Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models

Estimating a covariance matrix efficiently and discovering its structure are important statistical problems with applications in many fields. This article takes a Bayesian approach to estimate the covariance matrix of Gaussian data. We use ideas from Gaussian graphical models and model selection to construct a prior for the covariance matrix that is a mixture over all decomposable graphs, where a graph means the configuration of nonzero offdiagonal elements in the inverse of the covariance matrix. Our prior for the covariance matrix is such that the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We give empirical results that show the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the correct decomposable graph and in more efficiently estimating the covariance matrix. The advantage is greatest when the number of observations is small relative to the dimension of the covariance matrix. The article also shows empirically that there is minimal change in statistical efficiency in using the mixture over decomposable graphs prior for estimating a general covariance compared to the Bayesian estimator by Wong et al. (2003), even when the graph of the covariance matrix is nondecomposable. However, our approach has some important advantages over that of Wong et al. (2003). Our method requires the number of decomposable graphs for each graph size. We show how to estimate these numbers using simulation and that the simulation results agree with analytic results when such results are known. We also show how to estimate the posterior distribution of the covariance matrix using Markov chain Monte Carlo with the elements of the covariance matrix integrated out and give empirical results that show the sampler is computationally efficient and converges rapidly. Finally, we note that both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.Covariance selection; Graphical models; Reduced conditional sampling; Variable selection

Kajian Berbagai Metode Integrasi Langsung Untuk Analisis Dinamis

Proses perhitungan analisis dinamis dapat diselesaikan dengan bantuan program yang sudah ada, seperti SAP2000, Seismostruct, dan Opensees. Dalam beberapa program, pengguna dihadapkan dengan pilihan-pilihan metode penyelesaian analisis dinamis. Dilakukan kajian untuk mempelajari metode integrasi langsung pada analisis dinamis, dengan tinjauan keempat metode yaitu metode diferensiasi terpusat, metode Houbolt, metode Wilson dan metode Newmark, sehingga dapat diketahui perbedaan masing-masing metode integrasi langsung dalam analisis dinamis dari sisikeunggulan dan kekurangan. Didapatkan beberapa kesimpulan dari keempat metode integrasi langsung analisis dinamis, dimana beberapa kesimpulan dapat digunakan untuk menentukan metode integrasi langsung yang akan digunakan untuk menyelesaikan persamaan analisis dinamis

Pengembangan Penghalusan Jaring Elemen Segitiga Regangan Konstan Secara Adaptif

Penelitian ini menghasilkan program matlab yang mampu melakukan penghalusan secara adaptif pada diskretisasi awal yang kasar sampai mendapatkan diskretisasi optimal dimana nilai error pada hasil analisanya memenuhi syarat/target yang ditentukan. Elemen yang digunakan adalah elemen segitiga regangan konstan untuk menganalisa masalah tegangan dan regangan bidang. Pengujian program dilakukan dengan menggunakan berbagai benchmark problems yang disediakan oleh literature. Hasil pengujian menunjukkan bahwa parameter strain energy error dapat digunakan untuk perhitungan adaptifitas dan pada diskretisasi optimalnya menghasilkan nilai yang sangat mendekat solusi referensinya. Sebagian besar proses sudah dapat dilakukan secara otomatis namun untuk masalah tertentu diperlukan penyesuaian pada kondisi batas dan pembebanannya agar mengikuti diskretisai baru. Masalah otomasi juga muncul pada struktur dengan sisi lengkung. Diskretisasi optimal pada akhir dari proses adaptifitas memang memberikan hasil yang mendekati eksak, namun karena menggunakan metode element subdivision dan alat bantu delaunay triangulation, maka terdapat ketidakefektifan yaitu banyak elemen yang ukurannya lebih kecil dari ukuran yang diperlukan

