<p>Bridging the accuracy of ab initio (AI) QM/MM with the efficiency of semi-empirical<br> (SE) QM/MM methods has long been a goal in computational chemistry. This dissertation<br> presents four ∆-Machine learning schemes aimed at achieving this objective. Firstly, the in-<br> corporation of negative force observations into the Gaussian process regression (GPR) model,<br> resulting in GPR with derivative observations, demonstrates the remarkable capability to<br> attain high-quality potential energy surfaces, accurate Cartesian force descriptions, and reli-<br> able free energy profiles using a training set of just 80 points. Secondly, the adaptation of the<br> sparse streaming GPR algorithm showcases the potential of memory retention from previous<br> phasespace, enabling energy-only models to converge using simple descriptors while faith-<br> fully reproducing high-quality potential energy surfaces and accurate free energy profiles.<br> Thirdly, the utilization of GPR with atomic environmental vectors as input features proves<br> effective in enhancing both potential energy surface and free energy description. Further-<br> more, incorporating derivative information on solute atoms further improves the accuracy<br> of force predictions on molecular mechanical (MM) atoms, addressing discrepancies arising<br> from QM/MM interaction energies between the target and base levels of theory. Finally, a<br> comprehensive comparison of three distinct GPR schemes, namely GAP, GPR with an aver-<br> age kernel, and GPR with a system-specific sum kernel, is conducted to evaluate the impact<br> of permutational invariance and atomistic learning on the model’s quality. Additionally, this<br> dissertation introduces the adaptation of the GAP method to be compatible with the sparse<br> variational Gaussian processes scheme and the streaming sparse GPR scheme, enhancing<br> their efficiency and applicability. Through these four ∆-Machine learning schemes, this dis-<br> sertation makes significant contributions to the field of computational chemistry, advancing<br> the quest for accurate potential energy surfaces, reliable force descriptions, and informative<br> free energy profiles in QM/MM simulations.<br> </p>

