BERNOULLI, ISSN 1350-7265, 05/2019, Volume 25, Issue 2, pp. 1256 - 1288

Completely random measures (CRMs) and their normalizations are a rich source of Bayesian nonparametric priors. Examples include the beta, gamma, and Dirichlet...

Bayesian nonparametrics | REPRESENTATIONS | STATISTICS & PROBABILITY | normalized completely random measure | INFERENCE | completely random measure | BETA PROCESSES | Poisson point process | ESTIMATORS | STICK-BREAKING | DIRICHLET | truncation | FUNCTIONALS

Bayesian nonparametrics | REPRESENTATIONS | STATISTICS & PROBABILITY | normalized completely random measure | INFERENCE | completely random measure | BETA PROCESSES | Poisson point process | ESTIMATORS | STICK-BREAKING | DIRICHLET | truncation | FUNCTIONALS

Journal Article

Statistical Science, ISSN 0883-4237, 8/2013, Volume 28, Issue 3, pp. 335 - 359

This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure...

Datasets | Average linear density | Multilevel models | Atoms | Waveforms | Markov chains | Acidity | Random variables | Nonparametric models | Modeling | Slice sampling | Bayesian nonparametrics | Marginalized sampler | Hierarchical mixture model | Normalized random measure | Algorithm 8 | Conditional sampler | Dirichlet process | Completely random measure | Normalized generalized Gamma process | MCMC posterior sampling method | PRIORS | MONTE-CARLO METHODS | SAMPLING METHODS | COMPONENTS | STATISTICS & PROBABILITY | POINT-PROCESSES | slice sampling | BAYESIAN DENSITY-ESTIMATION | normalized random measure | conditional sampler | hierarchical mixture model | DISTRIBUTIONS | completely random measure | ESTIMATORS | noimalized generalized Gamma process | UNKNOWN NUMBER | marginalized sampler | DIRICHLET PROCESS PRIOR | Statistics - Methodology | normalized generalized Gamma process

Datasets | Average linear density | Multilevel models | Atoms | Waveforms | Markov chains | Acidity | Random variables | Nonparametric models | Modeling | Slice sampling | Bayesian nonparametrics | Marginalized sampler | Hierarchical mixture model | Normalized random measure | Algorithm 8 | Conditional sampler | Dirichlet process | Completely random measure | Normalized generalized Gamma process | MCMC posterior sampling method | PRIORS | MONTE-CARLO METHODS | SAMPLING METHODS | COMPONENTS | STATISTICS & PROBABILITY | POINT-PROCESSES | slice sampling | BAYESIAN DENSITY-ESTIMATION | normalized random measure | conditional sampler | hierarchical mixture model | DISTRIBUTIONS | completely random measure | ESTIMATORS | noimalized generalized Gamma process | UNKNOWN NUMBER | marginalized sampler | DIRICHLET PROCESS PRIOR | Statistics - Methodology | normalized generalized Gamma process

Journal Article

Bernoulli, ISSN 1350-7265, 11/2018, Volume 24, Issue 4B, pp. 3181 - 3221

We demonstrate how to calculate posteriors for general Bayesian nonparametric priors and likelihoods based on completely random measures (CRMs). We further...

Beta process | Bayesian nonparametrics | Size-biased | Conjugacy | Posterior | Indian buffet process | Exponential family | Completely random measure | SAMPLING METHODS | posterior | STATISTICS & PROBABILITY | INFERENCE | DISTRIBUTIONS | completely random measure | BETA PROCESSES | conjugacy | MODELS | ESTIMATORS | STICK-BREAKING | beta process | size-biased | DIRICHLET | exponential family

Beta process | Bayesian nonparametrics | Size-biased | Conjugacy | Posterior | Indian buffet process | Exponential family | Completely random measure | SAMPLING METHODS | posterior | STATISTICS & PROBABILITY | INFERENCE | DISTRIBUTIONS | completely random measure | BETA PROCESSES | conjugacy | MODELS | ESTIMATORS | STICK-BREAKING | beta process | size-biased | DIRICHLET | exponential family

Journal Article

Bernoulli, ISSN 1350-7265, 2014, Volume 20, Issue 3, pp. 1260 - 1291

The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we...

