This paper reviews Bayesian Nonparametric methods and discusses how parametric predictive densities can be constructed using nonparametric ideas.

background: colon cancer is the third cause of cancer deaths. although colon cancer survival time has increased in recent years, the mortality rate is still high. the cox model is the most common regression model often used in medical research in survival analysis, but most of the time the effect of at least one of the independent factors changes over time, so the model cannot be used. in the c...

the problem of hypothesis testing with a nuisance parameter is considered. two methods forusing fuzzy knowledge on the nuisance parameter to test hypotheses are suggested. these methods areneither a pure classical nor a pure bayesian approach to hypothesis testing, but rather related to both. afew known examples and their applications, which cannot be studied by the parametric statisticalmethod...

We analyze reduced basis acceleration of recently proposed deterministic Bayesian inversion algorithms for partial differential equations with uncertain distributed parameter, for observation data subject to additive, Gaussian observation noise. Specifically, Bayesian inversion of affine-parametric, linear operator families on possibly high-dimensional parameter spaces. We consider “high-fideli...

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a set of multiple parameters, which can be divided into two disjoint subsets. On one set, a frequentist method may be favored and on the other, the Bayesian. ...

In Bayesian paradigm of survival analysis, we can combine a nonparametric estimator and a parametric model by putting a prior distribution nonparametrically around the entire parametric family. This method can avoids the ineeciency of the nonparametric estimator due to ignoring partial information about a parametric model and at the same time avoids the pitfalls connected with an incorrectly sp...

The classical Gumbel probability distribution is modified in order to study the failure times of a given system. Bayesian estimates of the reliability function under five different parametric priors and the square error loss are studied. The Bayesian reliability estimate under the non-parametric kernel density prior is compared with those under the parametric priors and numerical computations a...

We consider the classical problem of missing-mass estimation, which deals with estimating total probability unseen elements in a sample. The estimation has various applications machine learning, statistics, language processing, ecology, sensor networks, and others. naive, constrained maximum likelihood (CML) estimator is inappropriate for this since it tends to overestimate observed elements. S...