Dimensional Distribution Research Articles

Efficient gravitational wave searches with pulsar timing arrays using Hamiltonian Monte Carlo

Pulsar timing arrays (PTAs) detect low-frequency gravitational waves (GWs) by looking for correlated deviations in pulse arrival times. Current Bayesian searches use Markov Chain Monte Carlo (MCMC) methods, which struggle to sample the large number of parameters needed to model the PTA and GW signals. As the data span and number of pulsars increase, this problem will only worsen. An alternative Monte Carlo sampling method, Hamiltonian Monte Carlo (HMC), utilizes Hamiltonian dynamics to produce sample proposals informed by first-order gradients of the model likelihood. This in turn allows it to converge faster to high dimensional distributions. We implement HMC as an alternative sampling method in our search for an isotropic stochastic GW background, and show that this method produces equivalent statistical results to similar analyses run with standard MCMC techniques, while requiring 100-200 times fewer samples. We show that the speed of HMC sample generation scales as $\mathcal{O}(N_\mathrm{psr}^{5/4})$ where $N_\mathrm{psr}$ is the number of pulsars, compared to $\mathcal{O}(N_\mathrm{psr}^2)$ for MCMC methods. These factors offset the increased time required to generate a sample using HMC, demonstrating the value of adopting HMC techniques for PTAs.

Testing the boundaries: Normalizing Flows for higher dimensional data sets

Normalizing Flows (NFs) are emerging as a powerful class of generative models, as they not only allow for efficient sampling, but also deliver, by construction, density estimation. They are of great potential usage in High Energy Physics (HEP), where complex high dimensional data and probability distributions are everyday’s meal. However, in order to fully leverage the potential of NFs it is crucial to explore their robustness as data dimensionality increases. Thus, in this contribution, we discuss the performances of some of the most popular types of NFs on the market, on some toy data sets with increasing number of dimensions.

Deep Learning–Based Dose Prediction for Automated, Individualized Quality Assurance of Head and Neck Radiation Therapy Plans

This study aimed to use deep learning-based dose prediction to assess head and neck (HN) plan quality and identify suboptimal plans. A total of 245 volumetric modulated arc therapy HN plans were created using RapidPlan knowledge-based planning (KBP). A subset of 112 high-quality plans was selected under the supervision of an HN radiation oncologist. We trained a 3D Dense Dilated U-Net architecture to predict 3-dimensional dose distributions using 3-fold cross-validation on 90 plans. Model inputs included computed tomography images, target prescriptions, and contours for targets and organs at risk (OARs). The model's performance was assessed on the remaining 22 test plans. We then tested the application of the dose prediction model for automated review of plan quality. Dose distributions were predicted on 14 clinical plans. The predicted versus clinical OAR dose metrics were compared to flag OARs with suboptimal normal tissue sparing using a 2 Gy dose difference or 3% dose-volume threshold. OAR flags were compared with manual flags by 3 HN radiation oncologists. The predicted dose distributions were of comparable quality to the KBP plans. The differences between the predicted and KBP-planned D1%,D95%, and D99% across the targets were within -2.53% ± 1.34%, -0.42% ± 1.27%, and -0.12% ± 1.97%, respectively, and the OAR mean and maximum doses were within -0.33 ± 1.40 Gy and -0.96 ± 2.08 Gy, respectively. For the plan quality assessment study, radiation oncologists flagged 47 OARs for possible plan improvement. There was high interphysician variability; 83% of physician-flagged OARs were flagged by only one of 3 physicians. The comparative dose prediction model flagged 63 OARs, including 30 of 47 physician-flagged OARs. Deep learning can predict high-quality dose distributions, which can be used as comparative dose distributions for automated, individualized assessment of HN plan quality.

