where K is the (fixed) number of mixture component, π is a vector of mixing weights, and p(x|k) are the densities for each component. We consider some examples below. 2 Gaussian mixture models Consider the dataset of height and weight in Figure 1. It is clear that there are two subpopulations in this data set, and in this case they are easy to interpret: one represents males and the other femal...

It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates. Toward this, a novel sieve for non-parametric mixture densities is explored, and its rate adaptability to various smoothness classes of densities in arbitrary dimension is demonstrated. This sieve construction is expected to offer a substantia...

2 Statistical problems 8 2.1 Introductory example . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 The independence problem . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 The symmetry problem . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.5 The role of mixture models . . . . . . . . . . . . . ....

Our paper provides a brief review and summary of issues and advances in the use of latent structure and other finite mixture models in the analysis of choice data. Focus is directed to three primary areas: (I) estimation and computational issues, (2) specification and interpretation issues, and (3) future research issues. We comment on what latent structure models have promised, what has been, ...

Various models have been implemented to explain long-term memory (Brady, et al., 2013; Lew, et al., 2015), with some being derived from studies of visual working memory (Bays, et al. 2009; Zhang & Luck, 2008). The implicit assumption is that processes and mechanisms of working memory also exist in long-term memory. However, the findings of fidelity and contributing factors are highly varied (e....