Parameter estimation is often considered as a post model selection problem, i.e., the parameters of interest are estimated based on “the best” model. However, this approach does not take into account that was selected from set possible models. Ignoring uncertainty may lead to bias in estimation. In paper, we present Bayesian variable (BVS) for averaging which would address uncertainty. Although...

One of the main problems in credit risk management is the correlated default. In large portfolios, computing the default dependencies among issuers is an essential part in quantifying the portfolio's credit. The most important problems related to credit risk management are understanding the complex dependence structure of the associated variables and lacking the data. This paper aims at introdu...

In this chapter, we introduce the basics of Bayesian data analysis. The key ingredients to a Bayesian analysis are the likelihood function, which reflects information about the parameters contained in the data, and the prior distribution, which quantifies what is known about the parameters before observing data. The prior distribution and likelihood can be easily combined to from the posterior ...

If, in the mid 1980’s, one had asked the average statistician about the difficulties of using Bayesian Statistics, his/her most likely answer would have been “Well, there is this problem of selecting a prior distribution and then, even if one agrees on the prior, the whole Bayesian inference is simply impossible to implement in practice!” The same question asked in the 21th Century does not pro...

A common problem in statistics, and other disciplines , is to approximate adequately a function of several variables. In this paper we review some possible nonparametric Bayesian models with which we can perform this multiple regression problem. We shall also demonstrate how these basic models can be extended to allow the analysis of time series , both conventional and nancial, survival analysi...

Within this talk I shall describe some of the work I have been involved with at Microsoft Research Cambridge on Bayesian methods. In particular I will cover the application of Bayesian methods to certain problems relating to the field of Computer Graphics. Bayesian methods provide a rational way of making inference about problems; including learning parameters that are so often set by hand, and...