Markov chain Monte Carlo for a hyperbolic Bayesian inverse problem in traffic flow modeling

As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we empirically explore the sampling challenges this approach offers which have to do with the strong correlations and multimodality of the posterior distribution. In particular, we provide a unified statistical model to estimate using motorway data both boundary conditions and fundamental diagram parameters in a motorway traffic flow model due to Lighthill, Whitham, and Richards known as LWR. This allows us to provide a traffic flow density estimation method that is shown to be superior to two methods found in the traffic flow literature. To sample from this challenging posterior distribution, we use a state-of-the-art gradient-free function space sampler augmented with parallel tempering

Characteristic and necessary minutiae in fingerprints

Fingerprints feature a ridge pattern with moderately varying ridge frequency (RF), following an orientation field (OF), which usually features some singularities. Additionally at some points, called minutiae, ridge lines end or fork and this point pattern is usually used for fingerprint identification and authentication. Whenever the OF features divergent ridge lines (e.g., near singularities), a nearly constant RF necessitates the generation of more ridge lines, originating at minutiae. We call these the necessary minutiae. It turns out that fingerprints feature additional minutiae which occur at rather arbitrary locations. We call these the random minutiae or, since they may convey fingerprint individuality beyond the OF, the characteristic minutiae. In consequence, the minutiae point pattern is assumed to be a realization of the superposition of two stochastic point processes: a Strauss point process (whose activity function is given by the divergence field) with an additional hard core, and a homogeneous Poisson point process, modelling the necessary and the characteristic minutiae, respectively. We perform Bayesian inference using an Markov-Chain-Monte-Carlo (MCMC)-based minutiae separating algorithm (MiSeal). In simulations, it provides good mixing and good estimation of underlying parameters. In application to fingerprints, we can separate the two minutiae patterns and verify by example of two different prints with similar OF that characteristic minutiae convey fingerprint individuality

Distribution of H-beta Hyperfine Couplings in a Tyrosyl Radical Revealed by 263 GHz ENDOR Spectroscopy

1H ENDOR spectra of tyrosyl radicals (Y∙) have been the subject of numerous EPR spectroscopic studies due to their importance in biology. Nevertheless, assignment of all internal 1H hyperfine couplings has been challenging because of substantial spectral overlap. Recently, using 263 GHz ENDOR in conjunction with statistical analysis, we could identify the signature of the Hβ2 coupling in the essential Y122 radical of Escherichia coli ribonucleotide reductase, and modeled it with a distribution of radical conformations. Here, we demonstrate that this analysis can be extended to the full-width 1H ENDOR spectra that contain the larger Hβ1 coupling. The Hβ2 and Hβ1 couplings are related to each other through the ring dihedral and report on the amino acid conformation. The 263 GHz ENDOR data, acquired in batches instead of averaging, and data processing by a new “drift model” allow reconstructing the ENDOR spectra with statistically meaningful confidence intervals and separating them from baseline distortions. Spectral simulations using a distribution of ring dihedral angles confirm the presence of a conformational distribution, consistent with the previous analysis of the Hβ2 coupling. The analysis was corroborated by 94 GHz 2H ENDOR of deuterated Y∙122. These studies provide a starting point to investigate low populated states of tyrosyl radicals in greater detail

Distribution of Hβ hyperfine couplings in a tyrosyl radical revealed by 263 GHz ENDOR spectroscopy