Generalized gamma distribution based on the Bayesian approach with application to investment modelling

The Generalized Gamma Distribution (GGD) is one of the most popular distributions in analyzing real lifetime datasets. Estimating the parameters of a high dimensional probability distribution is challenging due to the complexities associated with the resulting objectives function. When traditional estimation techniques fail due to complexity in the model objectives function, other powerful computational approaches are employed. In this study, a Bayesian approach to Generalized Gamma Distribution (GGD) based on Markov Chain Monte-Carlo (MCMC) has been employed to estimate model parameters. This study considers the Bayesian approach to GGD parameters using the Adaptive Rejection Metropolis Sampling (ARMS) technique of random variable generation within the Gibbs sampler. The MCMC approach has been used for estimating the multi-dimensional objectives function distribution. The results of the ARMS were compared to the existing Simulated annealing (SA) algorithm and Method of Moment (MM) based on modified internal rate of return data (MIRR). The performances of various derived estimators were recorded using the Markov chain Monte Carlo simulation technique for different sample sizes. The study reveals that ARMS's performance is marginally better than the existing SA and MA approaches. The efficiency of ARMS does not require a larger sample size as the SA does, in the case of simulated data. The performances of ARMS and SA are similar comparing them to the MM as an initial assumption in the case of real MIRR data. However, ARMS gives an acceptable estimated parameter for the different sample sizes due to its ability to evaluate the conditional distributions easily and sample from them exactly.

Analysis of superconducting silicon epilayers by atom probe tomography: composition and evaporation field

Three dimensional distributions of boron atoms incorporated into crystalline silicon (3-9 at.% of boron) well above the solubility limit are measured by atom probe tomography (APT). Samples have been prepared either by gas immersion laser doping (GILD) or by implantation followed by laser annealing (Pulsed Laser Induced Epitaxy: PLIE). GILD and PLIE silicon samples show superconducting properties at low temperatures due to the achieved their high doping level achieved. In both cases, boron atoms are found to be randomly distributed throughout the silicon as revealed by statistical distribution analysis. No clusters or precipitates are detected, which may be related to the high recrystallization rate of the Si:B alloy. A sharp 2D interface between the doped silicon region and the undoped substrate is also observed, characterizing a Si:B/Si epitaxy. Finally, the variation of the evaporation field is investigated by considering either the silicon charge state ratio or the variation of the total applied voltage during the analysis of the Si:B layer and silicon.

G-Gaussian processes under sublinear expectations and <inline-formula><tex-math id="M1">$ q $</tex-math></inline-formula>-Brownian motion in quantum mechanics

An important observation of this paper is that a non-trivial $ G $-Brownian motion is not a Gaussian process, e.g., finite dimensional distributions of $ G $-Brownian motion is not G-normal, or G-Gaussian. We then have to start from the very beginning, to establish the foundation of $ G $-Gaussian processes which is more suitable for space-parameter systems. It is known that the notion of classical Brownian motion is not suitable to model the random propagation of a quantum particle. In this paper we have rigorously defined a new stochastic process called $ q $-Brownian who's propagator exactly coincides with the one proposed by Feynman based on the solution of Schrödinger equation. The notion of expectation plays a fundamental base of the above results. This paper was originally published on [38].

Extending the EclipseTM AcurosXB output factor table for small field radiosurgery.

To investigate the necessity of extending the output factor table (OF Table) of the Varian EclipseTM Treatment Planning System for small field stereotactic radiosurgery (SRS) and stereotactic body radiosurgery (SBRT) treatments. A new AcurosXB 15.6 beam model was created in the Eclipse Beam Configuration, which is identical to the one that has been used in the clinic with a default 3×3cm to 40×40cm OF Table, except the OF Table in the new model was extended to cover the range from 1×1cm to 40×40cm. 80 small square and rectangular output factors were measured on a Varian TrueBeam utilizing a Standard Imaging Exradin W2-1×1 scintillator detector, inside a PTW BeamScan water tank with 95cm SSD at 5cm depth. Cerenkov contamination was corrected using a rectangular field method (2cm×15cm field). Nine Radiosurgery plans with primary jaw setting ranging from 0.7cm to 2.0cm were evaluated by both beam models. The monitor unit (MU) differences between the two beam models were calculated for identical 3-dimensional (3D) absolute dose distributions. Output factors, measured versus Eclipse calculated, were compared down to 0.5×0.5cm primary jaw setting. For the 6FFF beam, the difference between the two beam models was ∼ 6% for 1×1cm jaw settings and 4% at 1.5×1.5cm, with the extended OF Table requiring higher MUs for the same dose prescription and same 3-dimensional isodose distribution. For the 6MV beam, the corresponding difference is ∼7.5% for 1×1cm, 5% for 1.5×1.5cm, and 3% for 2×2cm jaw settings, with the extended OF Table requiring higher MUs. For jaw settings smaller than 1×1cm, measured dose can be considerably smaller than Eclipse predicted dose, even with the OF Table extension. This is reflected by the fact that the output factor for 0.5×0.5cm, calculated via Eclipse external beam, was more than 30% greater than that measured for both 6FFF and 6MV beams. Eclipse does a satisfactory job for primary jaw sizes down to 2cm. For jaw settings smaller than 1.5cm, the OF Table in Eclipse should be extended to improve the dose calculation accuracy.

