as diameter and competition variables, and the interval-censored nature of data collected from remeasured plots. The performance of the model is compared with the traditional logistic regression model as a tool to predict individual tree mortality. Validation of both approaches shows that the survival regression approach discriminates better between dead and alive trees for all species. In conclusion, I showed that the proposed techniques do increase the accuracy of individual tree mortality models, and are a promising first step towards the next generation of background mortality models. I have also identified the next steps to undertake in order to advance mortality models further.

Free Troposphere Ozone and Carbon Monoxide over the North Atlantic for 2001-2011

Carbon Monoxide (CO) and Ozone (O3) are considered to be one of the most important atmospheric pollutants in the troposphere with both having significant effects on human health. Both are included in the U.S. E.P.A list of criteria pollutants. CO is primarily emitted in the source region whereas O3 can be formed near the source, during transport of the pollution plumes containing O3 precursors or in a receptor region as the plumes subside. The long chemical lifetimes of both CO and O3 enable them to be transported over long distances. This transport is important on continental scales as well, commonly referred to as inter-continental transport and affects the concentrations of both CO and O3 in downwind receptor regions, thereby having significant implications for their air quality standards. Over the period 2001-2011, there have been decreases in the anthropogenic emissions of CO and NOx in North America and Europe whereas the emissions over Asia have increased. How these emission trends have affected concentrations at remote sites located downwind of these continents is an important question. The PICO-NARE observatory located on the Pico Mountain in Azores, Portugal is frequently impacted by North American pollution outflow (both anthropogenic and biomass burning) and is a unique site to investigate long range transport from North America. This study uses in-situ observations of CO and O3 for the period 2001-2011 at PICO-NARE coupled with output from the full chemistry (with normal and fixed anthropogenic emissions) and tagged CO simulations in GEOS-Chem, a global 3-D chemical transport model of atmospheric composition driven by meteorological input from the Goddard Earth Observing System (GEOS) of the NASA Global Modeling and Assimilation Office, to determine and interpret the trends in CO and O3 concentrations over the past decade. These trends would be useful in ascertaining the impacts emission reductions in the United States have had over Pico and in general over the North Atlantic. A regression model with sinusoidal functions and a linear trend term was fit to the in-situ observations and the GEOS-Chem output for CO and O3 at Pico respectively. The regression model yielded decreasing trends for CO and O3 with the observations (-0.314 ppbv/year & -0.208 ppbv/year respectively) and the full chemistry simulation with normal emissions (-0.343 ppbv/year & -0.526 ppbv/year respectively). Based on analysis of the results from the full chemistry simulation with fixed anthropogenic emissions and the tagged CO simulation it was concluded that the decreasing trends in CO were a consequence of the anthropogenic emission changes in regions such as USA and Asia. The emission reductions in USA are countered by Asian increases but the former have a greater impact resulting in decreasing trends for CO at PICO-NARE. For O3 however, it is the increase in water vapor content (which increases O3 destruction) along the pathways of transport from North America to PICO-NARE as well as around the site that has resulted in decreasing trends over this period. This decrease is offset by increase in O3 concentrations due to anthropogenic influence which could be due to increasing Asian emissions of O3 precursors as these emissions have decreased over the US. However, the anthropogenic influence does not change the final direction of the trend. It can thus be concluded that CO and O3 concentrations at PICO-NARE have decreased over 2001-2011.