We present dynesty, a public, open-source, Python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using Dynamic Nested Sampling. By adaptively allocating samples based on posterior structure, Dynamic Nested Sampling has the benefits of Markov Chain Monte Carlo algorithms that focus exclusively on posterior estimation while retaining Nested Sampling's ability to estimate evidences and sample from complex, multi-modal distributions. We provide an overview of Nested Sampling, its extension to Dynamic Nested Sampling, the algorithmic challenges involved, and the various approaches taken to solve them. We then examine dynesty's performance on a variety of toy problems along with several astronomical applications. We find in particular problems dynesty can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature. More detailed statistical results related to Nested Sampling are also included in the Appendix.

dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences

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Data Analysis A Bayesian Tutorial

Problem Given the number of times in which an unknown event has happened and failed: Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named. SECTION 1 Definition 1. Several events are inconsistent, when if one of them happens, none of the rest can. 2. Two events are contrary when one, or other of them must; and both together cannot happen. 3. An event is said to fail, when it cannot happen; or, which comes to the same thing, when its contrary has happened. 4. An event is said to be determined when it has either happened or failed. 5. The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon it’s 2 happening.

An essay towards solving a problem in the doctrine of chances. [Facsimil]

An international review of laser Doppler vibrometry: Making light work of vibration measurement

Recently, nested and coprime arrays have attracted considerable interest due to their capability of providing increased array aperture, enhanced degrees of freedom (DOFs), and reduced mutual coupling effect compared to uniform linear arrays (ULAs). These features are critical to improving the performance of direction-of-arrival estimation and adaptive beamforming. In this paper, a new sparse array configuration based on the maximum inter-element spacing constraint (MISC) is proposed. The MISC array configuration generally consists of three sparse ULAs plus two separate sensors that are appropriately placed. The MISC array configurations are designed based on the inter-element spacing set, which, for a given number of sensors, is uniquely determined by a closed-form expression. We also derive closed-form expressions for the number of uniform DOFs of the MISC arrays with any number of sensors. Compared with the existing sparse arrays, the MISC array enjoys two important advantages, namely, providing a higher number of DOFs and reducing the mutual coupling effects. Numerical simulations are conducted to verify the superiority of the MISC array over other sparse arrays.

MISC Array: A New Sparse Array Design Achieving Increased Degrees of Freedom and Reduced Mutual Coupling Effect

When an acoustic wave strikes the ground surface, energy is coupled into the motion of the fluid/solid frame comprising the ground. This phenomenon is termed acoustic-to-seismic (A/S) coupling In the ground, the Biot Type Il or Biot slow waves travel with a speed well below the speed of sound in air. The porous nature of the ground causes the entering acoustic wave to bend toward the normal and the acoustic wave propagates downward into the ground. When an object is buried a few cm below the ground surface, it distinctly changes the A/S coupled motion. These changes can be sensed by measuring vibrational particle velocity on the ground surface. Taking advantage of a noncontact remote measurement technique, the A/S coupling measurements for antitank landmine detection are conducted using a laser Doppler-vibrometer (LDV). Recent field measurements in both calibration and blind mine lanes and the resulting data analysts, which demonstrate the effectiveness of this technique, are described in this paper.

/pdf/an-investigation-of-acoustic-to-seismic-coupling-to-detect-2g8x3pywg2.pdf

An investigation of acoustic-to-seismic coupling to detect buried antitank landmines

During the early 1980s, the phenomenon of acoustic-to- seismic coupling was used to detect buried objects or mines. In these early measurements, large 2 Hz geophones measured the low frequency normal component of the soil particle velocity over buried targets. Several different, naturally- occurring ground types were studied in these measurement, including grass-covered ground; bare, sandy soil surfaces; and 'dirt' roads. Since the large geophone averages the particle velocity over the area of the sensor case, acoustic-to-seismic transfer function measurements were made with new, smaller-sized geophones. Higher frequency measurements were made using accelerometers. 3D maps of the surface particle velocity were made using measured seismic/acoustic transfer function data. Recognizing the need for a non-contact sensor and the need to investigate the geophone/soil coupling effect in the acoustic-to-seismic transfer function, additional measurements were made using a laser Doppler vibrometer (LDV). This paper explains the acoustic-to-seismic coupling mine detection measurement technique using both geophones and an LDV. The early measurements of the acoustic-to-seismic coupling transfer function for mine-like targets are discussed as well as some recent measurements using a LDV.

Land mine detection measurements using acoustic-to-seismic coupling

Airborne acoustic waves coupled into the surface of the ground excite Biot Type I and II compressional and shear waves. This coupling of airborne sound into the ground is termed acoustic-to-seismic coupling. If a land mine or other inhomogeneity is presented below the surface, the ground surface vibrational velocity or S/A ratio will increase due to reflection and scattering of the Type II compressional wave. The dispersion characteristics of this wave in solids determines the mine detection limits. The S/A ratio is read with a laser doppler vibrometer (LDV). The loud speaker and LDV were mounted onto a large forklift at Fort AP Hill. This system was used to scan patches of ground at the Fort AP Hill calibration mine lanes. An investigation on the variability of surface velocity over different background types and mine types is described. The results of these initial field exercises are described.

Laser-Doppler-based acoustic-to-seismic detection of buried mines

This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient V. Valeau et al., J. Acoust. Soc. Am. 119, 1504‐1513 2006 cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284‐3287 2007; A. Billon et al., Appl. Acoust. 69, 2008 has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem. © 2008 Acoustical Society of America. DOI: 10.1121/1.2805618

/pdf/on-boundary-conditions-for-the-diffusion-equation-in-room-4qosjl1o6q.pdf

On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments.

Reverberation decay curves can be obtained by the backward integration of room impulse responses proposed by M. R. Schroeder. The evaluation of reverberation times is often achieved by a linear regression line fitting the reverberation decay curves. However, under noisy conditions, the successful application of this method requires either a careful choice of the integration limit or a precise estimate of the mean‐square value of the background noise. In the present paper, an alternative method using a nonlinear iterative regression approach for evaluating reverberation times from Schroeder’s decay curves is proposed. A nonlinear model of the decay curves, established according to the nature of Schroeder’s decay curves, is used for the regression process rather than the linear model used in linear regression. The regression process is based on the generalized least‐squares error principle in which a rapid convergence can be observed. Preliminary experiments show a slight dependence of the reverberation tim...

Evaluation of reverberation times using a nonlinear regression approach

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