Forecasting the term structure of volatility of crude oil price changes

Peer reviewed

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Boron isotope and B/Ca ratios of planktonic foraminifera

Here a new analytical methodology is described for measuring the isotopic composition of boron in foraminifera using multicollector inductively coupled plasma mass spectrometry (MC-ICPMS). This new approach is fast (~10 samples analysed in duplicate per analytical session) and accurate (to better than 0.25 per mil at 95% confidence) with acceptable sample size requirements (1-3 mg of carbonate). A core top calibration of several common planktic and two benthic species from geographically widespread localities shows a very close agreement between the isotopic composition measured by MC-ICPMS and the isotopic composition of B(OH)-4 in seawater (as predicted using the recently measured isotopic equilibrium factor of 1.0272) at the depth of habitat. A down core and core top investigation of boron concentration (B/Ca ratio) shows that the partition coefficient is influenced by [CO2-3] complicating the application of this proxy. Nevertheless, it is demonstrated that these two proxies can be used to fully constrain the carbonate system of surface water in the Caribbean Sea (ODP Site 999A) over the last 130 kyr. This reconstruction shows that during much of the Holocene and the last interglacial period surface water at Site 999A was in equilibrium with the atmosphere with respect to CO2. During the intervening colder periods although the surface water pCO2 was lower than the Holocene, it was a minor to significant source of CO2 to the atmosphere possibly due to either an expansion of the eastern equatorial Atlantic upwelling zone, or a more local expansion of coastal upwelling in the southern Caribbean. Such reorganisation of the oceanic carbonate system in favour of a larger source of CO2 to the atmosphere from the equatorial ocean may require mechanisms responsible for lowering atmospheric CO2 during glacial periods to be more efficient than previously supposed.

Circuit-aware design of energy-efficient massive MIMO systems

Densification is a key to greater throughput in cellular networks. The full potential of coordinated multipoint (CoMP) can be realized by massive multiple-input multiple-output (MIMO) systems, where each base station (BS) has very many antennas. However, the improved throughput comes at the price of more infrastructure; hardware cost and circuit power consumption scale linearly/affinely with the number of antennas. In this paper, we show that one can make the circuit power increase with only the square root of the number of antennas by circuit-aware system design. To this end, we derive achievable user rates for a system model with hardware imperfections and show how the level of imperfections can be gradually increased while maintaining high throughput. The connection between this scaling law and the circuit power consumption is established for different circuits at the BS.

The Consequences of Not Looking at the Eosinophil Count: Pulmonary Infiltrates and Eosinophilia Syndrome (PIE) Probably Caused by Ciprofloxacin

Objectives: To describe a case of pulmonary infiltrates and eosinophilia (PIE syndrome) probably caused by ciprofloxacin. Materials and methods: A 64-year-old woman was admitted to our department with suspected hospital-acquired pneumonia and treated with antibiotics. She had no symptoms but had peripheral eosinophilia. She had recently been given ciprofloxacin for a urinary tract infection. Results: The patient spontaneously improved after exhaustive negative investigations. Conclusion: We concluded that this patient had PIE syndrome probably caused by ciprofloxacin.

Release currents of IP₃ receptor channel clusters and concentration profiles

We simulate currents and concentration profiles generated by Ca2+ release from the endoplasmic reticulum (ER) to the cytosol through IP3 receptor channel clusters. Clusters are described as conducting pores in the lumenal membrane with a diameter from 6 nm to 36 nm. The endoplasmic reticulum is modeled as a disc with a radius of 1–12 mm and an inner height of 28 nm. We adapt the dependence of the currents on the trans Ca2+ concentration (intralumenal) measured in lipid bilayer experiments to the cellular geometry. Simulated currents are compared with signal mass measurements in Xenopus oocytes. We find that release currents depend linearly on the concentration of free Ca2+ in the lumen. The release current is approximately proportional to the square root of the number of open channels in a cluster. Cytosolic concentrations at the location of the cluster range from 25 μM to 170 μM. Concentration increase due to puffs in a distance of a few micrometers from the puff site is found to be in the nanomolar range. Release currents decay biexponentially with timescales of < 1 s and a few seconds. Concentration profiles decay with timescales of 0.125–0.250 s upon termination of release.

