Abstract:
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In biology, we are often interested in how different characteristics or traits of an organism evolve together over time. In order to properly determine this relationship, however, we must take into account the shared evolutionary history of the organisms we are studying. Recently, we showed how exploratory factor analysis can be used to improve upon existing Brownian diffusion methods, but nevertheless scalability still remains quite poor. To improve the feasibility of our method we introduce sparsity on the loadings matrix used in our factor analysis. We use repulsive priors, which penalize loadings columns whose sparsity structures are too similar. We use non-local priors, or priors whose density tends to zero as the parameter tends to zero in order to select models more efficiently. We use reversible jump Monte Carlo to more quickly and accurately determine the number of factors without using inefficient model selection techniques. We ultimately are able to apply this method to achieve full Bayesian inference on phylogenetically adjusted morphometrics, which we can then use to infer the shapes of the ancient extinct ancestors of the measured species.
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