Marginally specified priors for non-parametric Bayesian estimation

Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for non-parametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard non-parametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables

Projected t-SNE for batch correction

Motivation: Low-dimensional representations of high-dimensional data are routinely employed in biomedical research to visualize, interpret and communicate results from different pipelines. In this article, we propose a novel procedure to directly estimate t-SNE embeddings that are not driven by batch effects. Without correction, interesting structure in the data can be obscured by batch effects. The proposed algorithm can therefore significantly aid visualization of high-dimensional data. Results: The proposed methods are based on linear algebra and constrained optimization, leading to efficient algorithms and fast computation in many high-dimensional settings. Results on artificial single-cell transcription profiling data show that the proposed procedure successfully removes multiple batch effects from t-SNE embeddings, while retaining fundamental information on cell types. When applied to single-cell gene expression data to investigate mouse medulloblastoma, the proposed method successfully removes batches related with mice identifiers and the date of the experiment, while preserving clusters of oligodendrocytes, astrocytes, and endothelial cells and microglia, which are expected to lie in the stroma within or adjacent to the tumours. Contact: [email protected]

Momentarily Excessive Construction As The Basis For Protoadaptation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137522/1/evo04677.pd

Evidence accumulation models with R: A practical guide to hierarchical Bayesian methods

Evidence accumulation models are a useful tool to allow researchers to investigate the latent cognitive variables that underlie response time and response accuracy. However, applying evidence accumulation models can be difficult because they lack easily computable forms. Numerical methods are required to determine the parameters of evidence accumulation that best correspond to the fitted data. When applied to complex cognitive models, such numerical methods can require substantial computational power which can lead to infeasibly long compute times. In this paper, we provide efficient, practical software and a step-by-step guide to fit evidence accumulation models with Bayesian methods. The software, written in C++, is provided in an R package: 'ggdmc'. The software incorporates three important ingredients of Bayesian computation, (1) the likelihood functions of two common response time models, (2) the Markov chain Monte Carlo (MCMC) algorithm (3) a population-based MCMC sampling method. The software has gone through stringent checks to be hosted on the Comprehensive R Archive Network (CRAN) and is free to download. We illustrate its basic use and an example of fitting complex hierarchical Wiener diffusion models to four shooting-decision data sets