Bayesian Multidimensional Scaling Research Articles

The structure of municipal voting in Vancouver

ABSTRACT We offer a new interpretation of the structure of municipal electoral competition in Vancouver, focusing on the city’s high-profile municipal election in 2018. Using novel “cast vote records”—a dataset containing each of the 176,450 ballots cast in the city’s municipal election—we use a Bayesian multidimensional scaling procedure to estimate the location of every 2018 candidate and voter in Vancouver in a shared two-dimensional political space. We then use data from the Canadian Municipal Election Study (CMES), a large election survey undertaken in Vancouver in 2018, to interpret this political space, assessing 96 possible correlates of CMES respondents’ locations in political space. We find evidence of a single primary dimension of competition, structured by left-right ideology, along with a secondary dimension dividing establishment from upstart parties of the right. Our paper supplies a new interpretation of Vancouver’s electoral landscape, clarifies our understanding of the role of left-right ideology in municipal electoral competition, and demonstrates the promise of cast vote records for research on municipal elections and voting.

BayMDS: An R Package for Bayesian Multidimensional Scaling and Choice of Dimension.

BayMDS: An R Package for Bayesian Multidimensional Scaling and Choice of Dimension.

Bayesian Multidimensional Scaling for Location Awareness in Hybrid-Internet of Underwater Things

Localization of sensor nodes in the internet of underwater things (IoUT) is of considerable significance due to its various applications, such as navigation, data tagging, and detection of underwater objects. Therefore, in this paper, we propose a hybrid Bayesian multidimensional scaling (BMDS) based localization technique that can work on a fully hybrid IoUT network where the nodes can communicate using either optical, magnetic induction, and acoustic technologies. These communication technologies are already used for communication in the underwater environment; however, lacking localization solutions. Optical and magnetic induction communication achieves higher data rates for short communication. On the contrary, acoustic waves provide a low data rate for long-range underwater communication. The proposed method collectively uses optical, magnetic induction, and acoustic communication-based ranging to estimate the underwater sensor nodes' final locations. Moreover, we also analyze the proposed scheme by deriving the hybrid Cramer-Rao lower bound (H-CRLB). Simulation results provide a complete comparative analysis of the proposed method with the literature.

Massive Parallelization Boosts Big Bayesian Multidimensional Scaling

Big Bayes is the computationally intensive co-application of big data and large, expressive Bayesian models for the analysis of complex phenomena in scientific inference and statistical learning. Standing as an example, Bayesian multidimensional scaling (MDS) can help scientists learn viral trajectories through space-time, but its computational burden prevents its wider use. Crucial MDS model calculations scale quadratically in the number of observations. We partially mitigate this limitation through massive parallelization using multi-core central processing units, instruction-level vectorization and graphics processing units (GPUs). Fitting the MDS model using Hamiltonian Monte Carlo, GPUs can deliver more than 100-fold speedups over serial calculations and thus extend Bayesian MDS to a big data setting. To illustrate, we employ Bayesian MDS to infer the rate at which different seasonal influenza virus subtypes use worldwide air traffic to spread around the globe. We examine 5392 viral sequences and their associated 14 million pairwise distances arising from the number of commercial airline seats per year between viral sampling locations. To adjust for shared evolutionary history of the viruses, we implement a phylogenetic extension to the MDS model and learn that subtype H3N2 spreads most effectively, consistent with its epidemic success relative to other seasonal influenza subtypes. Finally, we provide MassiveMDS, an open-source, stand-alone C++ library and rudimentary R package, and discuss program design and high-level implementation with an emphasis on important aspects of computing architecture that become relevant at scale.

Bayesian multidimensional scaling procedure with variable selection

Multidimensional scaling methods are frequently used by researchers and practitioners to project high dimensional data into a low dimensional space. However, it is a challenge to integrate side information which is available along with the dissimilarities to perform such dimension reduction analysis. A novel Bayesian integrative multidimensional scaling procedure, namely Bayesian multidimensional scaling with variable selection, is proposed to incorporate external information on the objects into the analysis through the use of a latent multivariate regression structure. The proposed Bayesian procedure allows the incorporation of covariate information into the dimension reduction analysis through the use of a variable selection strategy. An efficient computational algorithm to implement the procedure is also developed. A series of simulation experiments and a real data analysis are conducted, and the proposed model is shown to outperform several benchmark models based on some measures commonly used in the literature.

