Bayesian model selection for time series using Markov chain Monte Carlo

We present a stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset linear AR models, in which only significant lags are included. Joint sampling of the indicators and parameters is found to speed convergence. We discuss the possibility of model mixing where the model is not well determined by the data, and the extension of the approach to include non-linear model terms.

Monte Carlo Valuation of natural gas investments

This paper deals with the valuation of energy assets related to natural gas. In particular, we evaluate a baseload Natural Gas Combined Cycle (NGCC) power plant and an ancillary instalation, namely a Liquefied Natural Gas (LNG) facility, in a realistic setting; specifically, these investments enjoy a long useful life but require some non-negligible time to build. Then we focus on the valuation of several investment options again in a realistic setting. These include the option to invest in the power plant when there is uncertainty concerning the initial outlay, or the option's time to maturity, or the cost of CO2 emission permits, or when there is a chance to double the plant size in the future. Our model comprises three sources of risk. We consider uncertain gas prices with regard to both the current level and the long-run equilibrium level; the current electricity price is also uncertain. They all are assumed to show mean reversion. The two-factor model for natural gas price is calibrated using data from NYMEX NG futures contracts. Also, we calibrate the one-factor model for electricity price using data from the Spanish wholesale electricity market, respectively. Then we use the estimated parameter values alongside actual physical parameters from a case study to value natural gas plants. Finally, the calibrated parameters are also used in a Monte Carlo simulation framework to evaluate several American-type options to invest in these energy assets. We accomplish this by following the least squares MC approach.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

Monte Carlo optimization strategies for air-traffic control

The safety of the flights, and in particular conflict resolution for separation assurance, is one of the main tasks of Air Traffic Control. Conflict resolution requires decision making in the face of the considerable levels of uncertainty inherent in the motion of aircraft. We present a Monte Carlo framework for conflict resolution which allows one to take into account such levels of uncertainty through the use of a stochastic simulator. A simulation example inspired by current air traffic control practice illustrates the proposed conflict resolution strategy. Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

A Monte Carlo expectation maximisation algorithm for multiple target tracking

In this paper, we present an expectation-maximisation (EM) algorithm for maximum likelihood estimation in multiple target models (MTT) with Gaussian linear state-space dynamics. We show that estimation of sufficient statistics for EM in a single Gaussian linear state-space model can be extended to the MTT case along with a Monte Carlo approximation for inference of unknown associations of targets. The stochastic approximation EM algorithm that we present here can be used along with any Monte Carlo method which has been developed for tracking in MTT models, such as Markov chain Monte Carlo and sequential Monte Carlo methods. We demonstrate the performance of the algorithm with a simulation. © 2012 ISIF (Intl Society of Information Fusi).

