The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors

We consider the horseshoe estimator due to Carvalho, Polson and Scott (2010) for the multivariate normal mean model in the situation that the mean vector is sparse in the nearly black sense. We assume the frequentist framework where the data is generated according to a fixed mean vector. We show that if the number of nonzero parameters of the mean vector is known, the horseshoe estimator attains the minimax $\ell_2$ risk, possibly up to a multiplicative constant. We provide conditions under which the horseshoe estimator combined with an empirical Bayes estimate of the number of nonzero means still yields the minimax risk. We furthermore prove an upper bound on the rate of contraction of the posterior distribution around the horseshoe estimator, and a lower bound on the posterior variance. These bounds indicate that the posterior distribution of the horseshoe prior may be more informative than that of other one-component priors, including the Lasso.Comment: This version differs from the final published version in pagination and typographical detail; Available at http://projecteuclid.org/euclid.ejs/141813426

On the Bernstein-von Mises theorem for the Dirichlet process

We establish that Laplace transforms of the posterior Dirichlet process converge to those of the limiting Brownian bridge process in a neighbourhood about zero, uniformly over Glivenko-Cantelli function classes. For real-valued random variables and functions of bounded variation, we strengthen this result to hold for all real numbers. This last result is proved via an explicit strong approximation coupling inequality

Learning to Look at LiDAR: The Use of R-CNN in the Automated Detection of Archaeological Objects in LiDAR Data from the Netherlands

Digital Archaeolog

Environmental Perturbations Induce Correlations in Midge Swarms

Although collectively behaving animal groups often show large-scale order (such as in bird flocks), they need not always (such as in insect swarms). It has been suggested that the signature of collective behavior in disordered groups is a residual long-range correlation. However, results in the literature have reported contradictory results as to the presence of long-range correlation in insect swarms, with swarms in the wild displaying correlation but those in a controlled laboratory environment not. We resolve these apparently incompatible results by showing the external perturbations generically induce the emergence of correlations. We apply a range of different external stimuli to laboratory swarms of the non-biting midge Chironomus riparius, and show that in all cases correlations appear when perturbations are introduced. We confirm the generic nature of these results by showing that they can be reproduced in a stochastic model of swarms. Given that swarms in the wild will always have to contend with environmental stimuli, our results thus harmonize previous findings

Optimization Under Uncertainty Using the Generalized Inverse Distribution Function

A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of statistical moments as deterministic attributes that define the objectives of the optimization process, the inverse cumulative distribution function allows for the use of all the possible information available in the probabilistic domain. Furthermore, the use of a quantile based approach leads naturally to a multi-objective methodology which allows an a-posteriori selection of the candidate design based on risk/opportunity criteria defined by the designer. Finally, the error on the estimation of the objectives due to the resolution of the GIDF will be proven to be quantifiableComment: 20 pages, 25 figure

An equation of state for insect swarms

Collective behaviour in flocks, crowds, and swarms occurs throughout the biological world. Animal groups are generally assumed to be evolutionarily adapted to robustly achieve particular functions, so there is widespread interest in exploiting collective behaviour for bio-inspired engineering. However, this requires understanding the precise properties and function of groups, which remains a challenge. Here, we demonstrate that collective groups can be described in a thermodynamic framework. We define an appropriate set of state variables and extract an equation of state for laboratory midge swarms. We then drive swarms through “thermodynamic” cycles via external stimuli, and show that our equation of state holds throughout. Our findings demonstrate a new way of precisely quantifying the nature of collective groups and provide a cornerstone for potential future engineering design

Costs and benefits of social relationships in the collective motion of bird flocks

