Application of Bayesian graphs to SN Ia data analysis and compression

Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the joint light-curve analysis (JLA) data set. In contrast to the $\chi^2$ approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with $\chi^2$ analysis results, we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal 6 $\sigma$ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4 $\sigma$. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the $\chi^2$ analysis is due to neglecting the parameter-dependent log-determinant of the data covariance, which gives more statistical weight to larger values of the standardization parameters. We find a similar effect on compressed distance modulus data. To this end, we implement a fully consistent compression method of the JLA data set that uses a Gaussian approximation of the posterior distribution for fast generation of compressed data. Overall, the results of our analysis emphasize the need for a fully consistent Bayesian statistical approach in the analysis of future large SN Ia data sets.Comment: 14 pages, 13 figures, 5 tables. Submitted to MNRAS. Compression utility available at https://gitlab.com/congma/libsncompress/ and example cosmology code with machine-readable version of Tables A1 & A2 at https://gitlab.com/congma/sn-bayesian-model-example/ v2: corrected typo in author's name. v3: 15 pages, incl. corrections, matches the accepted versio

A Ridge-Regularised Jackknifed Anderson-Rubin Test

We consider hypothesis testing in instrumental variable regression models with few included exogenous covariates but many instruments -- possibly more than the number of observations. We show that a ridge-regularised version of the jackknifed Anderson Rubin (1949, henceforth AR) test controls asymptotic size in the presence of heteroskedasticity, and when the instruments may be arbitrarily weak. Asymptotic size control is established under weaker assumptions than those imposed for recently proposed jackknifed AR tests in the literature. Furthermore, ridge-regularisation extends the scope of jackknifed AR tests to situations in which there are more instruments than observations. Monte-Carlo simulations indicate that our method has favourable finite-sample size and power properties compared to recently proposed alternative approaches in the literature. An empirical application on the elasticity of substitution between immigrants and natives in the US illustrates the usefulness of the proposed method for practitioners

Development of a quantitative analysis system for greener and economically sustainable wind farms

This paper reports the development of a quantitative analysis system for selecting a greener and economically sustainable wind farm at the early design stage. A single wind turbine produces a limited amount of carbon emissions throughout its lifecycle. By taking a broader view, such as wind farms, collectively such an application would have a greater impact upon the environment and cost. Recent research on wind farms tends to focus on wind flow modelling to enable accurate prediction of power generation. Therefore, this paper presents a quantitative approach to predict a wind farm’s lifetime (i) carbon emissions and intensity; (ii) potential energy production; (iii) return on investment and (iv) payback time from an early design perspective. The overall contribution of this work is to develop a quantitative approach to enable the selection of ‘greener’ designs for reducing the environmental impacts of a wind farm with hub heights between 44 m and 135 m while still considering its economic feasibility assessment. This newly developed system could potentially be used by top-management and engineers of wind turbine manufacturers and wind energy service providers for cleaner energy provision

Integration of the environmental management aspect in the optimization of the design and planning of energy systems

The increasing concerns regarding the environmental pollution derived from anthropogenic activities, such as the use of fossil fuels for power generation, has driven many interested parties to seek different alternatives, e.g. use of renewable energy sources, use of “cleaner” fuels and use of more effective technologies, in order to minimize and control the quantity of emissions that are produced during the life cycle of conventional energy sources. In addition to these alternatives, the use of an integrated procedure in which the environmental aspect will be taken into account during the design and planning of energy systems could provide a basis on which emissions reduction will be dealt with a life cycle approach. The work presented in this paper focuses on the examination of the possibilities of integrating the environmental aspects in the preliminary phase of the conventional design and planning of energy systems in conjunction with other parameters, such as financial cost, availability, capacity, location, etc. The integration of the environmental parameter to the design is carried out within a context where Eco-design concepts are applied. Due to the multi-parameter nature of the design procedure, the tools that are used are Life Cycle Analysis and Multi-criteria Analysis. The proposed optimization model examines and identifies optimum available options of the use of different energy sources and technologies for the production of electricity and/or heat by minimizing both the financial cost and the environmental impacts, with regard to a multiple objective optimization subject to a set of specific constraints. Implementation of the proposed model in the form of a case study for the island of Rhodes in Greece revealed that an optimized solution both cost and environmental-wise, would be an almost balanced participation of renewables and non-renewable energy sources in the energy mix

Essays on weak identification in high-dimensional models with applications in macroeconomics

This thesis consists of four self-contained chapters. Chapter 2 (co-authored with Prof. Sophocles Mavroeidis and Prof. Anders Kock) considers hypothesis testing in instrumental variable (IV) regression models with few included exogenous covariates but many instruments--possibly more than the number of observations. We look for a method of inference that controls asymptotic size when there is heteroskedasticity and the instruments may be arbitrarily weak. We show that a ridge-regularised version of the jackknifed Anderson Rubin (1949, henceforth AR) test achieves this objective. This test weakens the assumptions needed for recently proposed jackknifed AR tests, and extends their scope to situations in which there are more instruments than observations. Monte-Carlo simulations indicate that our method has favourable finite-sample size and power properties compared to recently proposed alternative approaches in the literature. An empirical application on the elasticity of substitution between immigrants and natives in the US illustrates the usefulness of the proposed method for practitioners. Chapter 3 considers limited-information inference on New Keynesian Phillips Curves (NKPCs) in the presence of weak and high-dimensional IVs. Beyond the efficiency concerns previously raised in the literature, I show by simulation that ad-hoc selection procedures can lead to substantial biases in post-selection inference. I propose a Sup Score test that remains valid under dependent data, arbitrarily weak identification, and a number of IVs that increases exponentially with the sample size. Conducting inference on a standard NKPC with 361 IVs and 179 observations, I find substantially wider confidence sets than those commonly found. Chapter 4 (co-authored with Dr. Gerrit Koester and Dr. Christiane Nickel) addresses the endogeneity of slack in Phillips Curves in reduced-form contexts. Endogeneity of the labour market slack in reduced-form Phillips Curves is usually addressed either by including proxies for omitted supply shocks, or by using instrumental variables. Using the Kiviet (2022) Kinky Least Squares estimator, we find evidence that supply-shock proxies should not be omitted from PCs, and that many popular instrumental variables seem to be invalid. We estimate a standard backward-looking wage Phillips Curve by Kinky Least Squares and find that unless a large negative correlation between the slack variable and the error term is assumed, the coefficient of the slack variable is significantly negative. Chapter 5 provides a weak-identification robust IV method for identifying the structural covariance matrix in structural vector autoregressions (SVARs) where data for the reduced-form VAR are available over a longer horizon than for the IV. I apply this method to analyse the effect of US monetary shocks on real and financial variables in the US and other countries. While the effects on US real and financial variables are qualitatively similar to those reported previously in the literature, I find little evidence for US monetary policy spillovers in countries other than the US, in line with the theoretical predictions of the Mundellian Trilemma.</p

Energy Policy and Climate Change: A Multidisciplinary Approach to a Global Problem

In the period between the end of the Second World War and the oil crises of 1973 and 1979, the most critical issues in the energy debate were the impending depletion of non-renewable resources and the level of pollution that the environment is able to sustain. [...

Energy Policy and Climate Change: A Multidisciplinary Approach to a Global Problem

In the period between the end of the Second World War and the oil crises of 1973 and 1979, the most critical issues in the energy debate were the impending depletion of non-renewable resources and the level of pollution that the environment is able to sustain. [...