Bayesian Multidimensional Scaling and Choice of Dimension

Oh, Man-Suk; Raftery, Adrian E.

doi:10.21236/ada458817

Cited by 8 publications

(12 citation statements)

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“…However, in practice, we can let the chain wander through the ((q À 1)*s) À 1 dimensional hyperplane and postprocess the results by flipping the signs of each configuration in the chain back to a target configuration. This approach is very similar to that advocated by Bradlow and Schmittlein (2000), Oh and Raftery (2001), Hoff, Raftery, and Handcock (2002), and Gormley and Murphy (2006). For small similarities problems, we found that in addition to the origin and one fixed coordinate, simply adding three sign constraints to the three fixed coordinates isolated a single posterior.…”

Section: Multidimensional Bayesian Similarities/dissimilarites Scalingsupporting

confidence: 70%

“…Other researchers have used the truncated normal (Oh and Raftery 2001), the normal (Navarro and Lee 2003), and the normal with an exponential mean (Okada and Shigemasu 2010). We prefer the log-normal because we think it is a more realistic model of the noise process; namely, the smaller the observed distance, the smaller the variance of that distance.…”

Section: Multidimensional Bayesian Similarities/dissimilarites Scalingmentioning

confidence: 99%

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Bayesian Metric Multidimensional Scaling

Bakker

Poole²

2013

Polit. anal.

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In this article, we show how to apply Bayesian methods to noisy ratio scale distances for both the classical similarities problem as well as the unfolding problem. Bayesian methods produce essentially the same point estimates as the classical methods, but are superior in that they provide more accurate measures of uncertainty in the data. Identification is nontrivial for this class of problems because a configuration of points that reproduces the distances is identified only up to a choice of origin, angles of rotation, and sign flips on the dimensions. We prove that fixing the origin and rotation is sufficient to identify a configuration in the sense that the corresponding maxima/minima are inflection points with full-rank Hessians. However, an unavoidable result is multiple posterior distributions that are mirror images of one another. This poses a problem for Markov chain Monte Carlo (MCMC) methods. The approach we take is to find the optimal solution using standard optimizers. The configuration of points from the optimizers is then used to isolate a single Bayesian posterior that can then be easily analyzed with standard MCMC methods.

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Section: Multidimensional Bayesian Similarities/dissimilarites Scalingsupporting

confidence: 70%

Section: Multidimensional Bayesian Similarities/dissimilarites Scalingmentioning

confidence: 99%

Bayesian Metric Multidimensional Scaling

Bakker

Poole²

2013

Polit. anal.

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“…One of our initial goals is to find an optimal projection of the high-dimensional distance matrix H into this lower dimensional space. We conduct this projection using Bayesian multidimensional scaling (BMDS) ( Oh and Raftery, 2001 ) in which we construct a probabilistic model to quantify the fit of a particular configuration of cartographic locations to the observed matrix of serological measurements. Typically, P = 2, but higher or lower dimensions may better reflect the data.…”

Section: Methodsmentioning

confidence: 99%

Integrating influenza antigenic dynamics with molecular evolution

Bedford

Suchard

Lemey

et al. 2014

eLife

357

455

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Influenza viruses undergo continual antigenic evolution allowing mutant viruses to evade host immunity acquired to previous virus strains. Antigenic phenotype is often assessed through pairwise measurement of cross-reactivity between influenza strains using the hemagglutination inhibition (HI) assay. Here, we extend previous approaches to antigenic cartography, and simultaneously characterize antigenic and genetic evolution by modeling the diffusion of antigenic phenotype over a shared virus phylogeny. Using HI data from influenza lineages A/H3N2, A/H1N1, B/Victoria and B/Yamagata, we determine patterns of antigenic drift across viral lineages, showing that A/H3N2 evolves faster and in a more punctuated fashion than other influenza lineages. We also show that year-to-year antigenic drift appears to drive incidence patterns within each influenza lineage. This work makes possible substantial future advances in investigating the dynamics of influenza and other antigenically-variable pathogens by providing a model that intimately combines molecular and antigenic evolution.DOI: http://dx.doi.org/10.7554/eLife.01914.001

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“…Tim Futing Liao https://orcid.org/0000-0002-1296-7660 Notes 1. In a similar tradition, Oh and Raftery (2001) adapted BIC for assessing dimension choice in multidimensional scaling. 2.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“… 1. In a similar tradition, Oh and Raftery (2001) adapted BIC for assessing dimension choice in multidimensional scaling. …”

mentioning

confidence: 99%

Comparing Groups of Life-Course Sequences Using the Bayesian Information Criterion and the Likelihood-Ratio Test

Liao

Fasang

2020

Sociological Methodology

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How can we statistically assess differences in groups of life-course trajectories? The authors address a long-standing inadequacy of social sequence analysis by proposing an adaption of the Bayesian information criterion (BIC) and the likelihood-ratio test (LRT) for assessing differences in groups of sequence data. Unlike previous methods, this adaption provides a useful measure for degrees of difference, that is, the substantive significance, and the statistical significance of differences between predefined groups of life-course trajectories. The authors present a simulation study and an empirical application on whether employment life-courses converged after reunification in the former East Germany and West Germany, using data for six birth-cohort groups ages 15 to 40 years from the German National Education Panel Study. The new methods allow the authors to show that convergence of employment life-courses around reunification was stronger for men than for women and that it was most pronounced in terms of the duration of employment states but weaker for their order and timing in the life-course. Convergence of East German and West German women’s employment lives set in earlier and reflects a secular trend toward a more gender-egalitarian division of labor in West Germany that is unrelated to reunification. The simulation study and the substantive application demonstrate the usefulness of the proposed BIC and LRT methods for assessing group differences in sequence data.

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Bayesian Multidimensional Scaling and Choice of Dimension

Cited by 8 publications

References 0 publications

Bayesian Metric Multidimensional Scaling

Bayesian Metric Multidimensional Scaling

Integrating influenza antigenic dynamics with molecular evolution

Comparing Groups of Life-Course Sequences Using the Bayesian Information Criterion and the Likelihood-Ratio Test

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