2,122 research outputs found
Monotonic regression based on Bayesian P-splines: an application to estimating price response functions from store-level scanner data
Generalized additive models have become a widely used instrument for flexible regression analysis. In many practical situations, however, it is desirable to restrict the flexibility of nonparametric estimation in order to accommodate a presumed monotonic relationship between a covariate and the response variable. For example, consumers usually will buy less of a brand if its price increases, and therefore one expects a brand's unit sales to be a decreasing function in own price. We follow a Bayesian approach using penalized B-splines and incorporate the assumption of monotonicity in a natural way by an appropriate specification of the respective prior distributions. We illustrate the methodology in an empirical application modeling demand for a brand of orange juice and show that imposing monotonicity constraints for own- and cross-item price effects improves the predictive validity of the estimated sales response function considerably
A Bayesian Multivariate Functional Dynamic Linear Model
We present a Bayesian approach for modeling multivariate, dependent
functional data. To account for the three dominant structural features in the
data--functional, time dependent, and multivariate components--we extend
hierarchical dynamic linear models for multivariate time series to the
functional data setting. We also develop Bayesian spline theory in a more
general constrained optimization framework. The proposed methods identify a
time-invariant functional basis for the functional observations, which is
smooth and interpretable, and can be made common across multivariate
observations for additional information sharing. The Bayesian framework permits
joint estimation of the model parameters, provides exact inference (up to MCMC
error) on specific parameters, and allows generalized dependence structures.
Sampling from the posterior distribution is accomplished with an efficient
Gibbs sampling algorithm. We illustrate the proposed framework with two
applications: (1) multi-economy yield curve data from the recent global
recession, and (2) local field potential brain signals in rats, for which we
develop a multivariate functional time series approach for multivariate
time-frequency analysis. Supplementary materials, including R code and the
multi-economy yield curve data, are available online
Regional Agricultural Endowments and Shifts of Poverty Trap Equilibria: Evidence from Ethiopian Panel Data
We introduce new approaches to research on poverty traps, focusing on changes in patterns of equilibria over time and across regions, applied to the Ethiopia Rural Household Survey. We revisit the incidence of multiple equilibria using new nonparametric techniques; we also emphasize conditions of single equilibria that remain stagnant below the poverty line. We identify a single equilibrium in our initial interval (1994 - 1999) but and evidence that a second, higher equilibrium is emerging in the subsequent (1999 - 2004) interval. One of three major regions exhibits a deeply impoverished equilibrium that does not improve despite a national environment of pro-poor growth.poverty trap, Ethiopia, multiple equilibria, asset dynamics, regional poverty, sequence of equilibria
Bayesian Analysis for Penalized Spline Regression Using WinBUGS
Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. Good mixing properties of the MCMC chains are obtained by using low-rank thin-plate splines, while simulation times per iteration are reduced employing WinBUGS specific computational tricks.
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