我國股市的價格漲跌幅限制已逾三十年的歷史，主管機關維持此一機制的訴求是避免股價波動過於激烈、抑制投機行為。惟停板限制可能帶來的影響，除直覺上的其造成投資者持股風險指標扭曲等問題。經探究中亦歸結出（一）其被引為技術指標、（二）其引致財務風險指標扭曲等問題。 　　經探究GMM、Gibbs Sampler、與Two-Limit-Tobit Model模型的優劣。本研究發現一般使用的GMM估計量並非不偏，雖然可以藉修正增加其效率性，但仍無法藉以衡量各種的停板影響；Gibbs Sampler則過於依賴特定的先驗分佈，有可能因此而造成偏誤；而目前使用Tobit Model的文獻大都忽略停板限制對股價的影響力，據以產生的估計值亦附含偏誤。 　　本研究所採樣本期間為79年1月3日至84年10月9日，使用模型為Two-Limit-Tobit Model。為求嚴謹，在使用之前做資料的處理，並利用CAAR來驗證模型的正確性。實證顯示，漲跌停板的設立顯著改變投資人行為，在停板之前本研究發現存在技術指標與標準差統計量的向上偏誤，進而可能誤導實業界財務決策或學術研究結論。 / Thsi Study explores how price limits, which have remained in Taiwan Securities Exchange for over thirty years, affects both security price behavior and security risk indices. Its empirical results add to our understanding of the social costs and benefits of price limits. The SEC has been advocating the merits of price limits, emphasing that they help eliminating speculative trades and reducing security price volatility. In contrast, it remains a popular thought that price limits increase investors’holding costs and risks. To empirically examine the effects of price limits in Taiwan, this papers adopts Two-Limit-Tobit Model, together with CAAR as an indicator for specification validity. My test results lend support to the notion of (1).Technical Indicator Effect immediately before the price limits are hit; (2).Enhancement Effect the day after. Moreover, price limits contribute to bias in both systematic risk and total risk estimates (namely, β and σ) and thus distort investment decisions. 　　This Study also contributes to the contemporary literature by examining the merits and limitations of GMM, Gibbs Sampler, and Two-Limit-Tobit Model. GMM estimator is subject to statistical bias. One way may gain efficiency via adjustment. And yet GMM ahs pitfalls in directly measuring the price limit effects; The major limitation of the Gibbs Sampler is its reliance on specific prior information and it may lead to bias. And most of the papers adopting Tobit Model simply input the original data into the program, ignoring the fact that price limit may make the following day price data may be contaiminated.

In this thesis we develop a two component mixture model to perform a Bayesian regression. We implement our model computationally using the Gibbs sampler algorithm and apply it to a dataset of differences in time measurement between two clocks. The dataset has ``good" time measurements and ``bad" time measurements that were associated with the two components of our mixture model. From our theoretical work we show that latent variables are a useful tool to implement our Bayesian normal mixture model with two components. After applying our model to the data we found that the model reasonably assigned probabilities of occurrence to the two states of the phenomenon of study; it also identified two processes with the same slope, different intercepts and different variances. / McAnulty College and Graduate School of Liberal Arts; / Computational Mathematics / MS; / Thesis;

In this thesis, a mixture-model cluster analysis technique under different covariance structures of the component densities is developed and presented, to capture the compactness, orientation, shape, and the volume of component clusters in one expert system to handle Gaussian high dimensional heterogeneous data sets to achieve flexibility in currently practiced cluster analysis techniques. Two approaches to parameter estimation are considered and compared; one using the Expectation-Maximization (EM) algorithm and another following a Bayesian framework using the Gibbs sampler. We develop and score several forms of the ICOMP criterion of Bozdogan (1994, 2004) as our fitness function; to choose the number of component clusters, to choose the correct component covariance matrix structure among nine candidate covariance structures, and to select the optimal parameters and the best fitting mixture-model. We demonstrate our approach on simulated datasets and a real large data set, focusing on early detection of breast cancer. We show that our approach improves the probability of classification error over the existing methods.

