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Thesis (Ph.D.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2009/11/06). Includes bibliographical references.

In structural equation models, researchers often examine two types of causal effects: direct and indirect effects. Direct effects involve variables that "directly" influence other variables, whereas indirect effects are transmitted via intervening variables. While researchers have paid considerable attention to the distribution of sample direct effects, the distribution of sample indirect effects has only recently been considered. Using the (delta) method (Rao, 1973), Sobel (1982) derived the asymptotic distribution for estimators of indirect effects in recursive systems. Sobel (1986) then derived the asymptotic distribution for estimators of total indirect effects in the Joreskog covariance structure model (Joreskog, 1977). This study examined the applicability of the large sample theory described by Sobel (1986) in small samples. Monte Carlo methods were used to evaluate the behavior of estimated total indirect effects in sample sizes of 50, 100, 200, 400, and 800. Two models were used in the analysis. Model 1 was a nonrecursive model with latent variables, feedback, and functional constraints among the effects (Duncan, Haller, & Portes, 1968; Sobel, 1986). Model 2 was a recursive model with observable variables (Duncan, Featherman, & Duncan, 1972). In addition, variations in these models were studied by randomly increasing and decreasing model parameters. The principal findings of the study suggest certain guidelines for researchers who use Sobel's procedures to evaluate total indirect effects in structural equation models. In order for the behavior of the estimates to approximate the asymptotic properties, sample sizes of 400 or more are indicated for nonrecursive systems similar to Model 1, and for recursive systems such as Model 2, sample sizes of 200 or more are suggested. At these sample sizes, researchers can expect sample indirect effects to be accurate point estimators, and confidence intervals for the effects to behave as theory predicts. A caveat to the above guidelines is that, when the total indirect effects are "small" in magnitude, relative to the scale of the model, convergence to the asymptotic properties appears to be very slow. Under these conditions, sampling distributions for the "smaller" valued estimates were positively skewed. This caused estimates to be significantly different from true values, and confidence intervals to behave contrary to theoretical expectations.

A new Tropical Cyclone (TC) surface wind speed probability product from the National Hurricane Center (NHC) takes into account uncertainty in track, maximum wind speed, and wind radii. A Monte Carlo (MC) model is used that draws from probability distributions based on historic track errors. In this thesis, distributions of forecast track errors conditioned on forecast confidence are examined to determine if significant differences exist in distribution characteristics. Two predictors are used to define forecast confidence: the Goerss Predicted Consensus Error (GPCE) and the Global Forecast System (GFS) ensemble spread. The distributions of total-, along-, and crosstrack errors from NHC official forecasts are defined for low, average, and high forecast confidence. Also, distributions of the GFS ensemble mean total-track errors are defined based on similar confidence levels. Standard hypothesis testing methods are used to examine distribution characteristics. Using the GPCE values, significant differences in nearly all track error distributions existed for each level of forecast confidence. The GFS ensemble spread did not provide a basis for statistically different distributions. These results suggest that the NHC probability model would likely be improved if the MC model would draw from distributions of track errors based on the GPCE measures of forecast confidence / US Air Force (USAF) author.