The dissertation focuses on the different determinants of education, their effects on the educational outcome, and the overall effect of education on the lifetime consequences. The first chapter focuses on the inequality of educational opportunity across different demographic factors. This chapter employs a broader set of social factors to provide fresh insights into the inequality situation in the USA relative to those of the extant literature. The chapter employs polynomial trends for the effects of social factors to identify long-term trends in the determinants of the differences in attainment of each of four achievements (high school graduation, some college, college graduation, and post-college work) across different endogenous social groups. Using the Panel Study of Income Dynamics (PSID) data for the years of 1968-2013, we show how inequality of educational opportunity and its determinants have evolved over the years. The chapter utilizes the machine-learning process and logistic regression model to identify inequality of opportunity. The second chapter examines the age demographic distribution of graduates across cohorts from 1940 until 1990. Using the PSID data, the paper explored the first and second moment of the age of graduating from high school and college across the US. To deal with the data deficiencies, a large part of the chapter dealt with data preparation. The chapter provides a unique method of extracting information on the graduating age of the individuals both from high school and from college. The results show a large dispersion across the full sample. The data truncated to a standard length, however, provides a much smaller dispersion and much smaller moments. The chapter concludes that as the time passes, people tend to attain education at a younger age. The third chapter investigates the trends of the contribution of different factors of income starting from 1910 cohort. Following Mincer (1974), a wave of papers studied how various factors contribute to the earnings of individuals. This paper contributes to that literature in three ways: (i) using the PSID data, it computes the actual working experience of the individuals, (ii) it studies the cohorts who were born in 1910 or afterwards, unlike the existing papers, and (iii) it adds two variables—technological progress and the occupation with which individuals start their careers—to an extended Mincerian equation. The results re-emphasize the importance of education in lifetime earnings. The results also show that while some of the determinants of income have become more important over the years, other factors have not changed much in importance. / PHD / The reason for choosing the theme ‘Evolution of the Determinants of Educational Attainment and its Consequences’ was to investigate the different determinants of education, their effects on the educational outcome, and the overall effect of education on the lifetime consequences. Education is considered as one of the tools to eradicate poverty. Yet, countries with high educational coverage keeps suffering from poverty, a reason for which is higher inequality of opportunity. In the first chapter, entitled ‘Inequality in Educational Opportunity in the United States’, opportunity inequality in education is illustrated. Much inequality stems from differences in educational attainment. A lack of educational attainment puts an individual behind in the career race, even before the race has started. While individuals are responsible for some of the differences in educational attainment, there are factors outside the control of individuals that play substantial roles. The inequality that arises from these factors is known as inequality of opportunity. This paper focuses on inequality of educational opportunity across socioeconomic background, race, and sex. The factors that are analyzed for their contributions to inequality of educational opportunity are father’s education, father’s occupation, mother’s education, and economic status of the individual’s family. The results show that inequality of opportunity has seen a consistent decline for high school completion. The inequality of opportunity (IO) declines for obtaining some college education for the bottom two social groups and remained persistent for the relatively more advantaged group. For college/post-college education, the IO is much lower and, in general, remained persistent across the social strata. Although the females were behind the males – given the equal opportunity – regardless of the race and socioeconomic status during the beginning and the mid twentieth century, the scenario reversed in the late twentieth century. In terms of educational disparity among races, African Americans trail their White counterparts along all the years. The second chapter ‘First and Second Moments of the Age Distributions of Graduates’ looks into the age characteristics (mean and variance) in graduating from high school and college across the cohorts from 1940s to 1990s. The idea of the paper largely came from the first chapter of the dissertation as we assumed the lack of opportunity at the earlier age could delay the attainment of education. The paper intends to find out the average age of graduation over the years. In the process, the paper put forward a method to extract the information of age of graduation from the Panel Study of Income Dynamics (PSID) data, as the database does not readily avail the information. The chapter concludes that as the time passes, people tend to attain education at a much younger age. Titled as ‘Factors Affecting Income: Education, Experience, and Beyond’, the third chapter investigates the contribution of different factors – education, experience, parental endowments, and labor market conditions – in the returns to education using the PSID data and compare the more recent scenarios with the past. This paper focuses on the trend of the rate of return to different factors of income across the two cohorts – those born between 1910 and 1950, and those born after 1950 – while identifying the changes in the returns for the same education level over time. The paper aims to find out how the contribution of the different factors of earning has changed in the USA over the years. The paper also intends to find out the role of technological progress in reducing the earning gaps across the different social groups. The results re-emphasize the importance of education in lifetime earnings. Experience has become a more important factor of income over the years. The chapter also suggests that income of an individual is a monotonic function of socioeconomic endowments and better endowments resulted in higher returns. Lastly, the chapter finds that the technological investment is progressive in manner.

Pathway is a set of genes which are predefined and serve a particular celluar or physiological function. Ranking pathways relevant to a particular phenotype can help researchers focus on a few sets of genes in pathways. In this thesis, a Bayesian hierarchical latent model was proposed using generalized linear random effects model. The advantage of the approach was that it can easily incorporate prior knowledges when the sample size was small and the number of genes was large. For the covariance matrix of a set of random variables, two Gaussian random processes were considered to construct the dependencies among genes in a pathway. One was based on the polynomial kernel and the other was based on the Gaussian kernel. Then these two kernels were compared with constant covariance matrix of the random effect by using the ratio, which was based on the joint posterior distribution with respect to each model. For mixture models, log-likelihood values were computed at different values of the mixture proportion, compared among mixtures of selected kernels and point-mass density (or constant covariance matrix). The approach was applied to a data set (Mootha et al., 2003) containing the expression profiles of type II diabetes where the motivation was to identify pathways that can discriminate between normal patients and patients with type II diabetes. / Master of Science