In this thesis, we discuss some topics in random matrix theory which have applications to probability, statistics and quantum information theory. In Chapter 2, by relying on the spectral properties of an associated adjacency matrix, we find the distribution of the maximum of a Dyck path and show that it has the same distribution function as the unsigned Brownian excursion which was first derived in 1976 by Kennedy. We obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extends the results of Chung, Kennedy and Khorunzhiy and Marckert. In Chapter 3, we discuss a method of sampling called the Gibbs-slice sampler. This method is based on Neal's slice sampling combined with Gibbs sampling. In Chapter 4, we discuss several examples which have applications in physics and quantum information theory.

In this thesis, we discuss some topics in random matrix theory which have applications to probability, statistics and quantum information theory. In Chapter 2, by relying on the spectral properties of an associated adjacency matrix, we find the distribution of the maximum of a Dyck path and show that it has the same distribution function as the unsigned Brownian excursion which was first derived in 1976 by Kennedy. We obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extends the results of Chung, Kennedy and Khorunzhiy and Marckert. In Chapter 3, we discuss a method of sampling called the Gibbs-slice sampler. This method is based on Neal's slice sampling combined with Gibbs sampling. In Chapter 4, we discuss several examples which have applications in physics and quantum information theory.

Remote Explosives Scent Tracing (REST) is the concept of bringing the mine field to Mine Detection Dogs or Rats, instead of vice versa. This is done by collecting air or dust from minefields, and taking these samples to a laboratory environment, where they are subsequently analysed by the detection animals. REST has previously proven to be very fast and cost effective, but one of the issues facing the method is that there is yet no reliable tool for sampling dust. In earlier sampling units, air has been collected in filters. However, the concentration of scents related to mines has been seen to be a million times higher in dust particles than in air sampled from above the ground. The aim of this project was to evaluate and improve a dust sampling prototype constructed in the beginning of 2010. The project was initiated in cooperation with the GICHD (Geneva International Centre for Humanitarian demining), and carried out in cooperation with APOPO (Anti-Personnel Landmines Detection Product Development). During this project, information was gathered on the samplers that have previously been used for REST. A new prototype was made in Trondheim in cooperation with NTNU (Norwegian University of Science and Technology). With this new sampler prototype, tests were made in a laboratory environment at NTNU as well as at APOPO’s test mine field in Morogoro, Tanzania. Several obstacles were faced, such as difficulties to test and evaluate the sampler during the rainy season, insufficient air supply for the prototype, and issues with the laboratory equipment in Morogoro. Due to this, the number of tests performed and the number of repetitions of each test was not as high as would have been desired. The results of the information gathering and the tests are presented in this report, and the knowledge and experience gained resulted in several suggestions for improvements for the sampler prototype. A suggestion for a grid design that would cover the entire mouth piece, with a built-in distance to the suction inlet, in order to avoid both clogging of the grid and that too much dust is sucked in if the mouth piece touches the ground and a fully adjustable sampling unit. Several other recommendations are given that would reduce cross contamination risks and improve ergonomics and other aspects of the sampler prototype.

Currently, a lack of accurate emission data exits for particulate matter (PM) in agricultural air quality studies (USDA-AAQTF, 2000). PM samplers, however, tend to over estimate the concentration of most agricultural dusts because of the interaction of the particle size distribution (PSD) and performance characteristics of the sampler (Buser, 2004). This research attempts to find a practical method to characterize and correct this error for the Federal Reference Method (FRM) PM10 sampler. First, a new dust wind tunnel testing facility that satisfies the USEPA’s requirement of testing PM10 samplers was designed, built, and evaluated. Second, the wind tunnel testing protocol using poly-dispersed aerosol as the test dust was proved to be able to provide results consistent with mono-dispersed dusts. Third, this study quantified the variation of over sampling ratios for the various cut point and slopes of FRM PM10 samplers and proposed an averaged over sampling ratio as a correction factor for various ranges of PSD. Finally, a method of using total suspended particle (TSP) samplers as a field reference for determining PM10 concentrations and aerosol PSD was explored computationally. Overall, this dissertation developed successfully the methodology to correct the sampling error associated with the FRM PM10 sampler: (1) wind tunnel testing facilities and protocol for experimental evaluation of samplers; (2) the variation of the oversampling ratios of FRM PM10 samplers for computational evaluation of samplers; (3) the evaluation of TSP sampler effectiveness as a potential field reference for field evaluation of samplers.

