Graduate Student Seminar

Speaker 1: Elias Al-Najjar

Title

Hierarchical Principal Fitted Components

Abstract

In the principal fitted components model, it is assumed that all observations are independent. This is a helpful assumption for estimating a minimal sufficient dimension reduction subspace via inverse regression. However, consider data recorded on C subjects, where n_j observations of (X,Y) are recorded for each subject j . While the observations from subject to subject could be independent, the within-subject observations are likely dependent. Treating the within-subject observations as independent may not be appropriate, and may adversely affect estimation of the central subspace. We propose a model for estimation of the central subspace when the observations are dependent within cluster. We use what we call a hierarchical PFC model to estimate the minimal sufficient reduction, which can replace X in a forward population-averaged model.

Speaker 2: Sai Popouri

Title

Bayesian Analysis of a State-space Tobit Model for Daily Precipitation Data

Abstract

Downscaling is the process of bringing the data provided by Global Climate Models (GCM) from a coarser resolution (~100km) to a finer resolution (~10km). It is an important step in applications that assess the impact of large scale climate changes on local conditions. In this seminar, we will discuss a statistical method to improve the quality of spatially interpolated downscaled precipitation for prediction purposes. We discuss the results from an ongoing research on analyzing the daily precipitation time series at a location in the upper Missouri River Basin (MRB) by fitting a state-space model with the spatially interpolated daily historical simulated data provided by MIROC5, a Global Climate Model, as an independent variable using a Gibbs sampling scheme. The time series is from a mixed distribution with positive Probability of zero precipitation and shows strong seasonality. We use Kalman filtering in the context of censored data for estimation and forecasting. Statistical properties of the parameter estimates and long range forecasts are explored.