Regional variability of precipitation characteristics in Tropical Cyclones over the North Indian Ocean from GPM-DPR measurements

Global Precipitation Measurement mission (GPM) satellite carries a dual-frequency precipitation radar (DPR) which provides the three-dimensional structure of precipitating systems with a coarser spatial resolution of 5 km. GPM measurements provide a unique opportunity to examine the microphysical properties of precipitating systems over the ocean, where direct precipitation measurements are extremely rare. The present study uses GPM-DPR products such as surface rainfall rate, radar reflectivity factor, storm top height, mass-weighted mean diameter (Dm), and normalized intercept parameter (Nw) to examine the regional variability of precipitation characteristics in Tropical Cyclones (TCs). The precipitation characteristics are investigated in the Eye Wall (EW), Inner Rain band (IR), and Outer Rain band (OR) regions of TCs over the North Indian Ocean using 8 years of GPM-DPR data (2014–2021). The variation in precipitation characteristics is quantified in the light of predominant precipitation regimes and microphysical processes in different regions of TCs over two oceanic basins Arabian Sea (AS) and the Bay of Bengal (BOB). Our results suggested that the storms are more intense (higher reflectivity), taller and characterized by higher surface rain intensity with bigger Dm and higher Nw in the EW region as compared to the IR and OR regions. The stratiform rain fraction dominates over convective rain fraction in IR and OR regions of TCs. However, stratiform rain fraction is comparable to convective rain fraction in EW region of TCs over BOB. The two dimensional frequency distribution (CFAD) exhibits highly concentrated (broadly distributed) reflectivity values in EW (OR), whereas IR region depicts intermediate characteristics of EW/OR regions. Raindrops encounter significant amount of growth in convective rainfall than stratiform in EW region. The coalescence/break up process is relatively more apparent in EW region of TCs over BOB. Though the bulk of precipitation features are commonly observed over AS and BOB, EW regions of TCs show distinct features over AS and BOB. The observed variations in the precipitation and DSD characteristics have implications for cloud modeling parameterization schemes over the NIO.

VB-DeepONet: A Bayesian operator learning framework for uncertainty quantification

Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent prediction capabilities. Having said that, being set in a deterministic framework exposes DeepONet architecture to the risk of overfitting, poor generalization and in its unaltered form, it is incapable of quantifying the uncertainties associated with its predictions. To address these challenges, we propose a novel Bayesian operator learning framework referred to as the Variational Bayes DeepONet (VB-DeepONet). VB-DeepONet is rooted in Bayesian statistics and hence, (a) is less prone to overfitting as compared to its deterministic counterpart, (b) has better generalization, and (c) yields predictive uncertainty which is instrumental when decision making is concerned. VB-DeepONet exploits variational inference and hence has the capacity to take into account high dimensional posterior distributions while keeping the associated computational cost reasonable. Different examples covering mechanics problems like diffusion reaction, gravity pendulum, advection diffusion have been considered to illustrate the performance of the proposed VB-DeepONet and comparisons have been drawn against DeepONet set in deterministic framework, Proper Orthogonal Decomposition based Gaussian Process and DenseED. The results obtained illustrate the efficacy of the proposed approach in solving uncertainty quantification problems.

Simulation of dosimetric consequences of intrafraction variation of tumor drift in lung cancer stereotactic body radiotherapy.

