scholarly journals Nonparametric Bayesian inference for mean residual life functions in survival analysis

Biostatistics ◽  
2018 ◽  
Vol 20 (2) ◽  
pp. 240-255 ◽  
Author(s):  
Valerie Poynor ◽  
Athanasios Kottas
Keyword(s):  
Survival Analysis ◽  
Mixture Model ◽  
Dirichlet Process ◽  
Residual Life ◽  
Right Censoring ◽  
Mean Residual Life ◽  
Dirichlet Process Mixture ◽  
Data Set ◽  
Survival Distribution ◽  
Wide Range

SUMMARY Modeling and inference for survival analysis problems typically revolves around different functions related to the survival distribution. Here, we focus on the mean residual life (MRL) function, which provides the expected remaining lifetime given that a subject has survived (i.e. is event-free) up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the MRL function characterizes the survival distribution. We develop general Bayesian nonparametric inference for MRL functions built from a Dirichlet process mixture model for the associated survival distribution. The resulting model for the MRL function admits a representation as a mixture of the kernel MRL functions with time-dependent mixture weights. This model structure allows for a wide range of shapes for the MRL function. Particular emphasis is placed on the selection of the mixture kernel, taken to be a gamma distribution, to obtain desirable properties for the MRL function arising from the mixture model. The inference method is illustrated with a data set of two experimental groups and a data set involving right censoring. The supplementary material available at Biostatistics online provides further results on empirical performance of the model, using simulated data examples.

scholarly journals Identifying sub-populations of cells in single cell transcriptomic data - a Bayesian mixture model approach to zero-inflation of counts

2021 ◽  
Author(s):  
Thomas Thorne
Keyword(s):  
Single Cell ◽  
Mixture Model ◽  
Dirichlet Process ◽  
Negative Binomial ◽  
Cell Types ◽  
Rna Seq ◽  
Dirichlet Process Mixture ◽  
Zero Inflation ◽  
Data Set ◽  
Multiple Cell

Single cell RNA-seq data exhibit large numbers of zero count values, that we demonstrate can, for a subset of transcripts, be better modelled by a zero inflated negative binomial distribution. We develop a novel Dirichlet process mixture model which employs both a mixture at the cell level to model multiple cell types, and a mixture of single cell RNA-seq counts at the transcript level to model the transcript specific zero-inflation of counts. It is shown that this approach outperforms previous approaches that applied multinomial distributions to model single cell RNA-seq counts, and also performer better or comparably to existing top performing methods. By taking a Bayesian approach we are able to build interpretable models of expression within clusters, and to quantify uncertainty in cluster assignments. Applied to a publicly available data set of single cell RNA-seq counts of multiple cell types from the mouse cortex and hippocampus, we demonstrate how our approach can be used to distinguish sub-populations of cells as clusters in the data, and to identify gene sets that are indicative of membership of a sub-population.

scholarly journals A Gibbs Sampler for a Hierarchical Dirichlet Process Mixture Model

2019 ◽  
Author(s):  
Mark Andrews
Keyword(s):  
Mixture Model ◽  
Gibbs Sampler ◽  
Dirichlet Process ◽  
Dirichlet Process Mixture ◽  
Hierarchical Dirichlet Process ◽  
Dirichlet Process Mixture Model ◽  
Multinomial Data

A Gibbs sampler for the hierarchical Dirichlet process mixture model (HDPMM) when used with multinomial data.

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