By "simple situations" I mean those experimental designs commonly used in psychophysics, learning, and motivation, especially in studies intended to test one or another mathematical model. In fact, in this chapter only experiments for which the subject has two possible responses are discussed because mathematical theories are moderately well worked out only for these simple situations. Even the...

The goal of this paper is to indicate a new method for constructing normal confidence intervals the mean, when data coming from stochastic structures with possibly long memory, especially dependence structure not known or even existence density function. More precisely we introduce random smoothing suggested by kernel estimators regression are constructed under sole condition that sequence ergo...

We present a theory for describing the evolution of a galaxy caused by stochastic events such as weak mergers, transient spiral structure, orbiting blobs, etc. This noise excites large-scale patterns that drives the evolution of the galactic density profile. In dark-matter haloes, the repeated stochastic perturbations preferentially ring the lowest-order modes of the halo with only a very weak ...

Complex stochastic models are commonplace in epidemiology, but their utility depends on their calibration to empirical data. History matching is a (pre)calibration method that has been applied successfully to complex deterministic models. In this work, we adapt history matching to stochastic models, by emulating the variance in the model outputs, and therefore accounting for its dependence on t...

Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression. In this paper we propose a characteristic function-based estimation method for non-Gaussian Ornstein-Uhl...

In applications, it is often necessary to resort to approximations in the study of the properties of stochastic models. The original process can be replaced by a simpler one whose characteristics are already known or easier to study. This requires some stability of the model, which is usually represented in terms of integral probability metrics (Rachev, 1991, Müller, 1997). Among the many possi...

Abstract. The recent financial crisis, responsible for massive accumulations of credit events, emphasizes the urgent need for adequate portfolio default models. Due to the high dimensionality of real credit portfolios, balancing flexibility and numerical tractability is of uttermost importance. To acknowledge this, a multivariate default model with interesting stylized properties is introduced ...

Movements develop in coevolution with regimes and other actors in their environments. Movement trajectories evolve through stochastic processes and are constrained, but not determined, by structures. Coevolution provides a theoretical structure for organizing existing understandings of social movements and sharpening future research. Stochastic thinking is essential for recognizing the both the...