This is the author accepted manuscript. The final version is available from Nature Research via the DOI in this record.Supplementary Figs. 1–12 and Supplementary Tables 1–3 are available in the Supplementary Information. Raw images captured by one of the four cameras and the reconstructed birds’ 3D movement trajectories are provided in Supplementary Videos 1–6. Plain text files, each including bird ID number, position, time, velocity, acceleration and wingbeat frequency at every time step, are provided in Supplementary Data 1–7. A plain text file that includes mean wingbeat frequency, flight speed and local density (approximated by the number of neighbours within a distance of 5 m from the focal bird) for paired and unpaired birds in six flocks, as well as for birds flying alone, is provided in Supplementary Data 8. All data required to reproduce the results in this study are included in Supplementary Data 1–8. Supplementary Data and Supplementary Videos are available at https://figshare.com/s/c55eb82bab800571d25d.Current understanding of collective behaviour in nature is based largely on models that assume that identical agents obey the same interaction rules, but in reality interactions may be influenced by social relationships among group members. Here, we show that social relationships transform local interactions and collective dynamics. We tracked individuals’ three-dimensional trajectories within flocks of jackdaws, a species that forms lifelong pair-bonds. Reflecting this social system, we find that flocks contain internal sub-structure, with discrete pairs of individuals tied together by spring-like effective forces. Within flocks, paired birds interacted with fewer neighbours than unpaired birds and flapped their wings more slowly, which may result in energy savings. However, flocks with more paired birds had shorter correlation lengths, which is likely to inhibit efficient information transfer through the flock. Similar changes to group properties emerge naturally from a generic self-propelled particle model. These results reveal a critical tension between individual- and group-level benefits during collective behaviour in species with differentiated social relationships, and have major evolutionary and cognitive implications.Human Frontiers in Science Programm

Local interactions and their group-level consequences in flocking jackdaws

This is the author accepted manuscript. The final version is available from the Royal Society via the DOI in this recordData accessibility: Data and code are available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.kb8js06As one of nature's most striking examples of collective behaviour, bird flocks have attracted extensive research. However, we still lack an understanding of the attractive and repulsive forces that govern interactions between individuals within flocks and how these forces influence neighbours' relative positions and ultimately determine the shape of flocks. We address these issues by analysing the three-dimensional movements of wild jackdaws (Corvus monedula) in flocks containing 2–338 individuals. We quantify the social interaction forces in large, airborne flocks and find that these forces are highly anisotropic. The long-range attraction in the direction perpendicular to the movement direction is stronger than that along it, and the short-range repulsion is generated mainly by turning rather than changing speed. We explain this phenomenon by considering wingbeat frequency and the change in kinetic and gravitational potential energy during flight, and find that changing the direction of movement is less energetically costly than adjusting speed for birds. Furthermore, our data show that collision avoidance by turning can alter local neighbour distributions and ultimately change the group shape. Our results illustrate the macroscopic consequences of anisotropic interaction forces in bird flocks, and help to draw links between group structure, local interactions and the biophysics of animal locomotion.Human Frontiers in Science Programm

Derivation of the Statistical Distribution of the Mass Peak Centroids of Mass Spectrometers Employing Analog-to-Digital Converters and Electron Multipliers

The statistical distribution of mass peak centroids recorded on mass spectrometers employing analog-to-digital converters (ADCs) and electron multipliers is derived from the first principles of the data generation process. The resulting Gaussian model is discussed and is validated with experimental data and with Monte Carlo simulations

Bayesian recovery of the initial condition for the heat equation

We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying "smoothness" and show that the corresponding posterior distributions contract around the true parameter at a rate that depends on the smoothness of the true initial condition and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the optimal minimax rate. One type of priors leads to a rate-adaptive Bayesian procedure. The frequentist coverage of credible sets is shown to depend on the combination of the prior and true parameter as well, with smoother priors leading to zero coverage and rougher priors to (extremely) conservative results. In the latter case credible sets are much larger than frequentist confidence sets, in that the ratio of diameters diverges to infinity. The results are numerically illustrated by a simulated data example.Comment: 17 pages, 4 figures. Published in Comm. Statist. Theory Methods. This version differs from the original in pagination and typographic detail. arXiv admin note: text overlap with arXiv:1103.269