Bayesian Gaussian Copula Factor Models for Mixed Data.

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.

Latent Stick-Breaking Processes.

We develop a model for stochastic processes with random marginal distributions. Our model relies on a stick-breaking construction for the marginal distribution of the process, and introduces dependence across locations by using a latent Gaussian copula model as the mechanism for selecting the atoms. The resulting latent stick-breaking process (LaSBP) induces a random partition of the index space, with points closer in space having a higher probability of being in the same cluster. We develop an efficient and straightforward Markov chain Monte Carlo (MCMC) algorithm for computation and discuss applications in financial econometrics and ecology. This article has supplementary material online.

Radioactive in situ hybridization for detecting diverse gene expression patterns in tissue.

Knowing the timing, level, cellular localization, and cell type that a gene is expressed in contributes to our understanding of the function of the gene. Each of these features can be accomplished with in situ hybridization to mRNAs within cells. Here we present a radioactive in situ hybridization method modified from Clayton et al. (1988)(1) that has been working successfully in our lab for many years, especially for adult vertebrate brains(2-5). The long complementary RNA (cRNA) probes to the target sequence allows for detection of low abundance transcripts(6,7). Incorporation of radioactive nucleotides into the cRNA probes allows for further detection sensitivity of low abundance transcripts and quantitative analyses, either by light sensitive x-ray film or emulsion coated over the tissue. These detection methods provide a long-term record of target gene expression. Compared with non-radioactive probe methods, such as DIG-labeling, the radioactive probe hybridization method does not require multiple amplification steps using HRP-antibodies and/or TSA kit to detect low abundance transcripts. Therefore, this method provides a linear relation between signal intensity and targeted mRNA amounts for quantitative analysis. It allows processing 100-200 slides simultaneously. It works well for different developmental stages of embryos. Most developmental studies of gene expression use whole embryos and non-radioactive approaches(8,9), in part because embryonic tissue is more fragile than adult tissue, with less cohesion between cells, making it difficult to see boundaries between cell populations with tissue sections. In contrast, our radioactive approach, due to the larger range of sensitivity, is able to obtain higher contrast in resolution of gene expression between tissue regions, making it easier to see boundaries between populations. Using this method, researchers could reveal the possible significance of a newly identified gene, and further predict the function of the gene of interest.

Bayesian Learning with Dependency Structures via Latent Factors, Mixtures, and Copulas

Bayesian methods offer a flexible and convenient probabilistic learning framework to extract interpretable knowledge from complex and structured data. Such methods can characterize dependencies among multiple levels of hidden variables and share statistical strength across heterogeneous sources. In the first part of this dissertation, we develop two dependent variational inference methods for full posterior approximation in non-conjugate Bayesian models through hierarchical mixture- and copula-based variational proposals, respectively. The proposed methods move beyond the widely used factorized approximation to the posterior and provide generic applicability to a broad class of probabilistic models with minimal model-specific derivations. In the second part of this dissertation, we design probabilistic graphical models to accommodate multimodal data, describe dynamical behaviors and account for task heterogeneity. In particular, the sparse latent factor model is able to reveal common low-dimensional structures from high-dimensional data. We demonstrate the effectiveness of the proposed statistical learning methods on both synthetic and real-world data.

Makarios Now: Plundering Athens and Hippo

A Christian doctrine of happiness differs greatly from contemporary and pseudo-Christian conceptions of happiness, which are measured subjectively and by the accumulation of external goods. In order to develop a fresh account with objective standards, I critique, integrate and revise Aristotle and Augustine’s accounts of happiness. Additionally, I rely heavily on scriptures to present a telos of godlikeness that in turn informs a robust account of makarios. Throughout the thesis, the argument is made that happiness (eudaimonia) and blessedness (makarios) are equivalents. Despite the skepticism of liberal theologians, Christian happiness (makarios) is promised in the New Testament and achievable in this life. Fundamentally, makarios is relational, active, constant, and dependent.