Matching on-the-fly in Sequential Experiments for Higher Power and Efficiency

We propose a dynamic allocation procedure that increases power and efficiency when measuring an average treatment effect in sequential randomized trials. Subjects arrive iteratively and are either randomized or paired via a matching criterion to a previously randomized subject and administered the alternate treatment. We develop estimators for the average treatment effect that combine information from both the matched pairs and unmatched subjects as well as an exact test. Simulations illustrate the method's higher efficiency and power over competing allocation procedures in both controlled scenarios and historical experimental data.Comment: 20 pages, 1 algorithm, 2 figures, 8 table

The marginal likelihood of Structural Time Series Models, with application to the euroareaa nd US NAIRU

We propose a simple procedure for evaluating the marginal likelihood in univariate Structural Time Series (STS) models. For this we exploit the statistical properties of STS models and the results in Dickey (1968) to obtain the likelihood function marginally to the variance parameters. This strategy applies under normal-inverted gamma-2 prior distributions for the structural shocks and associated variances. For trend plus noise models such as the local level and the local linear trend, it yields the marginal likelihood by simple or double integration over the (0,1)-support. For trend plus cycle models, we show that marginalizing out the variance parameters greatly improves the accuracy of the Laplace method. We apply this ethodology to the analysis of US and euro area NAIRU.Marginal likelihood, Markov Chain Monte Carlo, unobserved components, bridge sampling, Laplace method, NAIRU

Matching On-the-Fly: Sequential Allocation with Higher Power and Efficiency

We propose a dynamic allocation procedure that increases power and efficiency when measuring an average treatment effect in fixed sample randomized trials with sequential allocation. Subjects arrive iteratively and are either randomized or paired via a matching criterion to a previously randomized subject and administered the alternate treatment. We develop estimators for the average treatment effect that combine information from both the matched pairs and unmatched subjects as well as an exact test. Simulations illustrate the method\u27s higher efficiency and power over several competing allocation procedures in both simulations and in data from a clinical trial

Decrypting geophysical signals at Stromboli Volcano (Italy): Integration of seismic and Ground-Based InSAR displacement data

We present the integration of seismic and Ground‐Based Interferometric Synthetic Aperture Radar system (GBInSAR) displacement data at Stromboli Volcano. Ground deformation in the area of summit vents is positively correlated with both seismic tremor amplitude and cumulative amplitudes of very long period (VLP) signals associated with Strombolian explosions. Changes in VLP amplitudes precede by a few days the variations in ground deformation and seismic tremor. We propose a model where the arrival of fresh, gas‐rich magma from depth enhances gas slug formation, promoting convection and gas transfer throughout the conduit system. At the shallowest portion of the conduit, an increase in volatile content causes a density decrease, expansion of the magmatic column and augmented degassing activity, which respectively induce inflation of the conduit, and increased tremor amplitudes. The temporal delay between increase of VLP and tremor amplitudes/conduit inflation can be interpreted in terms of the different timescales characterizing bulk gas transfer versus slug formation and ascent

Applications of stochastic simulation in two-stage multiple comparisons with the best problem and time average variance constant estimation

In this dissertation, we study two problems. In the first part, we consider the two-stage methods for comparing alternatives using simulation. Suppose there are a finite number of alternatives to compare, with each alternative having an unknown parameter that is the basis for comparison. The parameters are to be estimated using simulation, where the alternatives are simulated independently. We develop two-stage selection and multiple-comparison procedures for simulations under a general framework. The assumptions are that each alternative has a parameter estimation process that satisfies a random- time-change central limit theorem (CLT), and there is a weakly consistent variance estimator (WCVE) for the variance constant appearing in the CLT. The framework encompasses comparing means of independent populations, functions of means, and steady-state means. One problem we consider of considerable practical interest and not handled in previous work on two-stage multiple-comparison procedures is comparing quantiles of alternative populations. We establish the asymptotic validity of our procedures as the prescribed width of the confidence intervals or indifference-zone parameter shrinks to zero. Also, for the steady-state simulation context, we compare our procedures based on WCVEs with techniques that instead use standardized time series methods. In the second part, we propose a new technique of estimating the variance parameter of a wide variety of stochastic processes. This new technique is better than the existing techniques for some standard stochastic processes in terms of bias and variance properties, since it reduces bias at the cost of no significant increase in variance

Space-time discontinuous Galerkin finite element method for two-fluid flows

Multifluid and multiphase flows involve combinations of fluids and interfaces which separate these. These flows are of importance in many natural and industrial processes including fluidized beds and bubble columns. Often the interface is not static but moves with the fluid flow velocity. Also, interface topological changes due to breakup and coalescence processes may occur. Solutions typically have a discontinuous character at the interface between different fluids because of curvature and surface tension effects. In addition, the density and pressure differences across the interface can be very high, like in the case of liquid-gas flows. Also, the existence of shock or contact waves can introduce additional discontinuities into the problem. The aim of this research project was to develop a discontinuous Galerkin method for two-fluid flows, which is accurate, versatile and can alleviate some of the problems commonly encountered with existing methods. A novel numerical method for two-fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local {\it hp}-refinement. A front tracking approach is chosen because these methods ensure a sharp interface between the fluids are capable of high accuracy. The front tracking is incorporated by means of cut-cell mesh refinement, because this type of refinement is very local in nature and hence combines well with the STGD. To compute the interface dynamics the level set method (LSM) is chosen, because of its ability to deal with merging and breakup, since it was expected that the LSM combines well with the cut-cell mesh refinement and also because the LSM is easy to extend to higher dimensions. The small cell problem caused by the cut-cell refinement is solved by using a merging procedure involving bounding box elements, which improves stability and performance of the method. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative. All possible cuts the 0-level set can make with square and cube shaped background elements are identified and for each cut an element refinement is defined explicitly. To ensure connectivity of the refined mesh, the $dim$-dimensional face refinements are defined equal to the $dim-1$-dimensional element refinements. It is expected that this scheme can accurately solve smaller scale problems where the interface shape is of importance and where complex interface physics are involved. To investigate the numerical properties and performance of the numerical algorithm it is applied to a number of one and two dimensional single and two-fluid test problems, including a magma - ideal gas shocktube and a helium cylinder - shock wave interaction problem. To remove oscillations in the flow field near the interface a novel interface flux is presented, which is based on the HLLC flux for a contact discontinuity and can compensate for small errors in the interface position by allowing for a small mass loss. Slope limiting was found to reduce spikes in the solution at the cost of a decrease in accuracy. It was found that the level set deformation restricted the simulation lengths. This problem can be solved by adding a level set reinitialization procedure. To improve the efficiency and stability of the two-fluid numerical algorithm it is advised to incorporate {\it hp}-refinement and a multigrid algorithm. Next, the Object Oriented Programming (OOP) design and implementation of the two-fluid method were discussed. The choice for the OOP language C++ was motivated by the general advantages of OOP such as reusability, reliability, robustness, extensibility and maintainability. In addition the use of OOP allowed for a strong connection between the numerical method and its implementation. In addition, {\it hp}GEM, an OOP package for DG methods was presented. The use of {\it hp}GEM allowed for a reduction of the development time and provided quality control and a coding standard which benefitted the sharing and maintenance of the codes