Periodic emission of droplets from an oscillating electrified meniscus of a low-viscosity, highly conductive liquid

The generation of identical droplets of controllable size in the micrometer range is a problem of much interest owing to the numerous technological applications of such droplets. This work reports an investigation of the regime of periodic emission of droplets from an electrified oscillating meniscus of a liquid of low viscosity and high electrical conductivity attached to the end of a capillary tube, which may be used to produce droplets more than ten times smaller than the diameter of the tube. To attain this periodic microdripping regime, termed axial spray mode II by Juraschek and Röllgen [R. Juraschek and F. W. Röllgen, Int. J. Mass Spectrom. 177, 1 (1998)], liquid is continuously supplied through the tube at a given constant flow rate, while a dc voltage is applied between the tube and a nearby counter electrode. The resulting electric field induces a stress at the surface of the liquid that stretches the meniscus until, in certain ranges of voltage and flow rate, it develops a ligament that eventually detaches, forming a single droplet, in a process that repeats itself periodically. While it is being stretched, the ligament develops a conical tip that emits ultrafine droplets, but the total mass emitted is practically contained in the main droplet. In the parametrical domain studied, we find that the process depends on two main dimensionless parameters, the flow rate nondimensionalized with the diameter of the tube and the capillary time, q, and the electric Bond number BE, which is a nondimensional measure of the square of the applied voltage. The meniscus oscillation frequency made nondimensional with the capillary time, f, is of order unity for very small flow rates and tends to decrease as the inverse of the square root of q for larger values of this parameter. The product of the meniscus mean volume times the oscillation frequency is nearly constant. The characteristic length and width of the liquid ligament immediately before its detachment approximately scale as powers of the flow rate and depend only weakly on the applied voltage. The diameter of the main droplets nondimensionalized with the diameter of the tube satisfies dd≈(6/π)1/3(q/f)1/3, from mass conservation, while the electric charge of these droplets is about 1/4 of the Rayleigh charge. At the minimum flow rate compatible with the periodic regimen, the dimensionless diameter of the droplets is smaller than one-tenth, which presents a way to use electrohydrodynamic atomization to generate droplets of highly conducting liquids in the micron-size range, in marked contrast with the cone-jet electrospray whose typical droplet size is in the nanometric regime for these liquids. In contrast with other microdripping regimes where the mass is emitted upon the periodic formation of a narrow capillary jet, the present regime gives one single droplet per oscillation, except for the almost massless fine aerosol emitted in the form of an electrospray.

The Root of the Recycled: A Comparative Analysis of Shakespeare's "Hamlet" and the Mythological "Ur-Hamlet"

The purpose of my thesis was to explore the problem surrounding the sources believed to constitute the Ur-Hamlet from which Shakespeare derived Hamlet. By utilization of close reading, analysis, and archetypical criticism, my thesis confirms Shakespeare’s usage of the “Hero as Fool” archetype present in the Danish legend of Amleth, translated by Saxo Grammaticus and Francois Belleforest, as the Ur-Hamlet. My study is significant because it further develops the notion that the earlier legend served as the originary source for Hamlet, while providing evidence that rejects the validity of other sources of the Ur-Hamlet. The evidence was corroborated by presenting analytical comparisons of the framework both works share. Focusing on the archetypal origins of Shakespeare’s plot, characters and their actions revealed a more complex understanding of the play. These findings indicate and substantiate the claim that the Ur-Hamlet can be no other source but the Danish legend of Amleth.

Efficient genetic transformation and regeneration system from hairy root of Origanum vulgare.

2016

Flow and axial dispersion simulation for traveling axisymmetric Taylor vortices

Numerical experiments using a finite difference method were carried out to determine the motion of axisymmetric Taylor vortices for narrow-gap Taylor vortex flow. When a pressure gradient is imposed on the flow the vortices are observed to move with an axial speed of 1.16 +/- 0.005 times the mean axial flow velocity. The method of Brenner was used to calculate the long-time axial spread of material in the flow. For flows where there is no pressure gradient, the axial dispersion scales with the square root of the molecular diffusion, in agreement with the results of Rosen-bluth et al. for high Peclet number dispersion in spatially periodic flows with a roll structure. When a pressure gradient is imposed the dispersion increases by an amount approximately equal to 6.5 x 10(-4) (W) over bar(2)d(2)/D-m, where (W) over bar is the average axial velocity in the annulus, analogous to Taylor dispersion for laminar flow in an empty tube.