M.Com.(Econometrics) / The objective of this study is to evaluate different estimation techniques that can be used to estimate the coefficients of a model. The estimation techniques were applied to empirical data drawn from the South African economy. The Monte Carlo studies are unique in that data was statistically generated for the experiments. This approach was due to the fact that actual observations on economic variables contain several econometric problems, such as autocorrelation and MUlticollinearity, simultaneously. However, the approach in this study differs in that empirical data is used to evaluate the estimation techniques. The estimation techniques evaluated are : • Ordinary least squares method • Two stage least squares method • Limited information maximum likelihood method • Three stage least squares method • Full information maximum likelihood method. The estimates of the different coefficients are evaluated on the following criteria : • The bias of the estimates • The variance of the estimates • t-values of the estimates • The root mean square error. The ranking of the estimation techniques on the bias criterion is as follows : 1 Full information maximum likelihood method. 2 Ordinary least squares method 3 Three stage least squares method 4 Two stage least squares method 5 Limited information maximum likelihood method The ranking of the estimation techniques on the variance criterion is as follows : 1 Full information maximum likelihood method. 2 Ordinary least squares method 3 Three stage least squares method 4 Two stage least squares method 5 Limited information maximum.likelihood method All the estimation techniques performed poorly with regard to the statistical significance of the estimates. The ranking of the estimation techniques on the t-values of the estimates is thus as follows 1 Three stage least squares method 2 ordinary least squares method 3 Two stage least squares method and the limited information maximum likelihood method 4 Full information maximum likelihood method. The ranking of the estimation techniques on the root mean square error criterion is as follows : 1 Full information maximum likelihood method and the ordinary least squares method 2 Two stage least squares method 3 Limited information maximum likelihood method and the three stage least squares method The results achieved in this study are very similar to those of the Monte Carlo studies. The only exception is the ordinary least squares method that performed better on every criteria dealt with in this study. Though the full information maximum likelihood method performed the best on two of the criteria, its performance was extremely poor on the t-value criterion. The ordinary least squares method is shown, in this study, to be the most constant performer.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science. August 2016. / Monte Carlo Tree Search (MCTS) is a family of directed search algorithms that has gained widespread attention in recent years. It combines a traditional tree-search approach with Monte Carlo simulations, using the outcome of these simulations (also known as playouts or rollouts) to evaluate states in a look-ahead tree. That MCTS does not require an evaluation function makes it particularly well-suited to the game of Go — seen by many to be chess’s successor as a grand challenge of artificial intelligence — with MCTS-based agents recently able to achieve expert-level play on 19×19 boards. Furthermore, its domain-independent nature also makes it a focus in a variety of other fields, such as Bayesian reinforcement learning and general game-playing. Despite the vast amount of research into MCTS, the dynamics of the algorithm are still not yet fully understood. In particular, the effect of using knowledge-heavy or biased simulations in MCTS still remains unknown, with interesting results indicating that better-informed rollouts do not necessarily result in stronger agents. This research provides support for the notion that MCTS is well-suited to a class of domain possessing a smoothness property. In these domains, biased rollouts are more likely to produce strong agents. Conversely, any error due to incorrect bias is compounded in non-smooth domains, and in particular for low-variance simulations. This is demonstrated empirically in a number of single-agent domains. / LG2017

