Distance Estimation in Cosmology

In this paper we outline the framework of mathematical statistics with which one may study the properties of galaxy distance estimators. We describe, within this framework, how one may formulate the problem of distance estimation as a Bayesian inference problem, and highlight the crucial question of how one incorporates prior information in this approach. We contrast the Bayesian approach with the classical `frequentist' treatment of parameter estimation, and illustrate -- with the simple example of estimating the distance to a single galaxy in a redshift survey -- how one can obtain a significantly different result in the two cases. We also examine some examples of a Bayesian treatment of distance estimation -- involving the definition of Malmquist corrections -- which have been applied in recent literature, and discuss the validity of the assumptions on which such treatments have been based.Comment: Plain Latex version 3.1, 18 pages + 2 figures, `Vistas in Astronomy' in pres

The Minimum Distance Estimation with Multiple Integral in Panel Data

This paper studies the minimum distance estimation problem for panel data model. We propose the minimum distance estimators of regression parameters of the panel data model and investigate their asymptotic distributions. This paper contains two main contributions. First, the domain of application of the minimum distance estimation method is extended to the panel data model. Second, the proposed estimators are more efficient than other existing ones. Simulation studies compare performance of the proposed estimators with performance of others and demonstrate some superiority of our estimators.Comment: Minimum distance estimation; panel dat

Bounds on Distance Estimation via Diffusive Molecular Communication

This paper studies distance estimation for diffusive molecular communication. The Cramer-Rao lower bound on the variance of the distance estimation error is derived. The lower bound is derived for a physically unbounded environment with molecule degradation and steady uniform flow. The maximum likelihood distance estimator is derived and its accuracy is shown via simulation to perform very close to the Cramer-Rao lower bound. An existing protocol is shown to be equivalent to the maximum likelihood distance estimator if only one observation is made. Simulation results also show the accuracy of existing protocols with respect to the Cramer-Rao lower bound.Comment: 7 pages, 5 figures, 1 table. Will be presented at the 2014 IEEE Global Communications Conference (GLOBECOM) in Austin, TX, USA, on December 9, 201

Different distance measures for fuzzy linear regression with Monte Carlo methods

The aim of this study was to determine the best distance measure for estimating the fuzzy linear regression model parameters with Monte Carlo (MC) methods. It is pointed out that only one distance measure is used for fuzzy linear regression with MC methods within the literature. Therefore, three different definitions of distance measure between two fuzzy numbers are introduced. Estimation accuracies of existing and proposed distance measures are explored with the simulation study. Distance measures are compared to each other in terms of estimation accuracy; hence this study demonstrates that the best distance measures to estimate fuzzy linear regression model parameters with MC methods are the distance measures defined by Kaufmann and Gupta (Introduction to fuzzy arithmetic theory and applications. Van Nostrand Reinhold, New York, 1991), Heilpern-2 (Fuzzy Sets Syst 91(2):259–268, 1997) and Chen and Hsieh (Aust J Intell Inf Process Syst 6(4):217–229, 2000). One the other hand, the worst distance measure is the distance measure used by Abdalla and Buckley (Soft Comput 11:991–996, 2007; Soft Comput 12:463–468, 2008). These results would be useful to enrich the studies that have already focused on fuzzy linear regression models

Enhancing timbre model using MFCC and its time derivatives for music similarity estimation

One of the popular methods for content-based music similarity estimation is to model timbre with MFCC as a single multivariate Gaussian with full covariance matrix, then use symmetric Kullback-Leibler divergence. From the field of speech recognition, we propose to use the same approach on the MFCCs’ time derivatives to enhance the timbre model. The Gaussian models for the delta and acceleration coefficients are used to create their respective distance matrix. The distance matrices are then combined linearly to form a full distance matrix for music similarity estimation. In our experiments on two datasets, our novel approach performs better than using MFCC alone.Moreover, performing genre classification using k-NN showed that the accuracies obtained are already close to the state-of-the-art

Fast Shortest Path Distance Estimation in Large Networks

We study the problem of preprocessing a large graph so that point-to-point shortest-path queries can be answered very fast. Computing shortest paths is a well studied problem, but exact algorithms do not scale to huge graphs encountered on the web, social networks, and other applications. In this paper we focus on approximate methods for distance estimation, in particular using landmark-based distance indexing. This approach involves selecting a subset of nodes as landmarks and computing (offline) the distances from each node in the graph to those landmarks. At runtime, when the distance between a pair of nodes is needed, we can estimate it quickly by combining the precomputed distances of the two nodes to the landmarks. We prove that selecting the optimal set of landmarks is an NP-hard problem, and thus heuristic solutions need to be employed. Given a budget of memory for the index, which translates directly into a budget of landmarks, different landmark selection strategies can yield dramatically different results in terms of accuracy. A number of simple methods that scale well to large graphs are therefore developed and experimentally compared. The simplest methods choose central nodes of the graph, while the more elaborate ones select central nodes that are also far away from one another. The efficiency of the suggested techniques is tested experimentally using five different real world graphs with millions of edges; for a given accuracy, they require as much as 250 times less space than the current approach in the literature which considers selecting landmarks at random. Finally, we study applications of our method in two problems arising naturally in large-scale networks, namely, social search and community detection.Yahoo! Research (internship