Anomalous water absorption in porous materials

The absorption of fluid by unsaturated, rigid porous materials may be characterized by the sorptivity. This is a simple parameter to determine and is increasingly being used as a measure of a material's resistance to exposure to fluids (especially moisture and reactive solutes) in aggressive environments. The complete isothermal absorption process is described by a nonlinear diffusion equation, with the hydraulic diffusivity being a strongly nonlinear function of the degree of saturation of the material. This diffusivity can be estimated from the sorptivity test. In a typical test the cumulative absorption is proportional to the square root of time. However, a number of researchers have observed deviation from this behaviour when the infiltrating fluid is water and there is some potential for chemo-mechanical interaction with the material. In that case the current interpretation of the test and estimation of the hydraulic diffusivity is no longer appropriate. Kuntz and Lavallee (2001) discuss the anomalous behaviour and propose a non-Darcian model as a more appropriate physical description. We present an alternative Darcian explanation and theory that retrieves the earlier advantages of the simple sorptivity test in providing parametric information about the material's hydraulic properties and allowing simple predictive formulae for the wetting profile to be generated.

Ivabradine Improves Heart Rate Variability in Patients with Nonischemic Dilated Cardiomyopathy

Background: Ivabradine is a novel specific heart rate (HR)-lowering agent that improves event-free survival in patients with heart failure (HF). Objectives: We aimed to evaluate the effect of ivabradine on time domain indices of heart rate variability (HRV) in patients with HF. Methods: Forty-eight patients with compensated HF of nonischemic origin were included. Ivabradine treatment was initiated according to the latest HF guidelines. For HRV analysis, 24-h Holter recording was obtained from each patient before and after 8 weeks of treatment with ivabradine. Results: The mean RR interval, standard deviation of all normal to normal RR intervals (SDNN), the standard deviation of 5-min mean RR intervals (SDANN), the mean of the standard deviation of all normal-to-normal RR intervals for all 5-min segments (SDNN index), the percentage of successive normal RR intervals exceeding 50 ms (pNN50), and the square root of the mean of the squares of the differences between successive normal to normal RR intervals (RMSSD) were low at baseline before treatment with ivabradine. After 8 weeks of treatment with ivabradine, the mean HR (83.6 ± 8.0 and 64.6 ± 5.8, p < 0.0001), mean RR interval (713 ± 74 and 943 ± 101 ms, p < 0.0001), SDNN (56.2 ± 15.7 and 87.9 ± 19.4 ms, p < 0.0001), SDANN (49.5 ± 14.7 and 76.4 ± 19.5 ms, p < 0.0001), SDNN index (24.7 ± 8.8 and 38.3 ± 13.1 ms, p < 0.0001), pNN50 (2.4 ± 1.6 and 3.2 ± 2.2 %, p < 0.0001), and RMSSD (13.5 ± 4.6 and 17.8 ± 5.4 ms, p < 0.0001) substantially improved, which sustained during both when awake and while asleep. Conclusion: Our findings suggest that treatment with ivabradine improves HRV in nonischemic patients with HF.

Cardiovascular Autonomic Dysfunction in Patients with Morbid Obesity

Abstract Background: Morbid obesity is directly related to deterioration in cardiorespiratory capacity, including changes in cardiovascular autonomic modulation. Objective: This study aimed to assess the cardiovascular autonomic function in morbidly obese individuals. Methods: Cross-sectional study, including two groups of participants: Group I, composed by 50 morbidly obese subjects, and Group II, composed by 30 nonobese subjects. The autonomic function was assessed by heart rate variability in the time domain (standard deviation of all normal RR intervals [SDNN]; standard deviation of the normal R-R intervals [SDNN]; square root of the mean squared differences of successive R-R intervals [RMSSD]; and the percentage of interval differences of successive R-R intervals greater than 50 milliseconds [pNN50] than the adjacent interval), and in the frequency domain (high frequency [HF]; low frequency [LF]: integration of power spectral density function in high frequency and low frequency ranges respectively). Between-group comparisons were performed by the Student’s t-test, with a level of significance of 5%. Results: Obese subjects had lower values of SDNN (40.0 ± 18.0 ms vs. 70.0 ± 27.8 ms; p = 0.0004), RMSSD (23.7 ± 13.0 ms vs. 40.3 ± 22.4 ms; p = 0.0030), pNN50 (14.8 ± 10.4 % vs. 25.9 ± 7.2%; p = 0.0061) and HF (30.0 ± 17.5 Hz vs. 51.7 ± 25.5 Hz; p = 0.0023) than controls. Mean LF/HF ratio was higher in Group I (5.0 ± 2.8 vs. 1.0 ± 0.9; p = 0.0189), indicating changes in the sympathovagal balance. No statistical difference in LF was observed between Group I and Group II (50.1 ± 30.2 Hz vs. 40.9 ± 23.9 Hz; p = 0.9013). Conclusion: morbidly obese individuals have increased sympathetic activity and reduced parasympathetic activity, featuring cardiovascular autonomic dysfunction.