Nonparametric Bayes inference for concave distribution functions

Bayesian inference for concave distribution functions is investigated. This is made by transforming a mixture of Dirichlet processes on the space of distribution functions to the space of concave distribution functions. We

[1]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[2]  J. Florens,et al.  Semi‐ and Non‐parametric Bayesian Analysis of Duration Models with Dirichlet Priors: A Survey , 1999 .

[3]  Jean-Pierre Florens,et al.  Elements of Bayesian Statistics , 1990 .

[4]  J. Besag,et al.  Spatial Statistics and Bayesian Computation , 1993 .

[5]  Peter Green,et al.  A primer in Markov Chain Monte Carlo , 2001 .

[6]  B. Turnbull.  The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data , 1976 .

[7]  T. Mattfeldt.  Stochastic Geometry and Its Applications , 1996 .

[8]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[9]  B. Turnbull.  Nonparametric Estimation of a Survivorship Function with Doubly Censored Data , 1974 .

[10]  Hani Doss.  Bayesian Nonparametric Estimation for Incomplete Data Via Successive Substitution Sampling , 1994 .

[11]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[12]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[13]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[14]  Steffen L. Lauritzen,et al.  Independence properties of directed markov fields , 1990, Networks.

[15]  R. Phelps.  Lectures on Choquet's Theorem , 1966 .

[16]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Albert Y. Lo,et al.  Bayes Methods for a Symmetric Unimodal Density and its Mode , 1989 .

[18]  J. V. Ryzin,et al.  Nonparametric Bayesian Estimation of Survival Curves from Incomplete Observations , 1976 .

[19]  S. Walker,et al.  A Bayesian Non‐parametric Approach to Survival Analysis Using Polya Trees , 1997 .

[20]  Frank Proschan.  Theoretical Explanation of Observed Decreasing Failure Rate , 2000, Technometrics.

[21]  Michael I. Jordan.  Graphical Models , 2003 .

[22]  D. Blackwell,et al.  Ferguson Distributions Via Polya Urn Schemes , 1973 .

[23]  Yehuda Vardi,et al.  Multiplicative censoring, renewal processes, deconvolution and decreasing density: Nonparametric estimation , 1989 .

[24]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[25]  Albert Y. Lo,et al.  On a Class of Bayesian Nonparametric Estimates: I. Density Estimates , 1984 .

[26]  C. Antoniak.  Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[27]  Purushottam W. Laud,et al.  Implementation of bayesian non-parametric inference based on beta processes , 1996 .

[28]  David R. Cox,et al.  The statistical analysis of series of events , 1966 .

[29]  G. M. Laslett,et al.  The survival curve under monotone density constraints with applications to two-dimensional line segment processes , 1982 .

[30]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[31]  J. Sethuraman.  A CONSTRUCTIVE DEFINITION OF DIRICHLET PRIORS , 1991 .

[32]  Walter R. Gilks,et al.  A Language and Program for Complex Bayesian Modelling , 1994 .

[33]  Adrian Baddeley,et al.  Kaplan-Meier type estimators for linear contact distributions , 1996 .

[34]  L. J. Brunner,et al.  Using the gibbs sampler to simulate from the bayes estimate of a decreasing density , 1995 .

[35]  Michael,et al.  On a Class of Bayesian Nonparametric Estimates : I . Density Estimates , 2008 .

[36]  Frank E. Grubbs,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[37]  M. May.  Bayesian Survival Analysis. , 2002 .

[38]  M. Escobar.  Estimating Normal Means with a Dirichlet Process Prior , 1994 .

[39]  Michel Mouchart,et al.  Bayesian Analysis of Mixtures : Some results on Exact Estimability and Identification , 1992 .

[40]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[41]  L. J. Brunner.  Bayesian nonparametric methods for data from a unimodal density , 1992 .

[42]  S. MacEachern.  Estimating normal means with a conjugate style dirichlet process prior , 1994 .

[43]  N. Hjort.  Nonparametric Bayes Estimators Based on Beta Processes in Models for Life History Data , 1990 .

[44]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[45]  H. Barnett.  A Theory of Mortality , 1968 .

[46]  P. Groeneboom.  Estimating a monotone density , 1984 .

[47]  D. Freedman,et al.  On the consistency of Bayes estimates , 1986 .

[48]  Graham J. Wills,et al.  Introduction to graphical modelling , 1995 .

[49]  David R. Cox,et al.  The statistical analysis of series of events , 1966 .

[50]  Frank Proschan,et al.  Theoretical Explanation of Observed Decreasing Failure Rate , 2000, Technometrics.

[51]  U. Grenander.  On the theory of mortality measurement , 1956 .

[52]  Purushottam W. Laud,et al.  Bayesian Nonparametric Inference for Random Distributions and Related Functions , 1999 .

[53]  Paul Damien,et al.  Monte Carlo methods for approximating a posterior hazard rate process , 1996, Stat. Comput..

[54]  Isotonic estimators of monotone densities and distribution functions: basic facts , 1993 .

[55]  T. Ferguson.  Prior Distributions on Spaces of Probability Measures , 1974 .