Particulate matter (PM) concentrations in ambient air can be monitored by gravimetric sampling near a source using Federal Reference Method (FRM) samplers. PM is regulated by size, with PM10, which is comprised of particles with aerodynamic equivalent diameters less than or equal to 10 μm, being the main focus of this research. FRM PM10 samplers exhibit sampling errors when sampling dusts with mass median diameters (MMDs) that are larger than the 10 μm sampler cutpoint. For industries to be regulated equitably, these sampler errors must be quantified and understood. This research evaluates the performance of FRM PM10 and low volume total suspended particulate (TSP) samplers under the controlled conditions of a wind tunnel. The performance evaluation was conducted by observing the sampler cutpoints, slopes, and measured concentrations. These measured values were compared to values obtained using a collocated isokinetic reference sampler. The results of this research indicate that PM10 samplers do not operate as intended under all conditions. The cutpoint of the PM10 inlets was significantly higher than the maximum FRM limit of 10.5 μm when sampling dust with MMDs larger than the cutpoint of the sampler. The slope values for the PM10 inlets were significantly higher than the maximum FRM limit of 1.6. MMDs and geometric standard deviations of PM collected by TSP samplers were significantly different than those of PM collected using the collocated isokinetic sampler. The concentrations measured by the TSP samplers were significantly higher than the collocated isokinetic sampler. The results of this research provide a better understanding of the performance of TSP and PM10 samplers operating under different conditions and shows that these samplers are not operating as intended. Because of this, industries may be suffering the consequences of inequitable regulation.

<p>Remote Explosives Scent Tracing (REST) is the concept of bringing the mine field to Mine Detection Dogs or Rats, instead of vice versa. This is done by collecting air or dust from minefields, and taking these samples to a laboratory environment, where they are subsequently analysed by the detection animals.</p><p>REST has previously proven to be very fast and cost effective, but one of the issues facing the method is that there is yet no reliable tool for sampling dust. In earlier sampling units, air has been collected in filters. However, the concentration of scents related to mines has been seen to be a million times higher in dust particles than in air sampled from above the ground. The aim of this project was to evaluate and improve a dust sampling prototype constructed in the beginning of 2010. The project was initiated in cooperation with the GICHD (Geneva International Centre for Humanitarian demining), and carried out in cooperation with APOPO (Anti-Personnel Landmines Detection Product Development).</p><p>During this project, information was gathered on the samplers that have previously been used for REST. A new prototype was made in Trondheim in cooperation with NTNU (Norwegian University of Science and Technology). With this new sampler prototype, tests were made in a laboratory environment at NTNU as well as at APOPO’s test mine field in Morogoro, Tanzania. Several obstacles were faced, such as difficulties to test and evaluate the sampler during the rainy season, insufficient air supply for the prototype, and issues with the laboratory equipment in Morogoro. Due to this, the number of tests performed and the number of repetitions of each test was not as high as would have been desired.</p><p>The results of the information gathering and the tests are presented in this report, and the knowledge and experience gained resulted in several suggestions for improvements for the sampler prototype. A suggestion for a grid design that would cover the entire mouth piece, with a built-in distance to the suction inlet, in order to avoid both clogging of the grid and that too much dust is sucked in if the mouth piece touches the ground and a fully adjustable sampling unit. Several other recommendations are given that would reduce cross contamination risks and improve ergonomics and other aspects of the sampler prototype.</p>

Many prior distributions are suggested for variance parameters in the hierarchical model. The “Non-informative” interval of the conjugate inverse-gamma prior might cause problems. I consider three priors – conjugate inverse-gamma, log-normal and truncated normal for the variance parameters and do the numerical analysis on Gelman’s 8-schools data. Then with the posterior draws, I compare the Bayesian credible intervals of parameters using the three priors. I use predictive distributions to do predictions and then discuss the differences of the three priors suggested. / text