A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification

In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter $y$. The performance parameter $y$ is random due to the presence of various sources of uncertainty in the system, and our goal is to estimate the probability density function (PDF) of $y$. We propose to use the multicanonical Monte Carlo (MMC) method, a special type of adaptive importance sampling algorithm, to compute the PDF of interest. Moreover, we develop an adaptive algorithm to construct local Gaussian process surrogates to further accelerate the MMC iterations. With numerical examples we demonstrate that the proposed method can achieve several orders of magnitudes of speedup over the standard Monte Carlo method

Bayesian Methods for Analysis and Adaptive Scheduling of Exoplanet Observations

We describe work in progress by a collaboration of astronomers and statisticians developing a suite of Bayesian data analysis tools for extrasolar planet (exoplanet) detection, planetary orbit estimation, and adaptive scheduling of observations. Our work addresses analysis of stellar reflex motion data, where a planet is detected by observing the "wobble" of its host star as it responds to the gravitational tug of the orbiting planet. Newtonian mechanics specifies an analytical model for the resulting time series, but it is strongly nonlinear, yielding complex, multimodal likelihood functions; it is even more complex when multiple planets are present. The parameter spaces range in size from few-dimensional to dozens of dimensions, depending on the number of planets in the system, and the type of motion measured (line-of-sight velocity, or position on the sky). Since orbits are periodic, Bayesian generalizations of periodogram methods facilitate the analysis. This relies on the model being linearly separable, enabling partial analytical marginalization, reducing the dimension of the parameter space. Subsequent analysis uses adaptive Markov chain Monte Carlo methods and adaptive importance sampling to perform the integrals required for both inference (planet detection and orbit measurement), and information-maximizing sequential design (for adaptive scheduling of observations). We present an overview of our current techniques and highlight directions being explored by ongoing research.Comment: 29 pages, 11 figures. An abridged version is accepted for publication in Statistical Methodology for a special issue on astrostatistics, with selected (refereed) papers presented at the Astronomical Data Analysis Conference (ADA VI) held in Monastir, Tunisia, in May 2010. Update corrects equation (3

Probabilistic models of individual and collective animal behavior

Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and interpretation of such data represents a challenge: the timing of animal behaviors may be stochastic and modulated by kinematic variables, by the interaction with the environment or with the conspecifics within the animal group, and dependent on internal cognitive or behavioral state of the individual. Existing models for collective motion typically fail to incorporate the discrete, stochastic, and internal-state-dependent aspects of behavior, while models focusing on individual animal behavior typically ignore the spatial aspects of the problem. Here we propose a probabilistic modeling framework to address this gap. Each animal can switch stochastically between different behavioral states, with each state resulting in a possibly different law of motion through space. Switching rates for behavioral transitions can depend in a very general way, which we seek to identify from data, on the effects of the environment as well as the interaction between the animals. We represent the switching dynamics as a Generalized Linear Model and show that: (i) forward simulation of multiple interacting animals is possible using a variant of the Gillespie's Stochastic Simulation Algorithm; (ii) formulated properly, the maximum likelihood inference of switching rate functions is tractably solvable by gradient descent; (iii) model selection can be used to identify factors that modulate behavioral state switching and to appropriately adjust model complexity to data. To illustrate our framework, we apply it to two synthetic models of animal motion and to real zebrafish tracking data.Comment: 26 pages, 11 figure