Infinitely divisible vector | Generalized Polýa urn scheme | Normalizedσ-stable process | Partially exchangeable random partition | Dirichlet process | Dependent Poisson processes | Completely random measure | partially exchangeable random partition | NONPARAMETRIC PROBLEMS | PRIORS | completely random measure | infinitely divisible vector | dependent Poisson processes | MIXTURE-MODELS | DENSITY-ESTIMATION | STATISTICS & PROBABILITY | generalized Polya urn scheme | normalized sigma-stable process | generalized Polýa urn scheme | normalized \sigma-stable process

Infinitely divisible vector | Generalized Polýa urn scheme | Normalizedσ-stable process | Partially exchangeable random partition | Dirichlet process | Dependent Poisson processes | Completely random measure | partially exchangeable random partition | NONPARAMETRIC PROBLEMS | PRIORS | completely random measure | infinitely divisible vector | dependent Poisson processes | MIXTURE-MODELS | DENSITY-ESTIMATION | STATISTICS & PROBABILITY | generalized Polya urn scheme | normalized sigma-stable process | generalized Polýa urn scheme | normalized \sigma-stable process

Journal Article

Statistical Science, ISSN 0883-4237, 8/2013, Volume 28, Issue 3, pp. 313 - 334

The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models...

Datasets | A priori knowledge | Density estimation | Simulations | Barrios | Random variables | Nonparametric models | Density | Modeling | Estimators | Bayesian nonparametrics | Increasing additive process | Normalized inverse Gaussian process | Normalized stable process | Normalized random measure | Latent variables | Mixture model | Dirichlet process | Normalized generalized gamma process | Completely random measure | Clustering | HIERARCHICAL-MODELS | INVERSE-GAUSSIAN PRIORS | COMPONENTS | REPRESENTATION | STATISTICS & PROBABILITY | mixture model | BAYESIAN DENSITY-ESTIMATION | INFERENCE | noinialized inverse Gaussian process | normalized random measure | DISTRIBUTIONS | increasing additive process | completely random measure | normalized generalized gamma process | latent variables | clustering | normalized stable process | density estimation | Statistics - Methodology | normalized inverse Gaussian process

Datasets | A priori knowledge | Density estimation | Simulations | Barrios | Random variables | Nonparametric models | Density | Modeling | Estimators | Bayesian nonparametrics | Increasing additive process | Normalized inverse Gaussian process | Normalized stable process | Normalized random measure | Latent variables | Mixture model | Dirichlet process | Normalized generalized gamma process | Completely random measure | Clustering | HIERARCHICAL-MODELS | INVERSE-GAUSSIAN PRIORS | COMPONENTS | REPRESENTATION | STATISTICS & PROBABILITY | mixture model | BAYESIAN DENSITY-ESTIMATION | INFERENCE | noinialized inverse Gaussian process | normalized random measure | DISTRIBUTIONS | increasing additive process | completely random measure | normalized generalized gamma process | latent variables | clustering | normalized stable process | density estimation | Statistics - Methodology | normalized inverse Gaussian process

Journal Article

Methods of Functional Analysis and Topology, ISSN 1029-3531, 2018, Volume 24, Issue 3, pp. 207 - 239

Journal Article

Scandinavian Journal of Statistics, ISSN 0303-6898, 9/2012, Volume 39, Issue 3, pp. 444 - 460

In this article, we define and investigate a novel class of non-parametric prior distributions, termed the class C. Such class of priors is dense with respect...

Statistical variance | Random sampling | Markov chains | Polynomials | New species | Random variables | Sampling distributions | Crew resource management | Species | Probabilities | Gibbs‐type random probability measures | predictive distributions | species sampling problems | completely random measures | Dirichlet process | coupling from the past method | Bayesian non‐parametrics | normalized random measures with independent increments | Gibbs-type random probability measures | Coupling from the past method | Bayesian non-parametrics | Predictive distributions | Normalized random measures with independent increments | Species sampling problems | Completely random measures | PRIORS | STATISTICS & PROBABILITY | Analysis | Public health | Studies | Probability distribution | Statistical analysis | Sampling | Bayesian analysis

Statistical variance | Random sampling | Markov chains | Polynomials | New species | Random variables | Sampling distributions | Crew resource management | Species | Probabilities | Gibbs‐type random probability measures | predictive distributions | species sampling problems | completely random measures | Dirichlet process | coupling from the past method | Bayesian non‐parametrics | normalized random measures with independent increments | Gibbs-type random probability measures | Coupling from the past method | Bayesian non-parametrics | Predictive distributions | Normalized random measures with independent increments | Species sampling problems | Completely random measures | PRIORS | STATISTICS & PROBABILITY | Analysis | Public health | Studies | Probability distribution | Statistical analysis | Sampling | Bayesian analysis

Journal Article

8.
Full Text
Posterior sampling from ε-approximation of normalized completely random measure mixtures

Electronic Journal of Statistics, ISSN 1935-7524, 2016, Volume 10, Issue 2, pp. 3516 - 3547

This paper adopts a Bayesian nonparametric mixture model where the mixing distribution belongs to the wide class of normalized homogeneous completely random...

