Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables

We provide a scheme for inferring causal relations from uncontrolled statistical data based on tools from computational algebraic geometry, in particular, the computation of Groebner bases. We focus on causal structures containing just two observed variables, each of which is binary. We consider the consequences of imposing different restrictions on the number and cardinality of latent variables and of assuming different functional dependences of the observed variables on the latent ones (in particular, the noise need not be additive). We provide an inductive scheme for classifying functional causal structures into distinct observational equivalence classes. For each observational equivalence class, we provide a procedure for deriving constraints on the joint distribution that are necessary and sufficient conditions for it to arise from a model in that class. We also demonstrate how this sort of approach provides a means of determining which causal parameters are identifiable and how to solve for these. Prospects for expanding the scope of our scheme, in particular to the problem of quantum causal inference, are also discussed.Comment: Accepted for publication in Journal of Causal Inference. Revised and updated in response to referee feedback. 16+5 pages, 26+2 figures. Comments welcom

An MDL approach to the climate segmentation problem

This paper proposes an information theory approach to estimate the number of changepoints and their locations in a climatic time series. A model is introduced that has an unknown number of changepoints and allows for series autocorrelations, periodic dynamics, and a mean shift at each changepoint time. An objective function gauging the number of changepoints and their locations, based on a minimum description length (MDL) information criterion, is derived. A genetic algorithm is then developed to optimize the objective function. The methods are applied in the analysis of a century of monthly temperatures from Tuscaloosa, Alabama.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS289 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The effects of three forms of observing a basketball game on subsequent aggression

This experimental study was designed to test whether viewing a West Coast Athletic Conference Basketball Game in person had a significantly greater effect on spectators than watching the same event on television or listening to it on the radio. The literature revealed mixed opinions concerning this type of testing

First-principles study of the Young's modulus of Si <001> nanowires

We report the results of first-principles density functional theory calculations of the Young's modulus and other mechanical properties of hydrogen-passivated Si nanowires. The nanowires are taken to have predominantly {100} surfaces, with small {110} facets. The Young's modulus, the equilibrium length and the residual stress of a series of prismatic wires are found to have a size dependence that scales like the surface area to volume ratio for all but the smallest wires. We analyze the physical origin of the size dependence, and compare the results to two existing models.Comment: 5 pages, 3 figure

Advertising and Product Confusion: A Case Study of Grapefruit Juice

Demand relationships for two closely related products -- grapefruit juice and grapefruit-juice cocktail -- were estimated from grocery-store scanner data to analyze the contention that consumer confusion exists between the two products. Results suggest confusion may exist, with grapefruit-juice advertising not only increasing the demand for grapefruit juice but also for grapefruit-juice cocktail.advertising, demand, grapefruit juice, cocktail, scanner data, Agribusiness, Consumer/Household Economics, Demand and Price Analysis,

CONDITIONAL DEMAND AND ENDOGENEITY? A CASE STUDY OF DEMAND FOR JUICE PRODUCTS

The question of endogeneity of conditional expenditures, as well as prices, in conditional demand equations for justices is examined. Both conditional expenditures and prices were found to be uncorrelated with the conditional demand errors, based on Wu-Hausman tests. Conditional demand error variance/covariance estimates and corresponding Slutsky coefficient estimates were approximately proportional, as predicted by the theory of rational random behavior, further supporting independence of conditional expenditures and conditional errors for juice demands.Demand and Price Analysis,

Childhood and Intergenerational Poverty: The Long-Term Consequences of Growing Up Poor

Children growing up in low-income families face many challenges that children from more advantaged families do not. These children are more likely to experience multiple family transitions, move frequently, and change schools. The schools they attend are less well funded, and the neighborhoods they live in are more disadvantaged. The parents of these children have fewer resources to invest in them and, as a consequence, their homes have fewer cognitively-stimulating materials, and their parents invest less in their education. The stress of living in poverty and struggling to meet daily needs can also impair parenting. Social and economic deprivation during childhood and adolescence can have a lasting effect on individuals, making it difficult for children who grow up in low-income families to escape poverty when they become adults. Because the negative effects of deprivation on human development tend to cumulate, individuals with greater exposure to poverty during childhood are likely to have more difficulty escaping poverty as adults. In this research brief, we examine patterns of exposure to poverty during childhood and the association between these patterns and poverty in early and middle adulthood. Data for this study come from the Panel Study of Income Dynamics (PSID), which collects information on the social and economic status of PSID families and their offspring every year. We find that individuals who grow up in poor families are much more likely to be poor in early adulthood. Moreover, the chances of being poor in early adulthood increase sharply as the time spent living in poverty during childhood increases. At all levels of poverty during childhood, African-Americans are more likely than whites to be poor in early and middle adulthood

Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical process catalyst. We study a large-scale, industrially-relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pre-trained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models, or they may wish to optimize a discrete model that particularly well-represents a data set. We develop several heuristic methods to find feasible solutions, and an exact, branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on concrete mixture design instance and a chemical catalysis industrial instance