The purpose of this study was to investigate the target dose discrepancy caused by intrafraction variation during stereotactic body radiotherapy (SBRT) for lung cancer. Intensity-modulated radiation therapy (IMRT) plans were designed based on average computed tomography (AVG CT) utilizing the planning target volume (PTV) surrounding the 65% and 85% prescription isodoses in both phantom and patient cases. Variation was simulated by shifting the nominal plan isocenter along six directions from 0.5mm to 4.5mm with a 1-mm step size to produce a series of perturbed plans. The dose discrepancy between the initial plan and the perturbed plans was calculated as the percentage of the initial plan. Dose indices, including ΔD99 for internal target volume (ITV) and gross tumor volume (GTV), were adopted as endpoint samples. The mean dose discrepancy was calculated under the 3-dimensional space distribution. We found that motion can lead to serious dose degradation of the target and ITV in lung SBRT, especially during SBRT with PTV surrounding the lower isodose line. Lower isodose line may lead to larger dose discrepancy, while make steeper dose fall-off gradient. This phenomenon was compromised when 3-dimensional space distribution was considered. This result may provide a prospective reference for target dose degradation due to motion during lung SBRT treatment.

Phantom-based Quality Assurance of a Clinical Dose Accumulation Technique Used in an Online Adaptive Radiation Therapy Platform

This study aimed to develop a routine quality assurance method for a dose accumulation technique provided by a radiation therapy platform for online treatment adaptation. Two commonly used phantoms were selected for the dose accumulation QA: Electron density and anthropomorphic pelvis. On a computed tomography (CT) scan of the electron density phantom, 1 target (gross tumor volume [GTV]; insert at 6 o'clock), a subvolume within this target, and 7 organs at risk (OARs; other inserts) were contoured in the treatment planning system (TPS). Two adaptation sessions were performed in which the GTV was recontoured, first at 7 o'clock and then at 5 o'clock. The accumulated dose was exported from the TPS after delivery. Deformable vector fields were also exported to manually accumulate doses for comparison. For the pelvis phantom, synthetic Gaussian deformations were applied to the planning CT image to simulate organ changes. Two single-fraction adaptive plans were created based on the deformed planning CT and cone beam CT images acquired onboard the radiation therapy platform. A manual dose accumulation was performed after delivery using the exported deformable vector fields for comparison with the system-generated result. All plans were successfully delivered, and the accumulated dose was both manually calculated and derived from the TPS. For the electron density phantom, the average mean dose differences in the GTV, boost volume, and OARs 1 to 7 were 0.0%, -0.2%, 92.0%, 78.4%, 1.8%, 1.9%, 0.0%, 0.0%, and 2.3%, respectively, between the manually summed and platform-accumulated doses. The gamma passing rates for the 3-dimensional dose comparison between the manually generated and TPS-provided dose accumulations were >99% for both phantoms. This study demonstrated agreement between manually obtained and TPS-generated accumulated doses in terms of both mean structure doses and local 3-dimensional dose distributions. Large disagreements were observed for OAR1 and OAR2 defined on the electron density phantom due to OARs having lower deformation priority over the target in addition to artificially large changes in position induced for these structures fraction-by-fraction. The tests applied in this study to a commercial platform provide a straightforward approach toward the development of routine quality assurance of dose accumulation in online adaptation.

Die Rostocker Methode zur qualitativen und quantitativen Bewertung von Intraokularlinsen

For quantitative and qualitative evaluation of the imaging properties of IOLs, axial cross-sectional images can be obtained from the 3-dimensional light distribution by means of an optical bench, as is known from light sheet recordings in fluorescein baths. This paper presents a new image-processing algorithm to enhance the quality of generated axial cross-sectional images, and the two methods are then compared. The 3-dimensional point spread function of a diffractive trifocal IOL (AT LISA tri 839MP, Carl Zeiss Meditec AG, Jena, Germany) was recorded on an optical bench developed in Rostock for different pupil diameters. A specially adapted image processing algorithm was then applied to the measurements, allowing through-focus curves to be generated. In addition, cross-sectional images of the IOLs studied were acquired using the light sheet method in a fluorescein bath. The study clearly shows the superiority of the newly developed method over the light sheet method in terms of image quality. In addition to the individual focal points, fine focal structures as well as halos can be made visible in the cross-sectional images obtained using the new method. In the generated through-focus curves, 3 intensity peaks can be identified, which represent the near, intermediate and far focus of the tested MIOL and cannot be represented by light sheet methods. The interaction of the optical bench with the developed image processing algorithm allows a more detailed understanding of the image formation and false light phenomena of IOLs, which was restricted by the technical limitations of the existing light sheet method. In addition, other quantities such as the through-focus curve can be derived quantitatively.

