Bayesian subsampling of time-domain electromagnetic data using kernel density product

The Bayesian method is a powerful tool to estimate the resistivity distribution and associate uncertainty from time-domain electromagnetic (TDEM) data. As the forward simulation of the TDEM method is computationally expensive and a large number of samples are needed to globally explore the model space, the full Bayesian inversion of TDEM data is limited to layered models. To make high-dimensional Bayesian inversion tractable, we propose a divide-and-conquer strategy to speed up the Bayesian inversion of TDEM data. First, the full datasets and model spaces are divided into disjoint batches based on the coverage of the sources so that independent and highly efficient Bayesian subsampling can be conducted. Then, the samples from each subsampling procedure are combined to get the full posterior. To obtain an asymptotically unbiased approximation to the full posterior, a kernel density product method is used to reintegrate samples from each subposterior. The model parameters and their uncertainty are estimated from the full posterior. The proposed method is tested on synthetic examples and applied to a field dataset acquired with a large fixed-loop configuration. The 2D section from the Bayesian inversion revealed several mineralized zones, one of which matches well with the information from a nearby drill hole. The field example shows the ability of Bayesian inversion to infer reliable resistivity and uncertainty.

Shell evolution for neutron-rich 46–54Ar isotopes in the full and truncated fp neutron model spaces

The shell evolution of even–even drip line argon isotopes [Formula: see text] has been investigated via the shell model calculations using SDPF-U and SDPF-NR two-body effective interactions in two different shell model spaces [Formula: see text] and [Formula: see text]. In this work, the energy of first [Formula: see text], reduced transition probability [Formula: see text], excitation energy levels as well as how the proton shells evolve with [Formula: see text] have been studied. Excellent agreements were obtained for the first [Formula: see text] level along the investigated isotopes within [Formula: see text] and [Formula: see text] model spaces.

Measuring the Effects of Light Distribution on Spatial Brightness

<p><b>By changing the light distribution it is possible to double the apparent amount of light in a space without any increase in its overall luminance. If one simply assumes that the apparent amount of light in a space — its spatial brightness — is described by its mean luminance (or similar measures) then substantial errors may be made.</b></p> <p>We carried out two experiments, measuring the brightness of 19 different model spaces. Our results demonstrate that making light distributions more non-uniform can make spaces appear both significantly brighter and significantly darker, depending on how the light distribution is changed. This challenges most existing studies in the field that argue that non-uniformity of the luminance distribution simply makes spaces look darker. Indeed, the observed pattern in brightness between our conditions cannot be consistently explained by a simple measure of the uniformity of the luminance distribution. We thus reject all previously proposed models of light distribution and spatial brightness.</p> <p>The best explanation of this and the apparent disagreements in the literature over the effects of non-uniformity appears to be that spatial brightness is affected by the qualitative appearance of the luminances in the space. Light sources and non-luminous surfaces have different effects. We propose a ‘duel’-process model of spatial brightness in which it is the sum of two opposed processes: the effects of the surfaces, and the effects of the light source(s). Non-uniform patterns of surface reflectance and illumination tend to make a space appear brighter. Non-uniformity as a result of a large difference between luminance of the light source(s) and the surfaces makes a space appear darker. If the light source is hidden from direct view its darkening effect is removed, which can make the space appear significantly brighter. Depending on the relative strength of these two processes, a non-uniform luminance distribution may thus appear either brighter or darker than a more uniform distribution.</p> <p>Additionally, we highlight issues demonstrated in both the failure of models previously proposed by the literature, and our exploration of potential implementations of the ‘duel’-process model. It is very easy to produce a good correlation with a defensible metric that will not generalise to other data sets. A metric having a good correlation in a study provides very little reason to actually believe it. If we wish to develop a model of the effects of light distribution that we can trust, we need to demonstrate its robustness by testing its underlying assumptions and showing them to be well supported. As we show, there is a large variety of these that need to be worked through.</p>

