Nonparametric Bayesian Data Analysis
TLDR
For each inference problem, relevant nonparametric Bayesian models and approaches including Dirichlet process models and variations, Polya trees, wavelet based models, neural network models, spline regression, CART, dependent DP models and model validation with DP and Polya tree extensions of parametric models are reviewed.Abstract:
We review the current state of nonparametric Bayesian inference. The discussion follows a list of important statistical inference problems, including density estimation, regression, survival analysis, hierarchical models and model validation. For each inference problem we review relevant nonparametric Bayesian models and approaches including Dirichlet process (DP) models and variations, Polya trees, wavelet based models, neural network models, spline regression, CART, dependent DP models and model validation with DP and Polya tree extensions of parametric models.read more
Citations
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Journal ArticleDOI
Topics in semantic representation.
TL;DR: This article analyzes the abstract computational problem underlying the extraction and use of gist, formulating this problem as a rational statistical inference that leads to a novel approach to semantic representation in which word meanings are represented in terms of a set of probabilistic topics.
Journal ArticleDOI
Sampling the Dirichlet Mixture Model with Slices
TL;DR: The key to the algorithm detailed in this article, which also keeps the random distribution functions, is the introduction of a latent variable which allows a finite number of objects to be sampled within each iteration of a Gibbs sampler.
Journal ArticleDOI
Bayesian density regression
TL;DR: The paper considers Bayesian methods for density regression, allowing a random probability distribution to change flexibly with multiple predictors, and proposes a kernel‐based weighting scheme that incorporates weights that are dependent on the distance between subjects’ predictor values.
Book ChapterDOI
Model-Based Clustering for Expression Data via a Dirichlet Process Mixture Model
TL;DR: This chapter introduces a method to get a point estimate of the true clustering based on least-squares distances from the posterior probability that two genes are clustered, and compared to other clustering methods in a simulation study.
Book ChapterDOI
Models beyond the Dirichlet process
Antonio Lijoi,Igor Prünster +1 more
TL;DR: In this paper, the authors provide a review of Bayesian nonparametric models that go beyond the Dirichlet process, and show that in some cases of interest for statistical applications, the DPM is not an adequate prior choice.
References
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Book ChapterDOI
Nonparametric Estimation from Incomplete Observations
Edward L. Kaplan,Paul Meier +1 more
TL;DR: In this article, the product-limit (PL) estimator was proposed to estimate the proportion of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t).
Book ChapterDOI
Regression Models and Life-Tables
TL;DR: The analysis of censored failure times is considered in this paper, where the hazard function is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time.
Regression models and life tables (with discussion
TL;DR: The drum mallets disclosed in this article are adjustable, by the percussion player, as to balance, overall weight, head characteristics and tone production of the mallet, whereby the adjustment can be readily obtained.
Journal ArticleDOI
Multivariate Adaptive Regression Splines
TL;DR: In this article, a new method is presented for flexible regression modeling of high dimensional data, which takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data.
Journal ArticleDOI
Sampling-Based Approaches to Calculating Marginal Densities
TL;DR: In this paper, three sampling-based approaches, namely stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm, are compared and contrasted in relation to various joint probability structures frequently encountered in applications.