Hierarchical Graphical Models for Multigroup Shape Analysis using Expectation Maximization with Sampling in Kendall's Shape Space

This paper proposes a novel framework for multi-group shape analysis relying on a hierarchical graphical statistical model on shapes within a population.The framework represents individual shapes as point setsmodulo translation, rotation, and scale, following the notion in Kendall shape space.While individual shapes are derived from their group shape model, each group shape model is derived from a single population shape model. The hierarchical model follows the natural organization of population data and the top level in the hierarchy provides a common frame of reference for multigroup shape analysis, e.g. classification and hypothesis testing. Unlike typical shape-modeling approaches, the proposed model is a generative model that defines a joint distribution of object-boundary data and the shape-model variables. Furthermore, it naturally enforces optimal correspondences during the process of model fitting and thereby subsumes the so-called correspondence problem. The proposed inference scheme employs an expectation maximization (EM) algorithm that treats the individual and group shape variables as hidden random variables and integrates them out before estimating the parameters (population mean and variance and the group variances). The underpinning of the EM algorithm is the sampling of pointsets, in Kendall shape space, from their posterior distribution, for which we exploit a highly-efficient scheme based on Hamiltonian Monte Carlo simulation. Experiments in this paper use the fitted hierarchical model to perform (1) hypothesis testing for comparison between pairs of groups using permutation testing and (2) classification for image retrieval. The paper validates the proposed framework on simulated data and demonstrates results on real data.Comment: 9 pages, 7 figures, International Conference on Machine Learning 201

Seismic Response of a Tall Building to Recorded and Simulated Ground Motions

Seismological modeling technologies are advancing to the stage of enabling fundamental simulation of earthquake fault ruptures, which offer new opportunities to simulate extreme ground motions for collapse safety assessment and earthquake scenarios for community resilience studies. With the goal toward establishing the reliability of simulated ground motions for performance-based engineering, this paper examines the response of a 20-story concrete moment frame building analyzed by nonlinear dynamic analysis under corresponding sets of recorded and simulated ground motions. The simulated ground motions were obtained through a larger validation study via the Southern California Earthquake Center (SCEC) Broadband Platform (BBP) that simulates magnitude 5.9 to 7.3 earthquakes. Spectral shape and significant duration are considered when selecting ground motions in the development of comparable sets of simulated and recorded ground motions. Structural response is examined at different intensity levels up to collapse, to investigate whether a statistically significant difference exists between the responses to simulated and recorded ground motions. Results indicate that responses to simulated and recorded ground motions are generally similar at intensity levels prior to observation of collapses. Collapse capacities are also in good agreement for this structure. However, when the structure was made more sensitive to effects of ground motion duration, the differences between observed collapse responses increased. Research is ongoing to illuminate reasons for the difference and whether there is a systematic bias in the results that can be traced back to the ground motion simulation techniques

Mean reversion in stock index futures markets: a nonlinear analysis

Several stylized theoretical models of futures basis behavior under nonzero transactions costs predict nonlinear mean reversion of the futures basis towards its equilibrium value. Nonlinearly mean-reverting models are employed to characterize the basis of the SandP 500 and the FTSE 100 indices over the post-1987 crash period, capturing empirically these theoretical predictions and examining the view that the degree of mean reversion in the basis is a function of the size of the deviation from equilibrium. The estimated half lives of basis shocks, obtained using Monte Carlo integration methods, suggest that for smaller shocks to the basis level the basis displays substantial persistence, while for larger shocks the basis exhibits highly nonlinear mean reversion towards its equilibrium value. © 2002 Wiley Periodicals, Inc

Does Gravitational Clustering Stabilize On Small Scales?

The stable clustering hypothesis is a key analytical anchor on the nonlinear dynamics of gravitational clustering in cosmology. It states that on sufficiently small scales the mean pair velocity approaches zero, or equivalently, that the mean number of neighbours of a particle remains constant in time at a given physical separation. In this paper we use N-body simulations of scale free spectra P(k) \propto k^n with -2 \leq n \leq 0 and of the CDM spectrum to test for stable clustering using the time evolution and shape of the correlation function \xi(x,t), and the mean pair velocity on small scales. For all spectra the results are consistent with the stable clustering predictions on the smallest scales probed, x < 0.07 x_{nl}(t), where x_{nl}(t) is the correlation length. The measured stable clustering regime corresponds to a typical range of 200 \lsim \xi \lsim 2000, though spectra with more small scale power approach the stable clustering asymptote at larger values of \xi. We test the amplitude of \xi predicted by the analytical model of Sheth \& Jain (1996), and find agreement to within 20\% in the stable clustering regime for nearly all spectra. For the CDM spectrum the nonlinear \xi is accurately approximated by this model with n \simeq -2 on physical scales \lsim 100-300 h^{-1} kpc for \sigma_8 = 0.5-1, and on smaller scales at earlier times. The growth of \xi for CDM-like models is discussed in the context of a power law parameterization often used to describe galaxy clustering at high redshifts. The growth parameter \epsilon is computed as a function of time and length scale, and found to be larger than 1 in the moderately nonlinear regime -- thus the growth of \xi is much faster on scales of interest than is commonly assumed.Comment: 13 pages, 8 figures included; submitted to MNRA

3-Regime symmetric STAR modeling and exchange rate reversion

The breakdown of the Bretton Woods system and the adoption of generalised floating exchange rates ushered in a new era of exchange rate volatility and uncer­tainty. This increased volatility lead economists to search for economic models able to describe observed exchange rate behavior. In the present paper we propose more general STAR transition functions which encompass both threshold nonlinearity and asymmetric effects. Our framework allows for a gradual adjustment from one regime to another, and considers threshold effects by encompassing other existing models, such as TAR models. We apply our methodology to three different exchange rate data-sets, one for developing countries, and official nominal exchange rates, and the second for emerging market economies using black market exchange rates and the third for OECD economies.unit root tests, threshold autoregressive models, purchasing power parity.

A range unit root test

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analyse time series with strong serial dependence, the focus being placed in the detection of eventual unit roots in an autorregresive model fitted to the series. In this paper we propose a completely different method to test for the type of long-wave patterns observed not only in unit root time series but also in series following more complex data generating mechanisms. To this end, our testing device analyses the trend exhibit by the data, without imposing any constraint on the generating mechanism. We call our device the Range Unit Root (RUR) Test since it is constructed from running ranges of the series. These statistics allow a more general characterization of a strong serial dependence in the mean behavior, thus endowing our test with a number of desirable properties, among which its error-model-free asymptotic distribution, the invariance to nonlinear monotonic transformations of the series and the robustness to the presence of level shifts and additive outliers. In addition, the RUR test outperforms the power of standard unit root tests on near-unit-root stationary time series and is asymptotically immune to noise