The UK building stock accounts for about half of all energy consumed in the UK. A large portion of the energy is consumed by nondomestic buildings. Offices and retail are the most energy intensive typologies within the nondomestic building sector, typically accounting for over 50% of the nondomestic buildings’ total energy consumption. Heating, ventilating and air conditioning (HVAC) systems are the largest energy end use in the nondomestic sector, with energy consumption close to 50% of total energy consumption. Different HVAC systems have different energy requirements when responding to the same building heating and cooling demands. On the other hand, building heating and cooling demands depend on various parameters such as building fabrics, glazing ratio, building form, occupancy pattern, and many others. HVAC system energy requirements and building energy demands can be determined by mathematical modelling. A widely accepted approach among building professionals is to use building energy simulation tools such as EnergyPlus, IES, DOE2, etc. which can analyse in detail building energy consumption. However, preparing and running simulations in such tools is usually very complicated, time consuming and costly. Their complexity has been identified as the biggest obstacle. Adequate alternatives to complex building energy simulation tools are regression models which can provide results in an easier and faster way. This research deals with the development of regression models that enable the selection of HVAC systems for office buildings. In addition, the models are able to predict annual heating, cooling and auxiliary energy requirements of different HVAC systems as a function of office building heating and cooling demands. For the first part of the data set development used for the regression analysis, a data set of office building simulation archetypes was developed. The four most typical built forms (open plan sidelit, cellular sidelit, artificially lit open plan and composite sidelit cellular around artificially lit open plan built form) were coupled with five types of building fabric and three levels of glazing ratio. Furthermore, two measures of reducing solar heat gains were considered as well as implementation of daylight control. Also, building orientation was included in the analysis. In total 3840 different office buildings were then further coupled with five different HVAC systems: variable air volume system; constant air volume system; fan coil system with dedicated air; chilled ceiling system with embedded pipes, dedicated air and radiator heating; and chilled ceiling system with exposed aluminium panels, dedicated air and radiator heating. The total number of models simulated in EnergyPlus, in order to develop the input database for regression analysis, was 23,040. The results clearly indicate that it is possible to form a reliable judgement about each different HVAC system’s heating, cooling and auxiliary energy requirements based only on office building heating and cooling demands. High coefficients of determination of the proposed regression models show that HVAC system requirements can be predicted with high accuracy. The lowest coefficient of determination among cooling regression models was 0.94 in the case of the CAV system. HVAC system heating energy requirement regression models had a coefficient of determination above 0.96. The auxiliary energy requirement models had a coefficient of determination above 0.95, except in the case of chilled ceiling systems where the coefficient of determination was around 0.87. This research demonstrates that simplified regression models can be used to provide design decisions for the office building HVAC systems studied. Such models allow more rapid determination of HVAC systems energy requirements without the need for time-consuming (hence expensive) reconfigurations and runs of the simulation program.

This paper directs interest on country-specific labour market discrimination Roma may suffer in South East Europe. The study lies in the tradition of statistical Blinder-Oaxaca decomposition analysis. We use microdata from UNDP's 2004 survey of Roma minorities, and apply a Bayesian approach, proposed by Keith and LeSage (2004), for the decomposition analysis of wage differentials. This approach is based on a robust Bayesian heteroscedastic linear regression model in conjunction with Markov Chain Monte Carlo (MCMC) estimation. The results obtained indicate the presence of labour market discrimination in Albania and Kosovo, but point to its absence in Bulgaria, Croatia, and Serbia. (authors' abstract)