1H ENDOR spectra of tyrosyl radicals (Y∙) have been the subject of numerous EPR spectroscopic studies due to their importance in biology. Nevertheless, assignment of all internal 1H hyperfine couplings has been challenging because of substantial spectral overlap. Recently, using 263 GHz ENDOR in conjunction with statistical analysis, we could identify the signature of the Hβ2 coupling in the essential Y122 radical of Escherichia coli ribonucleotide reductase, and modeled it with a distribution of radical conformations. Here, we demonstrate that this analysis can be extended to the full-width 1H ENDOR spectra that contain the larger Hβ1 coupling. The Hβ2 and Hβ1 couplings are related to each other through the ring dihedral and report on the amino acid conformation. The 263 GHz ENDOR data, acquired in batches instead of averaging, and data processing by a new “drift model” allow reconstructing the ENDOR spectra with statistically meaningful confidence intervals and separating them from baseline distortions. Spectral simulations using a distribution of ring dihedral angles confirm the presence of a conformational distribution, consistent with the previous analysis of the Hβ2 coupling. The analysis was corroborated by 94 GHz 2H ENDOR of deuterated Y∙122. These studies provide a starting point to investigate low populated states of tyrosyl radicals in greater detail

Statistical analysis of ENDOR spectra

Electron–nuclear double resonance (ENDOR) measures the hyperfine interaction of magnetic nuclei with paramagnetic centers and is hence a powerful tool for spectroscopic investigations extending from biophysics to material science. Progress in microwave technology and the recent availability of commercial electron paramagnetic resonance (EPR) spectrometers up to an electron Larmor frequency of 263 GHz now open the opportunity for a more quantitative spectral analysis. Using representative spectra of a prototype amino acid radical in a biologically relevant enzyme, the Y∙122 in Escherichia coli ribonucleotide reductase, we developed a statistical model for ENDOR data and conducted statistical inference on the spectra including uncertainty estimation and hypothesis testing. Our approach in conjunction with 1H/2H isotopic labeling of Y∙122 in the protein unambiguously established new unexpected spectral contributions. Density functional theory (DFT) calculations and ENDOR spectral simulations indicated that these features result from the beta-methylene hyperfine coupling and are caused by a distribution of molecular conformations, likely important for the biological function of this essential radical. The results demonstrate that model-based statistical analysis in combination with state-of-the-art spectroscopy accesses information hitherto beyond standard approaches

Bayesian optimization to estimate hyperfine couplings from 19F ENDOR spectra

ENDOR spectroscopy is a fundamental method to detect nuclear spins in the vicinity of paramagnetic centers and their mutual hyperfine interaction. Recently, site-selective introduction of 19F as nuclear labels has been proposed as a tool for ENDOR-based distance determination in biomolecules, complementing pulsed dipolar spectroscopy in the range of angstrom to nanometer. Nevertheless, one main challenge of ENDOR still consists of its spectral analysis, which is aggravated by a large parameter space and broad resonances from hyperfine interactions. Additionally, at high EPR frequencies and fields (⩾94 GHz/3.4 Tesla), chemical shift anisotropy might contribute to broadening and asymmetry in the spectra. Here, we use two nitroxide-fluorine model systems to examine a statistical approach to finding the best parameter fit to experimental 263 GHz 19F ENDOR spectra. We propose Bayesian optimization for a rapid, global parameter search with little prior knowledge, followed by a refinement by more standard gradient-based fitting procedures. Indeed, the latter suffer from finding local rather than global minima of a suitably defined loss function. Using a new and accelerated simulation procedure, results for the semi-rigid nitroxide-fluorine two and three spin systems lead to physically reasonable solutions, if minima of similar loss can be distinguished by DFT predictions. The approach also delivers the stochastic error of the obtained parameter estimates. Future developments and perspectives are discussed

Posterior Consistency via Precision Operators for Bayesian Nonparametric Drift Estimation in SDEs

We study a Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data. Rewriting the likelihood in terms of local time of the process, and specifying a Gaussian prior with precision operator of differential form, we show that the posterior is also Gaussian with precision operator also of differential form. The resulting expressions are explicit and lead to algorithms which are readily implementable. Using new functional limit theorems for the local time of diffusions on the circle, we bound the rate at which the posterior contracts around the true drift function

Non-parametric Bayesian drift estimation for stochastic differential equations

We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are weaker than those previosly suggested in the literature, we establish posterior consistency in this context. Furthermore, we show that posterior consistency extends to the multidimensional setting as well, which, to the best of our knowledge, is a new result in this setting.Comment: 27 page