Marginally Specified Priors for Non-Parametric Bayesian Estimation

Kessler, David C.; Hoff, Peter D.; Dunson, David B.

doi:10.1111/rssb.12059

Cited by 13 publications

(8 citation statements)

References 32 publications

(58 reference statements)

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“…In the context of a single probability measure, Kessler, Hoff and Dunson (2015) proposed a clever construction of a BNP model with a given distribution on a finite set of functionals. Their approach is based on the conditional distribution of a standard BNP prior, given the functionals of interest.…”

Section: Discussionmentioning

confidence: 99%

The Dependent Dirichlet Process and Related Models

Quintana¹,

Müeller²,

Jara³

et al. 2020

Preprint

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Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate to assume a location/scale representation, where the error distribution has unchanging shape over the predictor space. In fact, it often happens in applied research that the distribution of responses under study changes with predictors in ways that cannot be reasonably represented by a finite dimensional functional form. This can seriously affect the answers to the scientific questions of interest, and therefore more general approaches are indeed needed. This gives rise to the study of fully nonparametric regression models. We review some of the main Bayesian approaches that have been employed to define probability models where the complete response distribution may vary flexibly with predictors. We focus on developments based on modifications of the Dirichlet process, historically termed dependent Dirichlet processes, and some of the extensions that have been proposed to tackle this general problem using nonparametric approaches.

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Section: Discussionmentioning

confidence: 99%

The Dependent Dirichlet Process and Related Models

Quintana¹,

Müeller²,

Jara³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…In such cases, it is of interest to use previous time points or previous samples results as prior information, in order to leverage all the information available to estimate the mixture. However, specifying prior information to Dirichlet process mixture models is not straightforward (Kessler et al, 2015). Here we propose to use the posterior MCMC draws obtained from previous dataset y (i) as prior information to analyze the next dataset y (i+1) .…”

Section: Sequential Posterior Approximationmentioning

confidence: 99%

Sequential Dirichlet process mixtures of multivariate skew $t$-distributions for model-based clustering of flow cytometry data

Hejblum¹,

Alkhassim²,

Gottardo³

et al. 2019

Ann. Appl. Stat.

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Flow cytometry is a high-throughput technology used to quantify multiple surface and intracellular markers at the level of a single cell. This enables to identify cell sub-types, and to determine their relative proportions. Improvements of this technology allow to describe millions of individual cells from a blood sample using multiple markers. This results in high-dimensional datasets, whose manual analysis is highly timeconsuming and poorly reproducible. While several methods have been developed to perform automatic recognition of cell populations, most of them treat and analyze each sample independently. However, in practice, individual samples are rarely independent (e.g. longitudinal studies). Here, we propose to use a Bayesian nonparametric approach with Dirichlet process mixture (DPM) of multivariate skew t-distributions to perform model based clustering of flow-cytometry data. DPM models directly estimate the number of cell populations from the data, avoiding model selection issues, and skew t-distributions provides robustness to outliers and non-elliptical shape of cell populations. To accommodate repeated measurements, we propose a sequential strategy relying on a parametric approximation of the posterior. We illustrate the good performance of our method on simulated data, on an experimental benchmark dataset, and on new longitudinal data from the DALIA-1 trial which evaluates a therapeutic vaccine against HIV. On the benchmark dataset, the sequential strategy outperforms all other methods evaluated, and similarly, leads to improved performance on the DALIA-1 data. We have made the method 1 arXiv:1702.04407v4 [stat.ML] 11 Sep 2017 available for the community in the R package NPflow.

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“…Thus, a natural future avenue of research is to combine nonparametric or highly flexible models of the distribution of Y with sequentially additive nonignorable missingness mechanisms. For example, we could incorporate information on summaries of distributions into nonparametric Bayesian models using the approach of Kessler et al (2015).…”

Section: Logitf (Mmentioning

confidence: 99%

Sequentially additive nonignorable missing data modelling using auxiliary marginal information

Sadinle

Reiter

2019

Biometrika

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Summary We study a class of missingness mechanisms, referred to as sequentially additive nonignorable, for modelling multivariate data with item nonresponse. These mechanisms explicitly allow the probability of nonresponse for each variable to depend on the value of that variable, thereby representing nonignorable missingness mechanisms. These missing data models are identified by making use of auxiliary information on marginal distributions, such as marginal probabilities for multivariate categorical variables or moments for numeric variables. We prove identification results and illustrate the use of these mechanisms in an application.

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Marginally Specified Priors for Non-Parametric Bayesian Estimation

Cited by 13 publications

References 32 publications

The Dependent Dirichlet Process and Related Models

The Dependent Dirichlet Process and Related Models

Sequential Dirichlet process mixtures of multivariate skew $t$-distributions for model-based clustering of flow cytometry data

Sequentially additive nonignorable missing data modelling using auxiliary marginal information

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