在我們建立迴歸模型時，必須針對研究的目的去探求與相依變數有關的自變數，而且 這些自變數應能合理的解釋相依變數，然而這些自變數的組合數一定很大；所以在一 般線性迴歸分析中，最重要也是最困難的問題是如何選取模式中的自變數，棄卻不太 重要的自變數，獲得最後的模型，以符合經濟原則。 而近年來非線性迴歸模型在各種領域裡廣泛地被使用，這些線性回歸模型之自變數的 選取較線性迴歸模型之自變數的選取困難，因其必須用反覆的技術來找最大概似估計 量，然後利用此最大概似估計量來做為選取自變數的基礎所以計算的成本較高。 本文將以處理相依變數為屬質變數的羅吉斯迴歸模型（LOGISTIC REGRESSION MODEL ）為主要研究對象；首先導出此模型的CP統計量，以CP來作為選取自變數的準則；其 次介紹一種透過對數概似近似函數及一些資料的轉換，將羅吉斯迴歸模型之自變數選 擇問題變換成一般線性迴歸模型的自變數選擇問題；然後作一個模擬分析比較不經變 數變換與經變數變換的方法，所選出的自變數組合是否大致相同，若其差異不大，則 表示此種變數變換方法確時有效，往後遇到類似的非線性迴歸之自變數的選取都可轉 換成一般線性迴歸的問題來解決，可簡化許多計算過程，此亦為本文研究的目的。 本文結構：本文共分六章 第一章 緒論，說明井究動機與目的 第二章 建立羅吉斯迴歸模型（LOGISTIC REGRESSION MODEL ）及定義其殘差（ RESIDUAI） 第三章 探討非線性模型之自變數選擇方法及針對LOGISTIC REGRESSION 求其CP統計 量。 第四章 介紹一重經過變數變換的自變數選擇程序及其應用的原理。 第五章 模擬分析，比較第三章與第四章所述二種方法的差異。 第六章 結論。

我國全面開放保險市場後，壽險業所面臨市場競爭更加激烈，經營風險亦隨之增加，甚至影響其經營績效。本文以資料包絡分析法（DEA）評估2002年至2004年我國人壽保險公司的經營效率，並找出相對無效率壽險公司改善空間,再以Tobit截斷迴歸模型探討可能造成壽險公司之間經營效率差異的影響因素。其中由DEA技術效率評估結果發現：(一) 壽險公司整體技術效率平均值介於50.98﹪與70.15﹪之間，代表我國壽險公司在投入資源運用與配置上仍存有改善空間，在產出不變下，平均而言，可以節省29.85%至49.02%的資源使用量。（二）純技術效率值大於規模效率平均值，顯示造成壽險公司技術無效率之來源，資源浪費及生產規模不適當所造成的情況均有，但大部分來自於前者。迴歸實證結果顯示：（一）外勤兼職人員比率與技術效率具正向關係，顯示壽險公司僱用兼職人員招攬業務，相對專職人員可減少人事成本，可提昇經營績效。（二）國外投資比例與技術效率具正向關係，即壽險公司因國外投資商品多樣化選擇，可靈活運用資金，提昇技術效率。（三）佣金率與技術效率具正向關係，代表壽險公司支付業務員佣金及津貼愈高，愈能激勵業務員積極招攬業務，增進公司業務績效，以提高技術效率。（四）逾期放款比率與技術效率為負向關係，即壽險公司逾期放款比率愈高，績營效率愈差。（五）市場占有率與技術效率為正向關係，顯示壽險公司市場占有率愈高，對市場的控制能力較佳，在產品銷售亦具有規模經濟，可提昇經營效率。（六）外內勤人員比例與技術效率為負向關係，表示外內勤人員比例愈高，壽險公司易忽略內勤行政人員在核保、理賠及客服等作業品質，將影響公司產品創新及保戶後續權益等，不利公司經營績效。

