Gaussian Process Structural Equation Models with Latent Variables

In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While linear non-Gaussian variants have been well-studied, inference in nonparametric structural equation models is still underdeveloped. We introduce a sparse Gaussian process parameterization that defines a non-linear structure connecting latent variables, unlike common formulations of Gaussian process latent variable models. The sparse parameterization is given a full Bayesian treatment without compromising Markov chain Monte Carlo efficiency. We compare the stability of the sampling procedure and the predictive ability of the model against the current practice.Comment: 12 pages, 6 figure

Control Variables, Discrete Instruments, and Identification of Structural Functions

Control variables provide an important means of controlling for endogeneity in econometric models with nonseparable and/or multidimensional heterogeneity. We allow for discrete instruments, giving identification results under a variety of restrictions on the way the endogenous variable and the control variables affect the outcome. We consider many structural objects of interest, such as average or quantile treatment effects. We illustrate our results with an empirical application to Engel curve estimation.Comment: 37 pages, 4 figure

Probabilistic structural analysis methods of hot engine structures

Development of probabilistic structural analysis methods for hot engine structures at Lewis Research Center is presented. Three elements of the research program are: (1) composite load spectra methodology; (2) probabilistic structural analysis methodology; and (3) probabilistic structural analysis application. Recent progress includes: (1) quantification of the effects of uncertainties for several variables on high pressure fuel turbopump (HPFT) turbine blade temperature, pressure, and torque of the space shuttle main engine (SSME); (2) the evaluation of the cumulative distribution function for various structural response variables based on assumed uncertainties in primitive structural variables; and (3) evaluation of the failure probability. Collectively, the results demonstrate that the structural durability of hot engine structural components can be effectively evaluated in a formal probabilistic/reliability framework

Exogenous impact and conditional quantile functions

An exogenous impact function is defined as the derivative of a structural function with respect to an endogenous variable, other variables, including unobservable variables held fixed. Unobservable variables are fixed at specific quantiles of their marginal distributions. Exogenous impact functions reveal the impact of an exogenous shift in a variable perhaps determined endogenously in the data generating process. They provide information about the variation in exogenous impacts across quantiles of the distributions of the unobservable variables that appear in the structural model. This paper considers nonparametric identification of exogenous impact functions under quantile independence conditions. It is shown that, when valid instrumental variables are present, exogenous impact functions can be identified as functionals of conditional quantile functions that involve only observable random variables. This suggests parametric, semiparametric and nonparametric strategies for estimating exogenous impact functions

Application of Change-Point Detection to a Structural Component of Water Quality Variables

In this study, methodologies were developed in statistical time series models, such as multivariate state-space models, to be applied to water quality variables in a river basin. In the modelling process it is considered a latent variable that allows incorporating a structural component, such as seasonality, in a dynamic way and a change-point detection method is applied to the structural component in order to identify possible changes in the water quality variables in consideration