Measuring the Effects of Light Distribution on Spatial Brightness

<p><b>By changing the light distribution it is possible to double the apparent amount of light in a space without any increase in its overall luminance. If one simply assumes that the apparent amount of light in a space — its spatial brightness — is described by its mean luminance (or similar measures) then substantial errors may be made.</b></p> <p>We carried out two experiments, measuring the brightness of 19 different model spaces. Our results demonstrate that making light distributions more non-uniform can make spaces appear both significantly brighter and significantly darker, depending on how the light distribution is changed. This challenges most existing studies in the field that argue that non-uniformity of the luminance distribution simply makes spaces look darker. Indeed, the observed pattern in brightness between our conditions cannot be consistently explained by a simple measure of the uniformity of the luminance distribution. We thus reject all previously proposed models of light distribution and spatial brightness.</p> <p>The best explanation of this and the apparent disagreements in the literature over the effects of non-uniformity appears to be that spatial brightness is affected by the qualitative appearance of the luminances in the space. Light sources and non-luminous surfaces have different effects. We propose a ‘duel’-process model of spatial brightness in which it is the sum of two opposed processes: the effects of the surfaces, and the effects of the light source(s). Non-uniform patterns of surface reflectance and illumination tend to make a space appear brighter. Non-uniformity as a result of a large difference between luminance of the light source(s) and the surfaces makes a space appear darker. If the light source is hidden from direct view its darkening effect is removed, which can make the space appear significantly brighter. Depending on the relative strength of these two processes, a non-uniform luminance distribution may thus appear either brighter or darker than a more uniform distribution.</p> <p>Additionally, we highlight issues demonstrated in both the failure of models previously proposed by the literature, and our exploration of potential implementations of the ‘duel’-process model. It is very easy to produce a good correlation with a defensible metric that will not generalise to other data sets. A metric having a good correlation in a study provides very little reason to actually believe it. If we wish to develop a model of the effects of light distribution that we can trust, we need to demonstrate its robustness by testing its underlying assumptions and showing them to be well supported. As we show, there is a large variety of these that need to be worked through.</p>

Asymmetric Truncated Hankel Operators: Rank One, Matrix Representation

Asymmetric truncated Hankel operators are the natural generalization of truncated Hankel operators. In this paper, we determine all rank one operators of this class. We explore these operators on finite-dimensional model spaces, in particular, their matrix representation. We also give their matrix representation and the one for asymmetric truncated Toeplitz operators in the case of model spaces associated to interpolating Blaschke products.

A common range problem for model spaces

We refine a result of [J. E. McCarthy, Common range of co-analytic Toeplitz operators, J. Amer. Math. Soc. 3 1990, 4, 793–799] and explore the common range of the co-analytic Toeplitz operators on a model space. The tools used to do this also yield information about when one can interpolate with an outer function.

Characterizing Network Search Algorithms Developed for Dynamic Causal Modeling

Dynamic causal modeling (DCM) is a widely used tool to estimate the effective connectivity of specified models of a brain network. Finding the model explaining measured data is one of the most important outstanding problems in Bayesian modeling. Using heuristic model search algorithms enables us to find an optimal model without having to define a model set a priori. However, the development of such methods is cumbersome in the case of large model-spaces. We aimed to utilize commonly used graph theoretical search algorithms for DCM to create a framework for characterizing them, and to investigate relevance of such methods for single-subject and group-level studies. Because of the enormous computational demand of DCM calculations, we separated the model estimation procedure from the search algorithm by providing a database containing the parameters of all models in a full model-space. For test data a publicly available fMRI dataset of 60 subjects was used. First, we reimplemented the deterministic bilinear DCM algorithm in the ReDCM R package, increasing computational speed during model estimation. Then, three network search algorithms have been adapted for DCM, and we demonstrated how modifications to these methods, based on DCM posterior parameter estimates, can enhance search performance. Comparison of the results are based on model evidence, structural similarities and the number of model estimations needed during search. An analytical approach using Bayesian model reduction (BMR) for efficient network discovery is already available for DCM. Comparing model search methods we found that topological algorithms often outperform analytical methods for single-subject analysis and achieve similar results for recovering common network properties of the winning model family, or set of models, obtained by multi-subject family-wise analysis. However, network search methods show their limitations in higher level statistical analysis of parametric empirical Bayes. Optimizing such linear modeling schemes the BMR methods are still considered the recommended approach. We envision the freely available database of estimated model-spaces to help further studies of the DCM model-space, and the ReDCM package to be a useful contribution for Bayesian inference within and beyond the field of neuroscience.