過去三、四十年來世界各地發生金融危機的頻率較從前高出許多，探究原因後可以發現，與各國陸續開放金融自由化以及國際金融市場快速成長有極大的關係。除此之外，在各國中，金融危機的發生通常具備一些共同特徵，諸如危機發生時會導致資金外流、匯率大幅貶值、股市重挫、產出減少、進出口減少…等影響。因此，面對這一波次級房貸風暴，本研究也即將檢視美國在總體經濟數據上各方面的表現，希望能利用1970年以來已開發國家和開發中國家歷年來所發生的貨幣、銀行危機下所代表的各種總體經濟數據，經過轉化整理後，透過Logistic迴歸模型建立一個迴歸方程式，以了解金融危機的發生與實質匯率、進出口…等其他解釋變數之間的關聯，並利用此模型探測現階段次級房貸風暴對美國可能引發金融危機的機率值，以探討其合理性。 / We find that the frequencies of the financial crises are higher for the past forty years in the world. It is due to the financial liberalization and international financial markets which grow rapidly. Besides, financial crises usually company with some common characteristics such as capital outflow, the depreciation of the foreign exchange, the shock of the stock market, the decreasing of the production and so on. Therefore, in order to understand this financial crisis of the subprime mortgage, this thesis surveys the economic data of developed countries and developing countries from 1970s and figures out the performances of these countries under balance-of -payments crises or banking crisis. We use the logistic regression model and transform the data to construct a regression model. After understanding the relationship between the explaining variables, we use this model to predict the probability of possible financial crisis in U.S. under the subprime mortgage crisis and then discuss the rationality of those predicted values.

China's economic development has performed spectacularly during the period of China's economic transition as a result of radical economic reform in the all markets. The country has also gone through extensive fiscal reforms in the last three decades. However, a number of problems have been associated with such rapid economic growth. One of these has been raising inequality. In both Keynesian and neoclassical endogenous growth theories, public spending can play an important role for economic growth and inequality. The majority of previous studies have focused on the relationship between public spending and economic growth, or between public spending and inequality separately. There is no doubt that public spending has an effect on both economic growth and equity simultaneously. In this respect, this thesis attempts to address the problems that have emerged during the period of China's fiscal reforms, and seeks to examine the effects of public spending on economic growth and equality in the same model. This thesis investigates the dynamic relationships among these three variables in China. For aggregate national data, vector error correction model (VECM) has been used. Analysis at the provincial level is based on the panel vector auto-regression (PVAR) model. These methods help to solve the endogeneity in estimations. The national level analysis indicates that total public spending shows a long term Granger causality with GDP per capita, which supports the positive growth effect of public spending in the Keynesian and endogenous growth model. Social public spending has a negative effect on real output per capita in both the short term and long term, but it also has a negative impact on income inequality. Moreover, we find that a higher level of real GDP per capita will increase the level of inequality, but a higher level of inequality has a negative effect on real GDP per capita in the long term. Furthermore, total provincial public spending and provincial social spending have either a non-significant effect on economic growth. On the other hand, the SOEs' investment has a significant, positive growth effect at both the national and provincial level. As for the redistributive role of the public spending, the provincial total public spending and social spending have played an important role on income distribution. Furthermore, the Gini coefficient has a positive effect on the per capita growth rate at the provincial level, but the economic growth has no significant impact on the Gini coefficient.

This thesis investigates which factors affecting savings behavior by using a fixed effect regression model. To see what affects the household savings rate the following independent variables is considered: Natural logarithm of trend per capita income, natural logarithm of deviation from trend per capita income, growth of disposable income, real interest rate, inflation, wealth in relation to household disposable income, foreign savings in relation to disposable income, dependency ratio and human development index. To see whether changes of human development within a county impacts the household´s savings ratio this variables was included in a separate regression. To avoid possible biasedness from ordinary least square, a panel data technique called fixed effect regression model is used. The investigated time period is between year 1999 and 2016 and to make a restriction, variables from 25 developed countries were studied. The involved economic theories in this work are Keynesianism, permanent income hypothesis and the savings theory behind Maslow´s behavioral pyramid. The result made by using this study is that growth in income and foreign savings in relation to disposable income is insignificant and can´t be used in explaining the differences between household´s savings. Human development index within a country has a negative effect on the savings ratio but a conclusion regarding whether changes in HDI´s does affect savings can´t be made and more research within that field is needed.