Normalized completely random measures | Bayesian nonparametric mixture models | Finite dimensional approximation | Blocked Gibbs sampler | PRIORS | DISTRIBUTIONS | FINITE NORMAL MIXTURES | MODELS | DIRICHLET PROCESSES | INFORMATION | blocked Gibbs sampler | BAYES | STATISTICS & PROBABILITY | finite dimensional approximation | normalized completely random measures

Normalized completely random measures | Bayesian nonparametric mixture models | Finite dimensional approximation | Blocked Gibbs sampler | PRIORS | DISTRIBUTIONS | FINITE NORMAL MIXTURES | MODELS | DIRICHLET PROCESSES | INFORMATION | blocked Gibbs sampler | BAYES | STATISTICS & PROBABILITY | finite dimensional approximation | normalized completely random measures

Journal Article

9.
Full Text
Frequency of Frequencies Distributions and Size-Dependent Exchangeable Random Partitions

Journal of the American Statistical Association, ISSN 0162-1459, 10/2017, Volume 112, Issue 520, pp. 1623 - 1635

Motivated by the fundamental problem of modeling the frequency of frequencies (FoF) distribution, this article introduces the concept of a cluster structure to...

Species sampling | Generalized negative binomial process | Exchangeable cluster/partition probability functions | Generalized Chinese restaurant sampling formula | Completely random measures | PRIORS | POPULATION | LAW | STATISTICS & PROBABILITY | DISCLOSURE RISK | MODELS | RNA-SEQ | DIRICHLET PROCESSES | COUNT | MICRODATA

Species sampling | Generalized negative binomial process | Exchangeable cluster/partition probability functions | Generalized Chinese restaurant sampling formula | Completely random measures | PRIORS | POPULATION | LAW | STATISTICS & PROBABILITY | DISCLOSURE RISK | MODELS | RNA-SEQ | DIRICHLET PROCESSES | COUNT | MICRODATA

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 02/2015, Volume 37, Issue 2, pp. 307 - 320

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the...

Atomic measurements | Completely Random Measures | Normalized Random Measures | Niobium | Poisson Factor Analysis | Topic Modeling | Count Modeling | Dirichlet Process | Analytical models | Mixture Modeling | Chinese Restaurant Process | Gamma Process | Negative Binomial Process | Mixed-Membership Modeling | Poisson Process | Bayesian Nonparametrics | Beta Process | Hierarchical Dirichlet Process | Data models | Random variables | Bayes methods | Joints | NONPARAMETRIC PROBLEMS | REGRESSION | negative binomial process | EXPANSIONS | Dirichlet process | topic modeling | normalized random measures | PROCESS HIERARCHICAL-MODELS | INFERENCE | Chinese restaurant process | Poisson process | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | CHAIN MONTE-CARLO | ENGINEERING, ELECTRICAL & ELECTRONIC | Beta process | mixture modeling | mixed-membership modeling | count modeling | ESTIMATORS | completely random measures | hierarchical Dirichlet process | Poisson factor analysis | DISPERSION PARAMETER | gamma process | Finite element method | Functions, Gamma | Usage | Machine learning | Innovations | Distribution (Probability theory) | Pattern recognition | Object recognition (Computers) | Poisson processes | Dirichlet problem | Bayesian analysis

Atomic measurements | Completely Random Measures | Normalized Random Measures | Niobium | Poisson Factor Analysis | Topic Modeling | Count Modeling | Dirichlet Process | Analytical models | Mixture Modeling | Chinese Restaurant Process | Gamma Process | Negative Binomial Process | Mixed-Membership Modeling | Poisson Process | Bayesian Nonparametrics | Beta Process | Hierarchical Dirichlet Process | Data models | Random variables | Bayes methods | Joints | NONPARAMETRIC PROBLEMS | REGRESSION | negative binomial process | EXPANSIONS | Dirichlet process | topic modeling | normalized random measures | PROCESS HIERARCHICAL-MODELS | INFERENCE | Chinese restaurant process | Poisson process | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | CHAIN MONTE-CARLO | ENGINEERING, ELECTRICAL & ELECTRONIC | Beta process | mixture modeling | mixed-membership modeling | count modeling | ESTIMATORS | completely random measures | hierarchical Dirichlet process | Poisson factor analysis | DISPERSION PARAMETER | gamma process | Finite element method | Functions, Gamma | Usage | Machine learning | Innovations | Distribution (Probability theory) | Pattern recognition | Object recognition (Computers) | Poisson processes | Dirichlet problem | Bayesian analysis