Variational Monte Carlo approach to partial differential equations with neural networks

The accurate numerical solution of partial differential equations (PDEs) is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here, we develop a variational approach for solving PDEs governing the evolution of high dimensional probability distributions. Our approach naturally works on the unbounded continuous domain and encodes the full probability density function through its variational parameters, which are adapted dynamically during the evolution to optimally reflect the dynamics of the density. In contrast to previous works, this dynamical adaptation of the parameters is carried out using an explicit prescription avoiding iterative gradient descent. For the considered benchmark cases we observe excellent agreement with numerical solutions as well as analytical solutions for tasks that are challenging for traditional computational approaches.

Functional Central Limit Theorems for Stick-Breaking Priors

We obtain the strong law of large numbers, Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various Bayesian nonparametric priors which include the stick-breaking process with general stick-breaking weights, the two-parameter Poisson-Dirichlet process, the normalized inverse Gaussian process, the normalized generalized gamma process, and the generalized Dirichlet process. For the stick-breaking process with general stick-breaking weights, we introduce two general conditions such that the central limit theorem and functional central limit theorem hold. Except in the case of the generalized Dirichlet process, since the finite dimensional distributions of these processes are either hard to obtain or are complicated to use even they are available, we use the method of moments to obtain the convergence results. For the generalized Dirichlet process we use its marginal distributions to obtain the asymptotics although the computations are highly technical.

Bayesian inference of axisymmetric plasma equilibrium

We present a Bayesian method for inferring axisymmetric plasma equilibria from the magnetic field and plasma pressure measurements. The method calculates all possible solutions for plasma current and pressure distributions consistent with the measurements and magnetohydrodynamic (MHD) force balance. Toroidal plasma current and magnetic field coils are modelled as a set of axisymmetric current-carrying solid beams. The other parameters such as plasma pressure and poloidal current flux are given as a function of poloidal magnetic flux, which is determined given a 2D current distribution. Plasma pressure and poloidal current flux profiles are modelled as Gaussian processes whose smoothness is optimally chosen based on the principle of Occam’s razor. To find equilibrium solutions, we introduce an MHD force balance constraint at every plasma current beam as a part of the prior knowledge. Given all these physical quantities, predictions calculated by the predictive (forward) models for diagnostics are compared to the observations. The high dimensional complex posterior probability distribution is explored by a new algorithm based on the Gibbs sampling scheme.

Metrology Benchmarking of 3D Scanning Sensors Using a Ceramic GD&T-Based Artefact.

The use of non-contact scanning equipment in metrology and in dimensional and geometric inspection applications is increasing due to its ease of use, the speed and density of scans, and the current costs. In fact, these technologies are becoming increasingly dominant in the industrial environment, thus moving from reverse engineering applications to metrological applications. However, this planned transfer requires actions to ensure the achievable accuracy by providing traceability of measurements. In the present study, a comparison between the devices is carried out and a specific standard artefact is designed, equipped with multiple ceramic optically friendly entities, and allowing a wide variety of geometric dimensioning and tolerancing (GD&T). Four different 3D scanning sensors are used in the experimentation. Three of them are based on laser triangulation, and the fourth is a structured blue light sensor (fringe pattern projection). The standard artefact is calibrated with a high accuracy, using a coordinate measuring machine (CMM) and probing sensors. With this CMM, reference values of multiple predefined GD&T are obtained. The evaluation methodology maximises the accuracy of each device in measuring the dimensions of the artefact due to the good dimensional (milling and turning), surface (control of machining variables), and the dimensional and spatial distribution characteristics. The procedure also includes the same treatment of the captured point clouds (trimming, filtering, and best-fit algorithm, etc.) in each of the four 3D scanning sensors considered. From this process, very reliable measurements of the maximum achievable accuracy of each device (deviations from the CMM measurements) are finally obtained, and a multi-characteristic comparison between the four sensors is performed, also with high reliability.

Multivariate Gaussian Random Fields over Generalized Product Spaces involving the Hypertorus

The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the covariance functions, being in this case matrix valued mappings. We start by considering the spectral representations that in turn allow for a characterization of such covariance functions. We then provide some methods for the construction of these matrix valued mappings. Finally, we consider strategies to evade radial symmetry (called isotropy in spatial statistics) and provide representation theorems for such a more general case.

