The variation of the posterior variance and Bayesian sample size determination

We consider Bayesian sample size determination using a criterion that utilizes the first two moments of the expected posterior variance. We study the resulting sample size in dependence on the chosen prior and explore the success rate for bounding the posterior variance below a prescribed limit under the true sampling distribution. Compared with sample size determination based on the expected average of the posterior variance the proposed criterion leads to an increase in sample size and significantly improved success rates. Generic asymptotic properties are proven, such as an asymptotic expression for the sample size and a sort of phase transition. Our study is illustrated using two real world datasets with Poisson and normally distributed data. Based on our results some recommendations are given

Compressive nano-FTIR chemical mapping

Nano-Fourier-transform infrared spectroscopy (nano-FTIR) combines infrared spectroscopy with scanning probe microscopy (SPM) techniques and enables spectroscopic imaging of molecular and electronic properties of matter at nanometer spatial resolution. The spectroscopic imaging can be used to derive chemical mappings, i.e. the spatial distribution of concentrations of the species contained in a given sample. However, due to the sequential scanning principle underlying SPM, recording the complete spectrum over a large spatial area leads to long measurement times. Furthermore, the acquired spectrum often contains additional signals from species and lineshape effects that are not explicitly accounted for. A compressive chemical mapping approach is proposed for undersampled nano-FTIR data that utilizes sparsity of these additional signals in the spectral domain. The approach combines a projection technique with standard compressed sensing, followed by a spatially regularized regression. Using real nano-FTIR measurements superimposed by simulated interferograms representing the chemical mapping of the contained species, it is demonstrated that the proposed procedure performs well even in cases in which the simulated interferograms and the sparse additional signals exhibit a strong spectral overlap

Dynamic Uncertainty for Compensated Second-Order Systems

The compensation of LTI systems and the evaluation of the according uncertainty is of growing interest in metrology. Uncertainty evaluation in metrology ought to follow specific guidelines, and recently two corresponding uncertainty evaluation schemes have been proposed for FIR and IIR filtering. We employ these schemes to compare an FIR and an IIR approach for compensating a second-order LTI system which has relevance in metrology. Our results suggest that the FIR approach is superior in the sense that it yields significantly smaller uncertainties when real-time evaluation of uncertainties is desired

Assessment of Subsampling Schemes for Compressive Nano-FTIR Imaging

Nano-Fourier transform infrared (FTIR) imaging is a powerful scanning-based technique at nanometer spatial resolution that combines FTIR spectroscopy and scattering-type scanning near-field optical microscopy (s-SNOM). Recording large spatial areas using nano-FTIR is, however, limited, because its sequential data acquisition entails long measurement times. Compressed sensing and low-rank matrix reconstruction are mathematical techniques that can reduce the number of these measurements significantly by requiring only a small fraction of randomly chosen measurements. However, choosing this small set of measurements in a random fashion poses practical challenges for scanning procedures and does not save as much time as desired. We, therefore, consider different subsampling schemes of practical relevance that ensure rapid data acquisition, much faster than random subsampling, in combination with a low-rank matrix reconstruction procedure. It is demonstrated that the quality of the results for almost all subsampling schemes considered, namely, original Lissajous, triangle Lissajous, and random reflection subsampling, is similar to that achieved for random subsampling. This implies that nano-FTIR imaging can be significantly extended to also cover samples extended over large areas while maintaining its high spatial resolution

Fundamental Design Criteria for Logical Scenarios in Simulation-based Safety Validation of Automated Driving Using Sensor Model Knowledge

Scenario-based virtual validation of automated driving functions is a promising method to reduce testing effort in real traffic. In this work, a method for deriving scenario design criteria from a sensor modeling point of view is proposed. Using basic sensor technology specific equations as rough but effective boundary conditions, the accessible information for the system under test are determined. Subsequently, initial conditions such as initial poses of dynamic objects are calculated using the derived boundary conditions for designing logical scenarios. Further interest is given on triggers starting movements of objects during scenarios that are not time but object dependent. The approach is demonstrated on the example of the radar equation and first exemplary results by identifying relevance regions are shown