Post-hoc power estimation for topological inference in fMRI

ABSTRACTThe paper presents 3D diffraction imaging based on the spectral decomposition of a different combination of selective or partial images. These images are obtained by the pre‐stack asymmetric migration procedure, which is weighted data summation. Spectral decomposition is done in the Fourier domain with respect to spatial dip and azimuth angles. Numerical examples with the application of different workflows for the synthetic and real data examples demonstrate detailed reliable reconstruction of the fractured zones and reliable reconstruction of fracture orientation on synthetic and real 3D data examples.

Chapter 12 - Specific Methods

In this paper we propose a longitudinal credit rating model which accounts for the serial correlation in the ratings. We achieve this by imposing an autoregressive structure of order one on the errors of a multivariate ordinal regression model. The longitudinal structure of the model improves significantly both the goodness-of-fit and predictive performance compared to static models. By modeling the joint distribution of the ratings over time, the framework allows us to obtain predictions conditional on the past rating history of a firm, which clearly out-perform the unconditional predictions both in- and out-of-sample. This shows the importance of incorporating past rating information in the prediction. Another upside lies in the framework’s ability to deal with missing rating observations. A real data example is provided by using a sample of US publicly traded corporates rated by S&P for the years 1985–2016. The determinants of corporate credit ratings are pre-selected using the ordinal version of the least absolute shrinkage and selection operator (LASSO). Additionally, as a model extension we allow the regression coefficients of the selected variables to vary over time in the longitudinal model. This allows us to gain a better understanding of the drivers and evolution of the rating behavior over the sample period. Finally, based on the longitudinal model with LASSO selected variables, we find evidence that S&P exhibits procyclical aspects in their rating behavior. • A credit rating model accounting for the serial correlation in the ratings. • A variable selection exercise is performed using ordinal LASSO. • Predictions conditional on the past rating history of a firm. • Longitudinal structure improves goodness-of-fit and predictive performance. • Real data example of US corporates rated by S&P for the years 1985–2016.

Most deconvolution algorithms try to transform the seismic wavelet into spikes by designing inverse filters that remove an estimated seismic wavelet from seismic data. We assume that seismic trace subtle discontinuities are associated with acoustic impedance contrasts and can be characterized by wavelet transform spectral ridges, also called modulus maxima lines (WTMML), allowing us to improve seismic resolution by using the wavelet transform. Specifically, we apply the complex Morlet continuous wavelet transform (CWT) to each seismic trace and compute the WTMMLs. Then, we reconstruct the seismic trace with the inverse continuous wavelet transform from the computed WTMMLs with a broader band complex Morlet wavelet than that used in the forward CWT. Because the reconstruction process preserves amplitude and phase along different scales, or frequencies, the result looks like a deconvolution method. Considering this high-resolution seismic representation as a reflectivity approximation, we estimate the relative acoustic impedance (RAI) by filtering and trace integrating it. Conventional deconvolution algorithms assume the seismic wavelet to be stochastic, while the CWT is implicitly time varying such that it can be applied to both depth and time-domain data. Using synthetic and real seismic data, we evaluated the effectiveness of the methodology on detecting seismic events associated with acoustic impedance changes. In the real data examples, time and in-depth RAI results, show good correlation with real P-impedance band-pass data computed using more rigorous commercial inversion software packages that require well logs and low-frequency velocity model information.

In the early stage of acoustic full-waveform inversion (AFWI), it is important to exploit the long-wavelength features of the gradient and suppress its short-wavelength features to update the background velocity. However, due to strong near-offset PP reflections and multiples within the pressure data, conventional AFWI sometimes primarily reconstructs the short-wavelength features of a given model and fails to converge on a reliable subsurface P-wave velocity model. Therefore, this study, we propose the usage of pseudo-horizontal particle acceleration (pseudo-ax) data for AFWI, rather than the original pressure data. Because the amplitudes of PP reflections are implicitly weighted according to the reflection angle in pseudo-ax data, the near-offset PP reflections and multiples of the pseudo-ax data are much weaker than those of the pressure data. As a result, AFWI using pseudo-ax data focuses on reconstructing the longer-wavelength features of a given model in the early iterations, and then gradually reconstructs short-wavelength features as the inversion process continues. Using synthetic and real data examples for the Volve oilfield in the North Sea, we examined the effects and feasibility of this strategy. In the synthetic data example, the proposed strategy rapidly reduced far-offset data misfits related to long-wavelength feature updates and achieved smaller model misfits than the conventional strategy. The real data example showed that the velocity model reconstructed using the proposed strategy flattened some of the reflectors at the angle-domain common-image gathers (ADCIGs) better than the velocity model obtained using the conventional strategy. These findings demonstrate that our strategy converges closer to the real P-wave velocity model than the conventional strategy by building a hierarchical velocity model from long- to short-wavelength structures.

Extension of SO-PLS to multi-way arrays: SO-N-PLS

This article highlights some numerical challenges when implementing the bounded integer model for composite score modeling and suggests an improved implementation. The improvement is based on an approximation of the logarithm of the error function. After presenting the derivation of the improved implementation, the article compares the performance of the algorithm to a naive implementation of the log-likelihood using both simulations and a real data example. In the simulation setting, the improved algorithm yielded more precise and less biased parameter estimates when the within-subject variability was small and estimation was performed using the Laplace algorithm. The estimation results did not differ between implementations when the SAEM algorithm was used. For the real data example, bootstrap results differed between implementations with the improved implementation producing identical or better objective function values. Based on the findings in this article, the improved implementation is suggested as the new default log-likelihood implementation for the bounded integer model.

