Abstract: The standard regression problem in statistics consists of
determining the relationship between a response variable and a set of
predictor variables through a regression function. Scientific information is
often available that suggests the regression function should have a certain
shape (e.g., monotonically increasing or concave) but not necessarily a
specific parametric form. Recently, Bernstein polynomials have been used to
impose certain shape restrictions on regression funct­ions. In this work, we
demonstrate a connection between the monotonic regression problem and the
variable selection problem in the linear model. We develop a Bayesian
procedure for fitting the monotonic regression model by adapting one of
popular the variable selection procedures. We demonstrate the effectiveness
of our method through simulations and the analysis of real data sets.



Remark: This talk is based on a joint work with Dr. S.Mckay Curtis at
University of Washington, Seattle, USA.