Journal Article

Journal of Multivariate Analysis, ISSN 0047-259X, 01/2020, Volume 175, p. 104560

Many Bayesian nonparametric approaches to multivariate time series rely on Whittle’s Likelihood, involving the second order structure of a stationary time...

Spectral density | Bayesian nonparametrics completely random measures | Stationary multivariate time series

Spectral density | Bayesian nonparametrics completely random measures | Stationary multivariate time series

Journal Article

Statistics Surveys, ISSN 1935-7516, 2009, Volume 3, pp. 47 - 95

Functionals of random probability measures | Bayesian nonparametrics | Two-parameter poisson-dirichlet process | Cifarelli-regazzini identity | Dirichlet process | Generalized stieltjes transform | Randomprobabilitymeasure | Completely random measures | Random means | Normalized random measures | Posterior distribution | Neutral to the right processes

Journal Article

Bernoulli, ISSN 1350-7265, 11/2013, Volume 19, Issue 5B, pp. 2590 - 2626

This article constructs a class of random probability measures based on exponentially and polynomially tilting operated on the laws of completely random...

Simulations | Cinerary urns | Average linear density | Positive laws | Statism | Random variables | Nonparametric models | Poisson process | Algebraic conjugates | Probabilities | Random probability measures | Tilting | Generalized gamma process | Poisson Dirichlet process | Dirichlet process | Bayesian non-parametric | Completely random measures | PRIORS | tilting | MIXTURE-MODELS | STATISTICS & PROBABILITY | generalized gamma process | DISTRIBUTIONS | DIRICHLET PROCESSES | completely random measures | PARTITIONS | random probability measures

Simulations | Cinerary urns | Average linear density | Positive laws | Statism | Random variables | Nonparametric models | Poisson process | Algebraic conjugates | Probabilities | Random probability measures | Tilting | Generalized gamma process | Poisson Dirichlet process | Dirichlet process | Bayesian non-parametric | Completely random measures | PRIORS | tilting | MIXTURE-MODELS | STATISTICS & PROBABILITY | generalized gamma process | DISTRIBUTIONS | DIRICHLET PROCESSES | completely random measures | PARTITIONS | random probability measures

Journal Article

14.
Full Text
On option pricing under a completely random measure via a generalized Esscher transform

Insurance Mathematics and Economics, ISSN 0167-6687, 2008, Volume 43, Issue 1, pp. 99 - 107

In this paper, we develop an option valuation model when the price dynamics of the underlying risky asset is governed by the exponential of a pure jump process...

Kernel-biased completely random measures | Esscher transform | Laplace functionals | Generalized Gamma processes | Option pricing | RISK MEASURES | FUNDAMENTAL THEOREM | CALCULUS | RETURNS | STATISTICS & PROBABILITY | laplace functionals | SPACE | measures | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | generalized gamma processes | kernel-biased completely random | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | option pricing | Analysis | Pricing

Kernel-biased completely random measures | Esscher transform | Laplace functionals | Generalized Gamma processes | Option pricing | RISK MEASURES | FUNDAMENTAL THEOREM | CALCULUS | RETURNS | STATISTICS & PROBABILITY | laplace functionals | SPACE | measures | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | generalized gamma processes | kernel-biased completely random | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | option pricing | Analysis | Pricing

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 11/2015, Volume 269, Issue 9, pp. 2947 - 2976

We consider the infinite-dimensional Lie group which is the semidirect product of the group of compactly supported diffeomorphisms of a Riemannian manifold and...