高分子溶液中物理凝胶化的Monte Carlo模拟和小角中子散射研究

高分子凝胶广泛地存在于自然界以及日常生活中，按其形成作用力不同分为化学凝胶和物理凝胶两大类。由于高分子物理凝胶具有凝胶化的可逆性及其对环境条件强烈的响应性，因此，在近半个世纪的研究与应用中受到极大的关注。高分子溶液中的物理凝胶因其结构及形成机制复杂，在实验方面，除了散射技术及流变技术能够有效地揭示它的部分信息外，其它的实验手段很难用于这个领域的研究；在理论方面，化学凝胶的理论已经比较成熟，而物理凝胶的粘弹性质以及凝胶化是一个远离平衡态的松弛过程，除了一些特征的标度指数外，人们还没有得到适用于高分子物理凝胶的普适规律。当前，由于计算机模拟理论及模拟方法的发展，使得计算机模拟成为除了实验和理论研究方法之外的第三个重要的研究方法。但是，由于物理凝胶化行为的复杂性，用实验和理论获得的信息很难较好地描述凝胶化过程，而计算机模拟的高度透明性及反映信息的完整性，有助于理解这一复杂过程中所涉及的物理本质。因此，利用计算机模拟结合实验及理论方法深入研究高分子物理凝胶的形成机制、结构与性能关系已成为目前最有效的手段之一。 本论文主要运用Monte Carlo模拟方法，并结合小角中子散射（Small-Angle Neutron Scattering, SANS）和流变（Rheology）等实验手段从多个角度探讨了以下几类典型的高分子溶液物理凝胶化行为。 1. 温度对遥爪型三嵌段共聚物在选择性溶剂中的自组装及凝胶化行为影响的研究：采用二维简单方格子Monte Carlo模拟方法，结合逾渗（Percolation）理论，建立了溶胶－凝胶转变相图在统计热力学中的确定方法；甄别了具有特征构象的链，讨论了链及胶束的聚集，明晰了相互作用（体现为约化温度）、构象转变、聚集与凝胶化的一致的关联关系；提出了构象转变模型，进而明确了此体系的凝胶化过程，在微观尺度上表现为桥型链和环型链之间的竞争。 2. 模拟模型改进及其应用到持续长度对稀溶液中高分子链构象影响的研究：考虑到原始八位置键涨落模型效率低，实现复杂且不能应用到复杂的高分子体系，对该模型进行了改进，使其实现简单、效率高，并拓宽了该模型的应用范围。然后，以刚性对均聚物构象的影响为例，发现随着刚性增加，均聚物构象从球形椭球到棒状椭球的转变，并对比了自由连接链（Free Joint Chain, FJC）模型和蠕虫链（Wormlike Chain, WLC）模型在不同刚性范围内对高分子链末端距预测的偏差，首次给出了这两个经典模型的半定量的适用边界。 3. 溶剂尺寸对遥爪型三嵌段共聚物在选择性溶剂中的自组装及凝胶化行为影响的研究：用改进后的八位置键涨落Monte Carlo模型，研究了遥爪型三嵌段共聚物在选择性溶剂条件下的聚集和凝胶化对溶剂尺寸的依赖性，发现溶剂尺寸效应对凝胶化的作用是非单调的。由一个均聚物体系的对比模拟证明这种作用主要是由熵驱动的，并给出了中分子溶剂的半定量定义。在均聚物和嵌段共聚物溶液中，不同尺寸的溶剂分子可以使溶液由于高分子聚集不同而具有不同的微结构，并影响高分子链构象和溶液的性质。从多个角度研究了三嵌段共聚物在不同尺寸溶剂的溶液中所遵循的三种不同的凝胶化机理。 4. 聚氧化乙烯－氧化丙稀－氧化乙烯三嵌段共聚物（poly(ethylene oxide)-poly (propylene oxide)-poly-(ethylene oxide), PEO-PPO-PEO）重水溶液凝胶化的小角中子散射（SANS）和Monte Carlo研究：结合Pluronic F127（EO65PO99EO65）/D2O三嵌段共聚物溶液的特征，对照SANS数据，用改进后的八位置键涨落模型成功地从模拟中获得了F127/D2O的溶胶－凝胶转变相图。详细地考察了体系的微观结构，提出此类高分子溶液中形成的物理凝胶包含高分子逾渗网络的生成，以及被束缚溶剂（Bound Solvent）必须超过离散组分体系逾渗的临界体积分数的机理。着重研究了一定浓度的F127水溶液随温度升高引起的溶胶－凝胶转变以及凝胶－溶胶转变的Reentrant相行为，发现体系在低温区域的溶胶－凝胶转变遵循相同的机理，而在中等温度和较高温度以及不同浓度区域中的凝胶－溶胶转变遵循不同的机理。 5. 极性基团饱和度和溶剂条件对两亲性聚合物在溶液中的聚集行为和凝胶化影响的研究：用改进后的八位置键涨落模型，针对两亲性聚合物在不同溶剂条件的溶液建立了粗粒化模型，以两亲性聚合物中极性基团的饱和度，溶剂条件和高分子浓度为变量，考察了其对链构象、聚集及其凝胶化的影响。 6. 多糖水溶液凝胶化的流变和小角中子散射研究：用流变和SANS考察了两个多糖水溶液中物理凝胶化过程，针对由氢键主导的水基凝胶体系的典型特征进行了讨论，从分子链构象，聚集体结构及其关联以及流变特征等方面对聚强电解质角叉胶（Carrageenan）水溶液和聚弱电解质明胶（Pectin）水溶液进行了详细的讨论。考察了不同多糖的种类（聚合物链的电荷密度），盐的种类和浓度，溶液温度等对凝胶化和凝胶结构的影响，分析了不同多糖溶液的凝胶化机理。

Monte Carlo studies of micromegas as a neutron detector and its track reconstruction

In this paper a two dimensional readout micromegas detector with a polyethylene foil as converter was simulated on GEANT4 toolkit and GARFIELD for fast neutron detection. A new track reconstruction method based on time coincidence technology was developed in the simulation to obtain the incident neutron position. The results showed that with this reconstruction method higher spatial resolution was achieved.