本論文主要包括三種量子蒙地卡羅(QMC)方法的介紹及將其應用到不同的強關聯系統的結果。當中所涉及的強關聯系統主要是兩個不同的量子液體系統--自旋液體及玻色液體。 / 第二章將詳細介紹三個QMC方法，包括針對非零溫巨正則系統的行列式蒙地卡羅方法(DQMC)，針對零溫正則系絶並解決部分負值問題的限制線軌蒙地卡羅方法(CPMC)，及主要應用在非零溫雜質系統上的Hirsch-Fye蒙地卡羅方法(HFQMC)。 / 自發現高溫起導體以後，其奇異特性如具有非費米液體特性的贗能隙(Pseudogap)引起科學界爭論，由此提出很多不同的理論嘗試解釋。RVB是其中一個具代表性的理論，當中把高溫超導體理解成輕度摻雜的莫特絶緣體(Mott insulator)及引入自旋－電荷分離(charge-spin separation)把系統兩個自由度分開處理，具費米特性的自旋子(spinon)及具玻色特性的空穴子(holon)因而產生。這兩種準粒子的特性在解釋高溫超導的奇異性中最為關鍵。 / 第三章將應用DQMC及CPMC研究擁有各向及各自旋相異費米面的吸引勢赫伯德模型。模型的起源在於有理論[1]提出玻色子的基態有可能因阻挫作用而不發生愛因斯坦-玻色凝聚，這種非凝聚的基態稱為d-波玻色液體。在本研究所採用的模型中，將由庫柏電子對取代原先的正則玻色子。模型在準一准雙排梯子晶格的特性最近已被密度矩阵重整化群(DMRG)方法詳細研究[2]，而本研究將率先使用QMC方法研究模型在準一維雙排、四排梯子及二維正方晶格的特性。QMC有部分證據顯示電子對液體確實在二維存在，在本論文中會作出交代。 / 第四章將應用CPMC研究阻挫作用(frustration)下的排斥勢赫伯德模型，而其具體晶格情況為在正方格子上加上單向斜線躍遷項，稱為t-t'-TH模型。有證據提出在此模型中有可能存自旋液體的基態，並可有效解釋最近在實驗中所觀察到的有機超導體超低溫自旋無序的特性[3]。t-t'-TH模型的導帶半滿情況被曾各種方法詳細研究，本項研究將採用不同 的導帶填充情況及阻挫作用強度，用其比較以觀察阻挫作用對模型基態自旋作用的影響。研究發現阻挫作用將對不同的長程自旋序作出不同程度的影響。 / 第五章則會說明HFQMC的可能應用，在雜質系統如安德遜模型中，HFQMC是研究其非零溫特性的有效方法。此外，這章亦會交代未來在這方面可能進行的研究，而最後一章則會總結全文。 / In this thesis, three quantum Monte Carlo(QMC) algorithms would be reviewed, including determinant Quantum Monte Carlo (DQMC), constraint path Quantum Monte Carlo(CPMC) and Hirsch-Fye Quantum Monte Carlo (HFQMC). These QMC methods would be used to study strongly correlated system. In chapter 3 and 4, DQMC and CPMC methods would be used to study two kinds of quantum liquid, Bose liquid and spin liquid. In chapter 5, the possible application of HFQMC would be discussed. / After the discovery of high T{U+ABB1} cuprate, intensive effort has been paid to construct its theoretical explanation. One of the most puzzling features in cuprate is the pseudogap(strange-metal) phase with non-Fermi liquid behaviour. To search for an non-Fermi liquid to represent this phase, resonating valence bond(RVB) theory proposed a picture of lightly doped spin liquid. Fermionic spinon and bosonic holon arise from the spin-charge separation, and the behaviors of these quasi-particle are important for explanation for high T{U+ABB1} superconductivity. / In chapter 3, we study possible Bose liquid. Motrunich and Fisher [1] proposed a possible uncondensed bosonic phase d-wave Bose liquid(DBL) which will not undergo BEC at ground state. A prior studies[2] has shown that Cooper pairs can be used to replace bosons and N-leg ladder lattice could be used to approach behaviour of 2D lattice. Inspired by them, determinant quantum Monte Carlo(DQMC) and constraint path Monte Carlo(CPMC) techniques are used to study the fermionic attractive Hubbard Model with spin-independent anisotropic Fermi surface. The probable (Local) Cooper Pair Bose metal is detected in 2-leg, 4-leg ladder and 2D lattice. / In chapter 4, we study possible spin liquid. The Hubbard model on an anisotropic triangular lattice called t - t¹ - TH model has been proposed to possess a non-magnetic insulating(spin liquid) state, induced by geometrical frustration. The effect of filling and degree of frustration on magnetic property is investigated by CPMC in the studies. / Chapter 5 is devoted to introducing the usages and possible research projects related to HFQMC. HFQMC is a quantum Monte Carlo method based on path integral formalism, and it is an efficient way to study impurity model at low temperature. A physical background of impurity model is also reviewed. In the last chapter, we would summarize this thesis by comparing the QMC methods used and discussing the result obtained. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Tang, Ho Kin = 強關聯系統的量子蒙地卡羅方法研究 / 鄧皓鍵. