Inference With Cross-Lagged Effects - Problems in Time and New Interpretations

The interpretation of cross-effects from vector autoregressive models to infer structure and causality amongst constructs is widespread and sometimes problematic. I first explain how hypothesis testing and regularization are invalidated when processes that are thought to fluctuate continuously in time are, as is typically done, modeled as changing only in discrete steps. I then describe an alternative interpretation of cross-effect parameters that incorporates correlated random changes for a potentially more realistic view of how process are temporally coupled. Using an example based on wellbeing data, I demonstrate how some classical concerns such as sign flipping and counter intuitive effect directions can disappear when using this combined deterministic / stochastic interpretation. Models that treat processes as continuously interacting offer both a resolution to the hypothesis testing problem, and the possibility of the combined stochastic / deterministic interpretation.

Subclasses of Starlike and Convex Functions Associated with the Limaçon Domain

Let ST L ( s ) and CV L ( s ) denote the family of analytic and normalized functions f in the unit disk D : = z : | z | < 1 , such that the quantity z f ′ ( z ) / f ( z ) or 1 + z f ″ ( z ) / f ′ ( z ) respectively are lying in the region bounded by the limaçon ( u − 1 ) 2 + v 2 − s 4 2 = 4 s 2 u − 1 + s 2 2 + v 2 , where 0 < s ≤ 1 / 2 . The limaçon of Pascal is a curve that possesses properties which qualify it for the several applications in mathematics, statistics (hypothesis testing problem) but also in mechanics (fluid processing applications, known limaçon technology is employed to extract electrical power from low-grade heat, etc.). In this paper we present some results concerning the behavior of f on the classes ST L ( s ) or CV L ( s ) . Some appropriate examples are given.

On Estimating Non-standard Discrete Distributions Using Adaptive MCMC Methods

In this paper, we compare empirically the performance of some adaptive MCMC methods, that is, Adaptive Metropolis (AM) algorithm, Single Component Adaptive Metropolis (SCAM) algorithm and Delayed Rejection Adaptive Metropolis (DRAM) algorithm. The context is the simulation of non-standard discrete distributions. The performance criterion used is the precision of the frequency estimator. An application to a Bayesian hypothesis testing problem shows the superiority of the DRAM algorithm over the other considered sampling schemes.