Extension Of Bayesian Nonparametric Process Beta-GOS And Its Application

In bayesian nonparametric field,fully nonparametric regression needs to put a suitable prior on related random probability distributions which usually are indexed by covariates.The most popular prior for such collection of random distributions is covariate dependent Dirichlet process.Usually,covariate dependent Dirichlet process can be re-expressed as the form of Dirichlet process mixture and works well for non-exchangeable data such as time series for the task of density estimation.However,some time series data will keep the same status in some period of time.In such continuity,time structure in this period of time will tend to be the same.Since Dirichlet process implies order of samples coming from it does not matter(exchangeability),even time dependent Dirichlet process is difficult to capture such correlation and continuity for time series data.Thus based on recent non-exchangeable Bayesian nonparametric process Beta-GOS,we propose covariate dependent Beta-GOS.Our model in theory extends Beta-GOS by including the effect of covariate and in application can succeed at finding out such continuity for time series data.And even under model misspecification,our model behaves similarly with dependent Dirichlet process,which makes our model has wider applications.