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 83-88). / Abstracts also in Chinese. / Tang, Ho Kin = Qiang guan lian xi tong de liang zi Mengdi Kaluo fang fa yan jiu / Deng Haojian. / Chapter 1 --- Introduction to Strongly Correlated System: High T{U+ABB1} superconductivity and Quantum Liquid --- p.1 / Chapter 1.1 --- Types of strongly correlated electron systems --- p.1 / Chapter 1.2 --- High T{U+ABB1} superconductivity --- p.3 / Chapter 1.2.1 --- Phase diagram --- p.4 / Chapter 1.2.2 --- Mott insulator and Anti-ferromagnetic(AFM) order --- p.6 / Chapter 1.2.3 --- Spin-glass --- p.7 / Chapter 1.2.4 --- Pseudogap --- p.7 / Chapter 1.2.5 --- Superconducting --- p.7 / Chapter 1.2.6 --- The complexity and related theory --- p.7 / Chapter 1.3 --- Importance of quantum liquids in high T{U+ABB1} superconductivity --- p.10 / Chapter 1.3.1 --- Spin liquid --- p.10 / Chapter 1.3.2 --- Bose Liquid --- p.11 / Chapter 2 --- Methods --- p.12 / Chapter 2.1 --- Introduction to Quantum Monte Carlo --- p.12 / Chapter 2.2 --- Determinant Quantum Monte Carlo(DQMC) --- p.13 / Chapter 2.2.1 --- Purpose of DQMC --- p.13 / Chapter 2.2.2 --- Overall information of DQMC --- p.14 / Chapter 2.2.3 --- Green function in DQMC --- p.20 / Chapter 2.2.4 --- Observable measurement --- p.21 / Chapter 2.2.5 --- Numerical Implementation --- p.24 / Chapter 2.2.6 --- Limitation --- p.26 / Chapter 2.3 --- Constraint Path Quantum Monte Carlo(CPMC) --- p.26 / Chapter 2.3.1 --- Purpose of CPMC --- p.26 / Chapter 2.3.2 --- Algorithm discussion --- p.28 / Chapter 2.3.3 --- Implementation Issues --- p.32 / Chapter 2.4 --- Hirsch-Fye Quantum Monte Carlo(HFQMC) --- p.35 / Chapter 2.4.1 --- Algorithm outline --- p.35 / Chapter 2.4.2 --- Program Structure --- p.38 / Chapter 3 --- A Possible Realization of Bose Liquid: Attractive Hubbard Model with Spin-dependent Anisotropic Hopping --- p.41 / Chapter 3.1 --- Idea of Bose metal --- p.41 / Chapter 3.2 --- Model Hamiltonian --- p.44 / Chapter 3.3 --- Phases and its detection --- p.45 / Chapter 3.3.1 --- Measurement --- p.45 / Chapter 3.3.2 --- Phases --- p.46 / Chapter 3.4 --- Multi-leg ladder Lattice --- p.47 / Chapter 3.4.1 --- Band structure --- p.47 / Chapter 3.4.2 --- Two-leg ladder: Cooper-pair Bose Metal Phase --- p.51 / Chapter 3.4.3 --- Four-leg ladder: Cooper-pair Bose Metal Phase --- p.55 / Chapter 3.5 --- 2D Lattice --- p.56 / Chapter 3.5.1 --- Band structure --- p.56 / Chapter 3.5.2 --- 2D Lattice: Local Cooper-pair Bose Metal(LCPBM) Phase --- p.60 / Chapter 3.6 --- Summary --- p.61 / Chapter 4 --- A Possible Realization of Spin Liquid: Square Lattice Hubbard Model with Geometrical Frustration --- p.65 / Chapter 4.1 --- Frustration and Spin Liquid --- p.65 / Chapter 4.1.1 --- Physical systems --- p.66 / Chapter 4.1.2 --- Recent developments of t-t’-TH model --- p.67 / Chapter 4.2 --- Model Hamiltonian --- p.67 / Chapter 4.3 --- Band structure --- p.68 / Chapter 4.4 --- Frustration Effect on Magnetism --- p.70 / Chapter 4.5 --- Summary --- p.73 / Chapter 5 --- Possible Application of HFQMC --- p.75 / Chapter 5.1 --- Anderson Model --- p.75 / Chapter 5.1.1 --- Physical Issues --- p.75 / Chapter 5.1.2 --- Model proposal and mean field result --- p.76 / Chapter 5.1.3 --- Properties of model with quantum degree of freedom --- p.77 / Chapter 5.2 --- The application cases --- p.78 / Chapter 6 --- Summary --- p.80 / Chapter 6.1 --- Three QMC methods --- p.80 / Chapter 6.2 --- Two practical models --- p.80 / Bibliography --- p.83

Summary in Chinese. / Thesis (M.B.A.)--Chinese University of Hong Kong. / Bibliography: leaves 65-67.

Tsang Yuk Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 59-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Sequential Monte Carlo --- p.5 / Chapter 2.1 --- Recursive Bayesian estimation --- p.7 / Chapter 2.2 --- Bayesian sequential importance sampling --- p.8 / Chapter 2.3 --- Sclcction of iiiipoitance function --- p.10 / Chapter 2.4 --- Particle filter --- p.12 / Chapter 3 --- Target tracking and data association --- p.15 / Chapter 3.1 --- Target tracking and its applications --- p.16 / Chapter 3.2 --- Data association and JPDA method --- p.16 / Chapter 4 --- Particle filter using the acceptance-rejection method --- p.21 / Chapter 4.1 --- Particle Filter using the acceptance-rejection method --- p.22 / Chapter 4.2 --- Modified accoptance-rcjoction algorithm --- p.24 / Chapter 4.3 --- Examples --- p.26 / Chapter 4.3.1 --- Example 1: One dimensional non-linear case --- p.26 / Chapter 4.3.2 --- Example 2: Bearings-only tracking example --- p.27 / Chapter 4.3.3 --- Example 3: Single-target tracking --- p.31 / Chapter 4.3.4 --- Example 4: Multi-target tracking --- p.33 / Chapter 4.4 --- A new importance weight for bearings-only tracking problem --- p.34 / Chapter 5 --- Conclusion --- p.41