Related papers: Likelihood Analysis for Mega-Pixel Maps
Large patterns could exist on the microwave sky as a result of various non-standard possibilities for the large-scale Universe -- rotation or shear, non-trivial topology, and single topological defects are specific examples. All-sky (or…
An NP-hard problem is considered of intersecting a given set of $n$ straight line segments on the plane with the smallest cardinality set of disks of fixed radii $r>0,$ where the set of segments forms a straight line drawing $G=(V,E)$ of a…
In exploratory factor analysis, model parameters are usually estimated by maximum likelihood method. The maximum likelihood estimate is obtained by solving a complicated multivariate algebraic equation. Since the solution to the equation is…
Consider that the coordinates of $N$ points are randomly generated along the edges of a $d$-dimensional hypercube (random point problem). The probability that an arbitrary point is the $m$th nearest neighbor to its own $n$th nearest…
A multiverse analysis evaluates all combinations of "reasonable" analytic decisions to promote robustness and transparency, but can lead to a combinatorial explosion of analyses to compute. Long delays before assessing results prevent users…
In many cosmological inference problems, the likelihood (the probability of the observed data as a function of the unknown parameters) is unknown or intractable. This necessitates approximations and assumptions, which can lead to incorrect…
Remote sensing can provide crucial information for planetary rovers. However, they must validate these orbital observations with in situ measurements. Typically, this involves validating hyperspectral data using a spectrometer on-board the…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
Applications in machine learning and data mining require computing pairwise Lp distances in a data matrix A. For massive high-dimensional data, computing all pairwise distances of A can be infeasible. In fact, even storing A or all pairwise…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
Last two decades, the problem of robotic mapping has made a lot of progress in the research community. However, since the data provided by the sensor still contains noise, how to obtain an accurate map is still an open problem. In this…
We present a method for ultra-fast confrontation of the WMAP cosmic microwave background observations with theoretical models, implemented as a publicly available software package called CMBfit, useful for anyone wishing to measure…
The first part of this report describes the following result that, logarithmic approximation factor for hard capacitated set cover can be achieved from Wolsey's work [9], using a simpler and more intuitive analysis. We further show in our…
We use an all--sky, complete sample of nearby galaxies, extracted from the LEDA data base, to map the optical galaxy density field in the nearby universe. In order to determine this field, we correct the redshift--dependent distances by…
Cosmological galaxy formation simulations are still limited by their spatial/mass resolution and cannot model from first principles some of the processes, like star formation, that are key in driving galaxy evolution. As a consequence they…
The estimation of spectroscopic and photometric redshifts (spec-z and photo-z) is crucial for future cosmological surveys. It can directly affect several powerful measurements of the Universe, e.g. weak lensing and galaxy clustering. In…
We develop a biased Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels. Given a trajectory with a fixed number of collisions, the algorithm modifies both the waiting…
Peak statistics in weak lensing maps access the non-Gaussian information contained in the large-scale distribution of matter in the Universe. They are therefore a promising complement to two-point and higher-order statistics to constrain…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…