Effect of polydispersity on the self-assembly structure of diblock copolymers under various confined states: A Monte Carlo study

We studied the self-assembly of polydisperse diblock copolymers under various confined states by Monte Carlo simulation. When the copolymers were confined within two parallel walls, it was found that the ordered strip structures appeared alternately with the increase in wall width. Moreover, the wall width at which the ordered structure appeared tended to increase with an increase in the polydispersity index (PDI). On the other hand, the simulation results showed that the copolymers were likely to form ordered concentric strip structures when they were confined within a circle wall.

Grafting of maleic anhydride onto linear polyethylene: A Monte Carlo study

Monte Carlo simulation was used to study the graft of maleic anhydride (MAH) onto linear polyethylene (PE-g-MAH) initiated by dicumyl peroxide (DCP). Simulation results revealed that major MAH monomers attached onto PE chains as branched graft at higher MAH content. However, at extremely low MAH content, the fraction of bridged graft was very close to that of branched graft. This conclusion was somewhat different from the conventional viewpoint, namely, the fraction of bridged graft was always much lower than that of branched graft under any condition. Moreover, the results indicated that the grafting degree increased almost linearly to MAH and DCP concentrations. On the other hand, it was found that the amount of grafted MAH dropped sharply with increasing the length of grafted MAH, indicating that MAH monomers were mainly attached onto the PE chain as single MAH groups or very short oligomers. With respect to the crosslink of PE, the results showed that the fraction of PE-(MAH)(n)-PE crosslink structure increased continuously, and hence the fraction of PE-PE crosslink decreased with increasing MAH concentration.

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

Monte Carlo Analysis and Physics Characterization of a Novel Nanoparticle Detector for Medical and Micro-dosimetry Applications

The outcomes for both (i) radiation therapy and (ii) preclinical small animal radio- biology studies are dependent on the delivery of a known quantity of radiation to a specific and intentional location. Adverse effects can result from these procedures if the dose to the target is too high or low, and can also result from an incorrect spatial distribution in which nearby normal healthy tissue can be undesirably damaged by poor radiation delivery techniques. Thus, in mice and humans alike, the spatial dose distributions from radiation sources should be well characterized in terms of the absolute dose quantity, and with pin-point accuracy. When dealing with the steep spatial dose gradients consequential to either (i) high dose rate (HDR) brachytherapy or (ii) within the small organs and tissue inhomogeneities of mice, obtaining accurate and highly precise dose results can be very challenging, considering commercially available radiation detection tools, such as ion chambers, are often too large for in-vivo use.

In this dissertation two tools are developed and applied for both clinical and preclinical radiation measurement. The first tool is a novel radiation detector for acquiring physical measurements, fabricated from an inorganic nano-crystalline scintillator that has been fixed on an optical fiber terminus. This dosimeter allows for the measurement of point doses to sub-millimeter resolution, and has the ability to be placed in-vivo in humans and small animals. Real-time data is displayed to the user to provide instant quality assurance and dose-rate information. The second tool utilizes an open source Monte Carlo particle transport code, and was applied for small animal dosimetry studies to calculate organ doses and recommend new techniques of dose prescription in mice, as well as to characterize dose to the murine bone marrow compartment with micron-scale resolution.