Laplace operator | Diffusion process | Representations of big groups | Completely random measure | MATHEMATICS | CONFIGURATION-SPACES | Algebra

Laplace operator | Diffusion process | Representations of big groups | Completely random measure | MATHEMATICS | CONFIGURATION-SPACES | Algebra

Journal Article

16.
Full Text
Pricing Risky Debts Under a Markov-modudated Merton Model with Completely Random Measures

Computational Economics, ISSN 0927-7099, 4/2008, Volume 31, Issue 3, pp. 255 - 288

We consider the pricing of both fixed rate and floating rate risky debts when the value of a firm is governed by a Markov-modulated generalized jump-diffusion...

Poisson Random measure | Markov-switching | Pricing | Economic Theory | Gamma process | Completely random measures | Economics / Management Science | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MANAGEMENT | completely random measures | ECONOMICS | gamma process | Poisson random measure | pricing | Completely random measures; Gamma process; Poisson Random measure; Markov-switching; Pricing | Economic models | Comparative studies | Pricing policies | Risk | Corporate finance | Markov analysis | Poisson distribution

Poisson Random measure | Markov-switching | Pricing | Economic Theory | Gamma process | Completely random measures | Economics / Management Science | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MANAGEMENT | completely random measures | ECONOMICS | gamma process | Poisson random measure | pricing | Completely random measures; Gamma process; Poisson Random measure; Markov-switching; Pricing | Economic models | Comparative studies | Pricing policies | Risk | Corporate finance | Markov analysis | Poisson distribution

Journal Article

17.
Full Text
Pricing risky debts under a Markov-modulated Merton model with completely random measures

Computational Economics, ISSN 0927-7099, 04/2008, Volume 31, Issue 3, pp. 255 - 288

Journal Article

18.
Full Text
A Class of Hazard Rate Mixtures for Combining Survival Data From Different Experiments

Journal of the American Statistical Association, ISSN 0162-1459, 04/2014, Volume 109, Issue 506, pp. 802 - 814

Mixture models for hazard rate functions are widely used tools for addressing the statistical analysis of survival data subject to a censoring mechanism. The...

Extended gamma processes | Bayesian nonparametrics | Dependent processes | Partial exchangeability | Completely random measures | DISTRIBUTIONS | FRAILTY MODELS | CENSORED-DATA | DIRICHLET PROCESSES | REGRESSION-MODELS | STATISTICS & PROBABILITY | PROPORTIONAL HAZARDS

Extended gamma processes | Bayesian nonparametrics | Dependent processes | Partial exchangeability | Completely random measures | DISTRIBUTIONS | FRAILTY MODELS | CENSORED-DATA | DIRICHLET PROCESSES | REGRESSION-MODELS | STATISTICS & PROBABILITY | PROPORTIONAL HAZARDS

Journal Article

Statistics and Computing, ISSN 0960-3174, 1/2017, Volume 27, Issue 1, pp. 3 - 17

Completely random measures (CRM) represent the key building block of a wide variety of popular stochastic models and play a pivotal role in modern Bayesian...

Statistics and Computing/Statistics Programs | Moment-matching | Artificial Intelligence (incl. Robotics) | Bayesian Nonparametrics | Statistical Theory and Methods | Ferguson & Klass algorithm | Posterior sampling | Statistics | Completely random measures | Normalized random measures | Probability and Statistics in Computer Science | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | DRIVEN | BETA | Analysis | Models | Algorithms | Methodology | Applications | Computation | Statistics Theory

Statistics and Computing/Statistics Programs | Moment-matching | Artificial Intelligence (incl. Robotics) | Bayesian Nonparametrics | Statistical Theory and Methods | Ferguson & Klass algorithm | Posterior sampling | Statistics | Completely random measures | Normalized random measures | Probability and Statistics in Computer Science | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | DRIVEN | BETA | Analysis | Models | Algorithms | Methodology | Applications | Computation | Statistics Theory

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 2003, Volume 65, Issue 4, pp. 363 - 368

A simple proof of the almost sure discreteness of a class of random measures which includes completely random measures is presented. The method of proof shows...

Dirichlet process | Disintegrations | Completely random measures | Poisson process | Generalized gamma process | Lévy measure | disintegrations | completely random measures | Levy measure | STATISTICS & PROBABILITY | generalized gamma process | Completely random measures Dirichlet process Disintegrations Generalized gamma process Lévy measure Poisson process

Dirichlet process | Disintegrations | Completely random measures | Poisson process | Generalized gamma process | Lévy measure | disintegrations | completely random measures | Levy measure | STATISTICS & PROBABILITY | generalized gamma process | Completely random measures Dirichlet process Disintegrations Generalized gamma process Lévy measure Poisson process

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.