We examine the accelerated failure time model for univariate failure time data with right censoring, with application to the failure times of Kevlar fibres from different spools, subject to different stress levels. We propose a semi-parametric modelling by letting the error distribution be a shape-scale mixture of Weibull densities, the mixing measure being a normalized generalized gamma measure. We obtain posterior estimates of the regression parameter and also of credibility intervals for the predictive distributions and their quantiles, by including in the MCMC scheme the posterior distribution of the random mixing probability. The number of components in the nonparametric mixture can be interpreted as the number of random effects, having a prior distribution induced by the nonparametric model, and is inferred from the data. Compared to previous results, we obtain narrower interval estimates of the quantiles of the predictive survival function.

Statistics, probability, and game theory : papers in honor of David Blackwell

A semiparametric Bayesian mixed-effects model for failure time data

Predicting the taxonomic affiliation of DNA sequences collected from biological samples is a fundamental step in biodiversity assessment. This task is performed by leveraging existing databases containing reference DNA sequences endowed with a taxonomic identification. However, environmental sequences can be from organisms that are either unknown to science or for which there are no reference sequences available. Thus, taxonomic novelty of a sequence needs to be accounted for when doing classification. We propose Bayesian nonparametric taxonomic classifiers, BayesANT, which use species sampling model priors to allow unobserved taxa to be discovered at each taxonomic rank. Using a simple product multinomial likelihood with conjugate Dirichlet priors at the lowest rank, a highly flexible supervised algorithm is developed to provide a probabilistic prediction of the taxa placement of each sequence at each rank. As an illustration, we run our algorithm on a carefully annotated library of Finnish arthropods (FinBOL). To assess the ability of BayesANT to recognize novelty and to predict known taxonomic affiliations correctly, we test it on two training‐test splitting scenarios, each with a different proportion of taxa unobserved in training. We show how our algorithm attains accurate predictions and reliably quantifies classification uncertainty, especially when many sequences in the test set are affiliated to taxa unknown in training. By enabling taxonomic predictions for DNA barcodes to identify unseen branches, we believe BayesANT will be of broad utility as a tool for DNA metabarcoding within bioinformatics pipelines.

Inferring taxonomic placement from DNA barcoding aiding in discovery of new taxa

We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of the Pitman sampling formula in Pitman (2006) and the birth-and-death process with immigration studied in Karlin and McGregor (1967), in turn related to the celebrated Ewens sampling formula. A biological basis for the scheme is provided in terms of a population of individuals grouped into families, that evolves according to a sequence of births, deaths and immigrations. We investigate the asymptotic behaviour of the chain and show that, as opposed to the birth-and-death process with immigration, this construction maintains in the temporal limit the mutual dependence among the multiplicities. When the death rate exceeds the birth rate, the system is shown to have reversible distribution identified as a mixture of Pitman sampling formulae, with negative binomial mixing distribution on the population size. The population therefore converges to a stationary random configuration, characterised by a finite number of families and individuals.

Statistics, probability, and game theory : papers in honor of David Blackwell

Citations

A semiparametric Bayesian mixed-effects model for failure time data

Inferring taxonomic placement from DNA barcoding aiding in discovery of new taxa

A reversible allelic partition process and Pitman sampling formula

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