In randomised controlled trials, the effect of treatment on those who comply with allocation to active treatment can be estimated by comparing their outcome to those in the comparison group who would have complied with active treatment had they been allocated to it. We compare three estimators of the causal effect of treatment on compliers when this is a parameter in a proportional hazards model and quantify the bias due to omitting baseline prognostic factors. Causal estimates are found directly by maximising a novel partial likelihood; based on a structural proportional hazards model; and based on a 'corrected dataset' derived after fitting a rank-preserving structural failure time model. Where necessary, we extend these methods to incorporate baseline covariates. Comparisons use simulated data and a real data example. Analysing the simulated data, we found that all three methods are accurate when an important covariate was included in the proportional hazards model (maximum bias 5.4%). However, failure to adjust for this prognostic factor meant that causal treatment effects were underestimated (maximum bias 11.4%), because estimators were based on a misspecified marginal proportional hazards model. Analysing the real data example, we found that adjusting causal estimators is important to correct for residual imbalances in prognostic factors present between trial arms after randomisation. Our results show that methods of estimating causal treatment effects for time-to-event outcomes should be extended to incorporate covariates, thus providing an informative compliment to the corresponding intention-to-treat analysis.

Trade-off Analysis for Infrastructure Management: New Approaches to Cross-asset Challenges

ABSTRACTAutomatic feature detection from seismic data is a demanding task in today's interpretation workstations. Channels are among important stratigraphic features in seismic data both due to their reservoir capability or drilling hazard potential. Shearlet transform as a multi‐scale and multi‐directional transformation is capable of detecting anisotropic singularities in two and higher dimensional data. Channels occur as edges in seismic data, which can be detected based on maximizing the shearlet coefficients through all sub‐volumes at the finest scale of decomposition. The detected edges may require further refinement through the application of a thinning methodology. In this study, a three‐dimensional, pyramid‐adapted, compactly supported shearlet transform was applied to synthetic and real channelised, three‐dimensional post‐stack seismic data in order to decompose the data into different scales and directions for the purpose of channel boundary detection. In order to be able to compare the edge detection results based on three‐dimensional shearlet transform with some famous gradient‐based edge detectors, such as Sobel and Canny, a thresholding scheme is necessary. In both synthetic and real data examples, the three‐dimensional shearlet edge detection algorithm outperformed Sobel and Canny operators even in the presence of Gaussian random noise.

Enhancing the detection of small coal structures by seismic diffraction imaging

We developed a sparse multichannel blind deconvolution (SMBD) method. The method is a modification of the multichannel blind deconvolution technique often called Euclid deconvolution, in which the multichannel impulse response of the earth is estimated by solving an homogeneous system of equations. Classical Euclid deconvolution is unstable in the presence of noise and requires the correct estimation of the length of the seismic wavelet. The proposed method, on the other hand, can tolerate moderate levels of noise and does not require a priori knowledge of the length of the wavelet. SMBD solves the homogeneous system of equations arising in Euclid deconvolution by imposing sparsity on the unknown multichannel impulse response. Trivial solutions to the aforementioned homogeneous system of equations are avoided by seeking sparse solutions on the unit sphere. We tested SMBD with synthetic and real data examples. Synthetic examples were used to judge the viability of the method in terms of noise. We found that SMBD gives reasonable estimates of the wavelet and reflectivity series for [Formula: see text]. The results clearly deteriorated when we tried to work on data that were severely contaminated by noise. A real marine data set was also used to test SMBD. In this case, the estimated wavelet was compared with a wavelet estimated by averaging first breaks. The estimated wavelet showed a noticeable resemblance to the average first break with normalized correlation coefficient of 0.92.

Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this paper we address the common setting in which one of the graphs to match is a bipartite network and one is unipartite. Commonly, the bipartite networks are collapsed or projected into a unipartite graph, and graph matching proceeds as in the classical setting. This potentially leads to noisy edge estimates and loss of information. We formulate the graph matching problem between a bipartite and a unipartite graph using an undirected graphical model, and introduce methods to find the alignment with this model without collapsing. We theoretically demonstrate that our methodology is consistent, and provide non-asymptotic conditions that ensure exact recovery of the matching solution. In simulations and real data examples, we show how our methods can result in a more accurate matching than the naive approach of transforming the bipartite networks into unipartite, and we demonstrate the performance gains achieved by our method in simulated and real data networks, including a co-authorship-citation network pair, and brain structural and functional data.

Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically update the estimates of mean and covariance functions for functional data. The kernel-type estimates can be decomposed into two sufficient statistics depending on the data-driven bandwidths. We propose to approximate the future optimal bandwidths by a sequence of dynamically changing candidates and combine the corresponding statistics across blocks to form the updated estimation. The proposed online method is easy to compute based on the stored sufficient statistics and the current data block. We derive the asymptotic normality and, more importantly, the relative efficiency lower bounds of the online estimates of mean and covariance functions. This provides insight into the relationship between estimation accuracy and computational cost driven by the length of candidate bandwidth sequence. Simulations and real data examples are provided to support such findings. Supplementary materials for this article are available online.

An M-estimator for reduced-rank system identification