Scalable implementation of (d+1) mutually unbiased bases for d -dimensional quantum key distribution

A high-dimensional quantum key distribution (QKD) can improve error rate tolerance and the secret key rate. Many $d$-dimensional QKDs have used two mutually unbiased bases (MUBs), while $(d+1)$ MUBs enable a more robust QKD, especially against correlated errors. However, a scalable implementation has not been achieved because the setups have required $d$ devices even for two MUBs or a flexible convertor for a specific optical mode. Here, we propose a scalable and general implementation of $(d+1)$ MUBs using $\log_p d$ interferometers in prime power dimensions $d=p^N$. We implemented the setup for time-bin states and observed an average error rate of 3.8% for phase bases, which is lower than the 23.17% required for a secure QKD against coherent attack in $d=4$.

Fast Neutron Tomography of Fuel Cells Enabled By Seeded Tomography Reconstruction

Neutron imaging provides high sensitivity to liquid water while being able to penetrate materials typically used to construct fuel cells. Water distribution measurements in operating fuel cells are typically performed using neutron radiography as the neutron fluence rate of the beam requires long acquisition times for high resolution making tomography difficult. Radiography only provides a two-dimensional look at the water distribution with an operating fuel cell making tomography preferable to understand three-dimensional distribution of water. NIST developed a fuel cell hardware design to allow for simultaneous neutron and X-ray tomography and as first reported in 2017 [1], initial efforts for tomography required acquisition times of 18 hours while the cell continuously operated at steady state conditions. Progress was made to improve acquisition settings and reconstruction methods to reduce the time required. These improvements were presented in 2019 [2] and demonstrated that scan times could be reduced to 8 hours and provided ground work for reducing acquisition times down to 1 hour to 2 hours.Since 2019, further progress has been made in applying dose reduction iterative reconstruction algorithms to the fuel cell datasets to allow faster acquisition times. Faster acquisition scans were simulated by reducing the number of projection angles from the high-resolution datasets from the 2019 work. The high-resolution scan was acquired with 851 projections from 0° to 360° and the fast scan consisted of only 51 projections. Reducing the number of projections from 851 to 51 simulates a scan that requires only 29 minutes to acquire, which is close to the typical length of time for acquiring high resolution radiography images. Figure 1 shows the comparison of a single slice from the 3D volumes with (A) representing the 8 hour, 851 projection scan, (C) the iteratively reconstructed 51 projection scan, and (E) the 51 projection scan reconstructed with filtered back projection algorithm used for the 851 projection scan. The iterative reconstruction gives favorable results when compared to the 851 projection reconstruction and shows that flux limitations on speed can be overcome to achieve high-speed tomography at high resolution on a neutron beam.This talk will describe the methodology for acquiring neutron tomography scans of operating fuel cells in under 30 minutes and give insights into how this can be used towards solving water management issues. It will be possible to combine radiography and tomography into a hybrid scan at each operating condition that can be acquired in 1 hour that will provide highly quantifiable water content measurements with 3-dimensional distribution information. The short scan times are beneficial for materials sets that are sensitive to long constant current hold durations such as new non-platinum catalysts. Additionally, new cameras are being commissioned that will improve resolution and push X-ray resolution to the point of resolving the fiber and macropore distribution of the gas diffusion layer (GDL) that can be coupled with the water content information. Figure 1

Adaptive variational Hamiltonian Monte Carlo sampling with application to ocean acoustics

The Hamiltonian Monte Carlo (HMC) algorithm is a variant Markov Chain Monte Carlo (MCMC) excelling at sampling high dimensional target distributions. The HMC explores a distribution as a particle trajectory in a Hamiltonian system by augmenting distribution parameters with auxiliary momentum variables. A particle trajectory is numerically integrated from initial point to some distant low-correlation point. Projecting back to parameter space yields a proposal point with high acceptance probability leading to faster exploration of the target distribution. The Leap-frog integrator is commonly used for its volume preservation (symplecticity) and reversibility traits that maintain the detailed balance condition of MCMC. Although effective, Leap-frog has sensitivity to choice of integration step-size and number of integration steps. Poor choices cause slow exploration or bias when regions of the distribution are not explored. Adaptive step methods could remove step size issues and explore regions of a distribution where Leap-frog fails. Existing adaptive methods self-adjust step-size while maintaining symplecticity and reversibility. In this work, we apply adaptive step methods to simulated target distributions and real world ocean acoustic data and compare performance. [Work supported by Office of Naval Research.]