Joint localization of pursuit quadcopters and target using monocular cues

Pursuit robots (autonomous robots tasked with tracking and pursuing a moving target) require accurate tracking of the target's position over time. One possibly effective pursuit platform is a quadcopter equipped with basic sensors and a monocular camera. However, combined noise of the quadcopter's sensors causes large disturbances of target's 3D position estimate. To solve this problem, in this paper, we propose a novel method for joint localization of a quadcopter pursuer with a monocular camera and an arbitrary target. Our method localizes both the pursuer and target with respect to a common reference frame. The joint localization method fuses the quadcopter's kinematics and the target's dynamics in a joint state space model. We show that predicting and correcting pursuer and target trajectories simultaneously produces better results than standard approaches to estimating relative target trajectories in a 3D coordinate system. Our method also comprises a computationally efficient visual tracking method capable of redetecting a temporarily lost target. The efficiency of the proposed method is demonstrated by a series of experiments with a real quadcopter pursuing a human. The results show that the visual tracker can deal effectively with target occlusions and that joint localization outperforms standard localization methods

Comparison of different integral histogram based tracking algorithms

Object tracking is an important subject in computer vision with a wide range of applications – security and surveillance, motion-based recognition, driver assistance systems, and human-computer interaction. The proliferation of high-powered computers, the availability of high quality and inexpensive video cameras, and the increasing need for automated video analysis have generated a great deal of interest in object tracking algorithms. Tracking is usually performed in the context of high-level applications that require the location and/or shape of the object in every frame. Research is being conducted in the development of object tracking algorithms over decades and a number of approaches have been proposed. These approaches differ from each other in object representation, feature selection, and modeling the shape and appearance of the object. Histogram-based tracking has been proved to be an efficient approach in many applications. Integral histogram is a novel method which allows the extraction of histograms of multiple rectangular regions in an image in a very efficient manner. A number of algorithms have used this function in their approaches in the recent years, which made an attempt to use the integral histogram in a more efficient manner. In this paper different algorithms which used this method as a part of their tracking function, are evaluated by comparing their tracking results and an effort is made to modify some of the algorithms for better performance. The sequences used for the tracking experiments are of gray scale (non-colored) and have significant shape and appearance variations for evaluating the performance of the algorithms. Extensive experimental results on these challenging sequences are presented, which demonstrate the tracking abilities of these algorithms

Numerical calculations of a high brilliance synchrotron source and on issues with characterizing strong radiation damping effects in non-linear Thomson/Compton backscattering experiments

A number of theoretical calculations have studied the effect of radiation reaction forces on radiation distributions in strong field counter-propagating electron beam-laser interactions, but could these effects - including quantum corrections - be observed in interactions with realistic bunches and focusing fields, as is hoped in a number of soon to be proposed experiments? We present numerical calculations of the angularly resolved radiation spectrum from an electron bunch with parameters similar to those produced in laser wakefield acceleration experiments, interacting with an intense, ultrashort laser pulse. For our parameters, the effects of radiation damping on the angular distribution and energy distribution of \emph{photons} is not easily discernible for a "realistic" moderate emittance electron beam. However, experiments using such a counter-propagating beam-laser geometry should be able to measure such effects using current laser systems through measurement of the \emph{electron beam} properties. In addition, the brilliance of this source is very high, with peak spectral brilliance exceeding $10^{29}$ photons$\,$s$^{-1}$mm$^{-2}$mrad$^{-2}(0.1$% bandwidth$)^{-1}$ with approximately 2% efficiency and with a peak energy of 10 MeV.Comment: 11 figures, 11 page

The supervised IBP: neighbourhood preserving infinite latent feature models

We propose a probabilistic model to infer supervised latent variables in the Hamming space from observed data. Our model allows simultaneous inference of the number of binary latent variables, and their values. The latent variables preserve neighbourhood structure of the data in a sense that objects in the same semantic concept have similar latent values, and objects in different concepts have dissimilar latent values. We formulate the supervised infinite latent variable problem based on an intuitive principle of pulling objects together if they are of the same type, and pushing them apart if they are not. We then combine this principle with a flexible Indian Buffet Process prior on the latent variables. We show that the inferred supervised latent variables can be directly used to perform a nearest neighbour search for the purpose of retrieval. We introduce a new application of dynamically extending hash codes, and show how to effectively couple the structure of the hash codes with continuously growing structure of the neighbourhood preserving infinite latent feature space