Hardware design changes were implemented to reduce the overall fiber diameter to <0.9 mm for the nano-crystalline scintillator based fiber optic detector (NanoFOD) system. Lower limits of device sensitivity were found to be approximately 0.05 cGy/s. Herein, this detector was demonstrated to perform quality assurance of clinical 192Ir HDR brachytherapy procedures, providing comparable dose measurements as thermo-luminescent dosimeters and accuracy within 20% of the treatment planning software (TPS) for 27 treatments conducted, with an inter-quartile range ratio to the TPS dose value of (1.02-0.94=0.08). After removing contaminant signals (Cerenkov and diode background), calibration of the detector enabled accurate dose measurements for vaginal applicator brachytherapy procedures. For 192Ir use, energy response changed by a factor of 2.25 over the SDD values of 3 to 9 cm; however a cap made of 0.2 mm thickness silver reduced energy dependence to a factor of 1.25 over the same SDD range, but had the consequence of reducing overall sensitivity by 33%.

For preclinical measurements, dose accuracy of the NanoFOD was within 1.3% of MOSFET measured dose values in a cylindrical mouse phantom at 225 kV for x-ray irradiation at angles of 0, 90, 180, and 270˝. The NanoFOD exhibited small changes in angular sensitivity, with a coefficient of variation (COV) of 3.6% at 120 kV and 1% at 225 kV. When the NanoFOD was placed alongside a MOSFET in the liver of a sacrificed mouse and treatment was delivered at 225 kV with 0.3 mm Cu filter, the dose difference was only 1.09% with use of the 4x4 cm collimator, and -0.03% with no collimation. Additionally, the NanoFOD utilized a scintillator of 11 µm thickness to measure small x-ray fields for microbeam radiation therapy (MRT) applications, and achieved 2.7% dose accuracy of the microbeam peak in comparison to radiochromic film. Modest differences between the full-width at half maximum measured lateral dimension of the MRT system were observed between the NanoFOD (420 µm) and radiochromic film (320 µm), but these differences have been explained mostly as an artifact due to the geometry used and volumetric effects in the scintillator material. Characterization of the energy dependence for the yttrium-oxide based scintillator material was performed in the range of 40-320 kV (2 mm Al filtration), and the maximum device sensitivity was achieved at 100 kV. Tissue maximum ratio data measurements were carried out on a small animal x-ray irradiator system at 320 kV and demonstrated an average difference of 0.9% as compared to a MOSFET dosimeter in the range of 2.5 to 33 cm depth in tissue equivalent plastic blocks. Irradiation of the NanoFOD fiber and scintillator material on a 137Cs gamma irradiator to 1600 Gy did not produce any measurable change in light output, suggesting that the NanoFOD system may be re-used without the need for replacement or recalibration over its lifetime.

For small animal irradiator systems, researchers can deliver a given dose to a target organ by controlling exposure time. Currently, researchers calculate this exposure time by dividing the total dose that they wish to deliver by a single provided dose rate value. This method is independent of the target organ. Studies conducted here used Monte Carlo particle transport codes to justify a new method of dose prescription in mice, that considers organ specific doses. Monte Carlo simulations were performed in the Geant4 Application for Tomographic Emission (GATE) toolkit using a MOBY mouse whole-body phantom. The non-homogeneous phantom was comprised of 256x256x800 voxels of size 0.145x0.145x0.145 mm3. Differences of up to 20-30% in dose to soft-tissue target organs was demonstrated, and methods for alleviating these errors were suggested during whole body radiation of mice by utilizing organ specific and x-ray tube filter specific dose rates for all irradiations.

Monte Carlo analysis was used on 1 µm resolution CT images of a mouse femur and a mouse vertebra to calculate the dose gradients within the bone marrow (BM) compartment of mice based on different radiation beam qualities relevant to x-ray and isotope type irradiators. Results and findings indicated that soft x-ray beams (160 kV at 0.62 mm Cu HVL and 320 kV at 1 mm Cu HVL) lead to substantially higher dose to BM within close proximity to mineral bone (within about 60 µm) as compared to hard x-ray beams (320 kV at 4 mm Cu HVL) and isotope based gamma irradiators (137Cs). The average dose increases to the BM in the vertebra for these four aforementioned radiation beam qualities were found to be 31%, 17%, 8%, and 1%, respectively. Both in-vitro and in-vivo experimental studies confirmed these simulation results, demonstrating that the 320 kV, 1 mm Cu HVL beam caused statistically significant increased killing to the BM cells at 6 Gy dose levels in comparison to both the 320 kV, 4 mm Cu HVL and the 662 keV, 137Cs beams.