Analysis of Genetic Relationship Among 11 Iranian Ethnic Groups with Bayesian Multidimensional Scaling Using HLA Class II Data

Background: The key feature of Bayesian methods is their lack of dependence on defaults necessary for classical statistics. Because of the high volume of simulation, Bayesian methods have a high degree of accuracy. They are efficient in data mining and analyzing large volumes of data, and can be upgraded by entering new data. Objective: We used Bayesian multidimensional scaling (MDS) to analyze the genetic relationships among 11 Iranian ethnic groups based on HLA class II data. Method: Allele frequencies of three HLA loci from 816 unrelated individuals belonging to 11 Iranian ethnic groups were analyzed by Bayesian MDS using R and WinBUGS software. Results: like the results of correspondence analysis as a prototype of classical MDS analysis, the results of Bayesian MDS also showed Arabs from Famur, Balochis, Zoroastrians and Jews to be separate from other Iranian ethnic groups. Decreases stress in Bayesian MDS method compared to classical method revealed the accuracy of Bayesian MDS for HLA data analyses. Conclusion: This study reports the first application of Bayesian multidimensional scaling to HLA data analysis with Nei’s DA genetic distances. Stress reduction in Bayesian MDS compared to classical MDS showed that the Bayesian approach can improve the accuracy of genetic data analysis.

Bayesian multidimensional scaling for the estimation of a Minkowski exponent

The Minkowski property of psychological space has long been of interest to researchers. A common strategy has been calculating the stress in multidimensional scaling for many Minkowski exponent values and choosing the one that results in the lowest stress. However, this strategy has an arbitrariness problem-that is, a loss function. Although a recently proposed Bayesian approach could solve this problem, the method was intended for individual subject data. It is unknown whether this method is directly applicable to averaged or single data, which are common in psychology and behavioral science. Therefore, we first conducted a simulation study to evaluate the applicability of the method to the averaged data problem and found that it failed to recover the true Minkowski exponent. Therefore, a new method is proposed that is a simple extension of the existing Euclidean Bayesian multidimensional scaling to the Minkowski metric. Another simulation study revealed that the proposed method could successfully recover the true Minkowski exponent. BUGS codes used in this study are given in the Appendix.

A Hierarchical Bayesian Multidimensional Scaling Methodology for Accommodating Both Structural and Preference Heterogeneity

Multidimensional scaling (MDS) models for the analysis of dominance data have been developed in the psychometric and classification literature to simultaneously capture subjects’ preference heterogeneity and the underlying dimensional structure for a set of designated stimuli in a parsimonious manner. There are two major types of latent utility models for such MDS models that have been traditionally used to represent subjects’ underlying utility functions: the scalar product or vector model and the ideal point or unfolding model. Although both models have been widely applied in various social science applications, implicit in the assumption of such MDS methods is that all subjects are homogeneous with respect to their underlying utility function; i.e., they all follow a vector model or an ideal point model. We extend these traditional approaches by presenting a Bayesian MDS model that combines both the vector model and the ideal point model in a generalized framework for modeling metric dominance data. This new Bayesian MDS methodology explicitly allows for mixtures of the vector and the ideal point models thereby accounting for both preference heterogeneity and structural heterogeneity. We use a marketing application regarding physicians’ prescription behavior of antidepressant drugs to estimate and compare a variety of spatial models.

A Bayesian multidimensional scaling procedure for the spatial analysis of revealed choice data

We present a new Bayesian formulation of a vector multidimensional scaling procedure for the spatial analysis of binary choice data. The Gibbs sampler is gainfully employed to estimate the posterior distribution of the specified scalar products, bilinear model parameters. The computational procedure allows for the explicit estimation of a covariance matrix which can accommodate violations of IIA due to context effects. In addition, posterior standard errors can be estimated which reflect differential degrees of consumer choice uncertainty and/or brand position instability. A marketing application concerning the analysis of consumers' consideration sets for luxury automobiles is provided to illustrate the use of the proposed methodology.