Generalizing empirical adequacy I: multiplicity and approximation

Geometries of sensor outputs, inference and information processing

We describe signal processing tools to extract structure and information from arbitrary digital data sets. In particular heterogeneous multi-sensor measurements which involve corrupt data, either noisy or with missing entries present formidable challenges. We sketch methodologies for using the network of inferences and similarities between the data points to create robust nonlinear estimators f...

Exact Multiplicity Results for Boundary Value Problems with Nonlinearities Generalizing Cubic

Empirical Adequacy in the Received View

I show that the central notion of Constructive Empiricism, empirical adequacy, can be expressed syntactically and specifically in the Received View of the logical empiricists. The formalization shows that the Received View is superior to Constructive Empiricism in the treatment of theories involving unobservable objects or functions from observable to unobservable objects. It also suggests a fo...

An Exact Multiplicity Result for a Class of Semilinear Equations

For a class of Dirichlet problems in two dimensions, generalizing the model case ∆u+ λu(u− b)(c− u) = 0 in |x| < R,u = 0 on |x| = R, ∗Supported in part by the National Science Foundation.

Factors Affecting the Adequacy and Preferability of Semiparametric Groups-Based Approximations of Continuous Growth Trajectories.

Psychologists have long been interested in characterizing individual differences in change over time. It is often plausible to assume that the distribution of these individual differences is continuous in nature, yet theory is seldom so specific as to designate its parametric form (e.g., normal). Semiparametric groups-based trajectory models (SPGMs) were thus developed to provide a discrete app...