Corpus ID: 128259615

Is infinity that far? A Bayesian nonparametric perspective of finite mixture models

@article{Argiento2019IsIT,
  title={Is infinity that far? A Bayesian nonparametric perspective of finite mixture models},
  author={Raffaele Argiento and Maria De Iorio},
  journal={arXiv: Methodology},
  year={2019}
}
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling strategies together, by showing that a finite mixture is simply a realization of a point process. Following a Bayesian nonparametric perspective, we introduce a new class of prior: the Normalized Independent Point Processes. We investigate the probabilistic… Expand
6 Citations

Figures and Tables from this paper

The Pitman–Yor multinomial process for mixture modelling
Discrete nonparametric priors play a central role in a variety of Bayesian procedures, most notably when used to model latent features as in clustering, mixtures and curve fitting. They are effectiveExpand
On a class of repulsive mixture models
Finite or infinite mixture models are routinely used in Bayesian statistical practice for tasks such as clustering or density estimation. Such models are very attractive due to their flexibility andExpand
Seemingly Unrelated Multi-State processes: a Bayesian semiparametric approach
Many applications in medical statistics as well as in other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In thisExpand
MCMC computations for Bayesian mixture models using repulsive point processes
Repulsive mixture models have recently gained popularity for Bayesian cluster detection. Compared to more traditional mixture models, repulsive mixture models produce a smaller number of wellExpand
Spatially dependent mixture models via the logistic multivariate CAR prior
We consider the problem of spatially dependent areal data, where for each area independent observations are available, and propose to model the density of each area through a finite mixture ofExpand
Generalized mixtures of finite mixtures and telescoping sampling
Within a Bayesian framework, a comprehensive investigation of the model class of mixtures of finite mixtures (MFMs) where a prior on the number of components is specified is performed. This modelExpand

References

SHOWING 1-10 OF 71 REFERENCES
A Computational Approach for Full Nonparametric Bayesian Inference Under Dirichlet Process Mixture Models
Widely used parametric generalized linear models are, unfortunately, a somewhat limited class of specifications. Nonparametric aspects are often introduced to enrich this class, resulting inExpand
Finite Mixture and Markov Switching Models
TLDR
This book should help newcomers to the field to understand how finite mixture and Markov switching models are formulated, what structures they imply on the data, what they could be used for, and how they are estimated. Expand
MCMC for Normalized Random Measure Mixture Models
This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure priors. Making use of some recentExpand
Bayesian analysis of mixture models with an unknown number of components- an alternative to reversible jump methods
Richardson and Green present a method of performing a Bayesian analysis of data from a finite mixture distribution with an unknown number of components. Their method is a Markov Chain Monte CarloExpand
Mixtures of Gamma Distributions With Applications
This article proposes a Bayesian density estimation method based upon mixtures of gamma distributions. It considers both the cases of known mixture size, using a Gibbs sampling scheme with aExpand
Slice sampling mixture models
TLDR
A more efficient version of the slice sampler for Dirichlet process mixture models described by Walker allows for the fitting of infinite mixture models with a wide-range of prior specifications and considers priors defined through infinite sequences of independent positive random variables. Expand
Posterior sampling from ε-approximation of normalized completely random measure mixtures
This paper adopts a Bayesian nonparametric mixture model where the mixing distribution belongs to the wide class of normalized homogeneous completely random measures. We propose a truncation methodExpand
Controlling the reinforcement in Bayesian non‐parametric mixture models
The paper deals with the problem of determining the number of components in a mixture model. We take a Bayesian non-parametric approach and adopt a hierarchical model with a suitable non-parametricExpand
Mixture Models With a Prior on the Number of Components
TLDR
It turns out that many of the essential properties of DPMs are also exhibited by MFMs, and the MFM analogues are simple enough that they can be used much like the corresponding DPM properties; this simplifies the implementation of MFMs and can substantially improve mixing. Expand
Models Beyond the Dirichlet Process
Bayesian nonparametric inference is a relatively young area of research and it has recently undergone a strong development. Most of its success can be explained by the considerable degree ofExpand
...
1
2
3
4
5
...