A state-space model of the burst suppression ratio

Burst suppression is an electroencephalogram pattern observed in states of severely reduced brain activity, such as general anesthesia, hypothermia and anoxic brain injuries. The burst suppression ratio (BSR), defined as the fraction of EEG spent in suppression per epoch, is the standard quantitative measure used to characterize burst suppression. We present a state space model to compute a dynamic estimate of the BSR as the instantaneous probability of suppression. We estimate the model using an approximate EM algorithm and illustrate its application in the analysis of rodent burst suppression recordings under general anesthesia. Our approach removes the need to artificially average the ratio over long epochs and allows us to make formal statistical comparisons of burst activity at different time points. Our state-space model suggests a more principled way to analyze this key EEG feature that may offer more informative assessments of its associated brain state.Massachusetts General Hospital. Dept. of Anesthesia and Critical CareNational Institutes of Health (U.S.) (Grant DP1 OD003646-01)National Institutes of Health (U.S.) (Grant R01 MH071847)National Institutes of Health (U.S.) (Grant K08 GM094394

J/Psi Propagation in Hadronic Matter

We study J/$\psi$ propagation in hot hadronic matter using a four-flavor chiral Lagrangian to model the dynamics and using QCD sum rules to model the finite size effects manifested in vertex interactions through form factors. Charmonium breakup due to scattering with light mesons is the primary impediment to continued propagation. Breakup rates introduce nontrivial temperature and momentum dependence into the J/$\psi$ spectral function.Comment: 6 Pages LaTeX, 3 postscript figures. Proceedings for Strangeness in Quark Matter 2003, Atlantic Beach, NC, March 12-17, 2003; minor corrections in version 2, to appear in J. Phys.

Haiyan Song is a Chair Professor of Tourism in the School of Hotel and Tourism Management, The Hong Kong Polytechnic University, Hong Kong. Stephen Witt is a Visiting Professor in the School of Hotel and Tourism Management

The advantages of error correction models (ECMs) and time varying parameter (TVP) models have been discussed in the tourism forecasting literature. These models are now combined to give a new single-equation model, the time varying parameter error correction model (TVP-ECM), which is applied for the first time in the context of tourism demand forecasting. The empirical study focuses on tourism demand, measured by tourism spending per capita, by UK residents for 5 key Western European destinations. Based on the discussion of how the series considered related to most, the empirical results show that the TVP-ECM can be expected to outperform a number of alternative econometric and time series models in forecasting the demand for tourism. By measuring performance in terms of the accuracy of the forecasts of growth (rates of change) and showing that TVP-ECM performs very well for this as well as conventional assessment of the level of demand in this study, it is suggested that forecasters of tourism demand levels and growth rates can feel comfortable using TVP-ECM given that it is expected to perform well

Survival of Chondrocytes in Rabbit Septal Cartilage After Electromechanical Reshaping

Electromechanical reshaping (EMR) has been recently described as an alternative method for reshaping facial cartilage without the need for incisions or sutures. This study focuses on determining the short- and long-term viability of chondrocytes following EMR in cartilage grafts maintained in tissue culture. Flat rabbit nasal septal cartilage specimens were bent into semi-cylindrical shapes by an aluminum jig while a constant electric voltage was applied across the concave and convex surfaces. After EMR, specimens were maintained in culture media for 64 days. Over this time period, specimens were serially biopsied and then stained with a fluorescent live–dead assay system and imaged using laser scanning confocal microscopy. In addition, the fraction of viable chondrocytes was measured, correlated with voltage, voltage application time, electric field configuration, and examined serially. The fraction of viable chondrocytes decreased with voltage and application time. High local electric field intensity and proximity to the positive electrode also focally reduced chondrocyte viability. The density of viable chondrocytes decreased over time and reached a steady state after 2–4 weeks. Viable cells were concentrated within the central region of the specimen. Approximately 20% of original chondrocytes remained viable after reshaping with optimal voltage and application time parameters and compared favorably with conventional surgical shape change techniques such as morselization