Search results for "Probability Theory"
showing 9 items of 269 documents
All-Possible-Couplings Approach to Measuring Probabilistic Context.
2013
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly" influence them, but (iii) other inputs provide a "context" for this response by influencing its probabilistic relations to other responses. These contextual influences are very different, say, in classical kinetic theory and in the entanglement paradigm of quantum mechanics, which are traditionally interpreted as representing different forms of physical determinism. One can mathematically construct systems with other types of contextuality, whether or not …
Combining Sequence Analysis and Hidden Markov Models in the Analysis of Complex Life Sequence Data
2018
Life course data often consists of multiple parallel sequences, one for each life domain of interest. Multichannel sequence analysis has been used for computing pairwise dissimilarities and finding clusters in this type of multichannel (or multidimensional) sequence data. Describing and visualizing such data is, however, often challenging. We propose an approach for compressing, interpreting, and visualizing the information within multichannel sequences by finding (1) groups of similar trajectories and (2) similar phases within trajectories belonging to the same group. For these tasks we combine multichannel sequence analysis and hidden Markov modelling. We illustrate this approach with an …
What drives increases in hindsight impressions after the reception of biased media content?
2021
Prior research has shown that reading biased media content (e.g., Wikipedia articles) can increase recipients' hindsight bias. It remained unclear, however, which features of the biased texts led to such an increase. We examined this question in a longitudinal experimental study (N = 190). Specifically, we tested whether repeated exposure to already known information (H₁), a more coherent presentation of the information (H₂), or the presentation of novel information (H₃) affected readers' hindsight impressions of likelihood, inevitability, and foreseeability. To this end, participants initially learned about an event by reading several short news, and, 1 week later, received one of several …
Guidelines for time-to-event end point definitions in sarcomas and gastrointestinal stromal tumors (GIST) trials: results of the DATECAN initiative (…
2015
ABSTRACT The DATECAN initiative (Definition for the Assessment of Time-to-event Endpoints in CANcer trials) aims to provide recommendations for definitions of time-to-event end points in cancer randomized controlled trials. We relied on a consensus method based on a multidisciplinary panel of experts to develop these guidelines for trials on sarcomas and gastrointestinal stromal tumors. Background The use of potential surrogate end points for overall survival, such as disease-free survival (DFS) or time-to-treatment failure (TTF) is increasingly common in randomized controlled trials (RCTs) in cancer. However, the definition of time-to-event (TTE) end points is rarely precise and lacks unif…
Shape identification in inverse medium scattering problems with a single far-field pattern
2016
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset {\mathbb R}^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be Holder continuous near the corners. If $D\subset {\mathbb R}^2$ is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions $N \geq 3$, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of nonscattering waven…
An Examination of Tourist Arrivals Dynamics Using Short-Term Time Series Data: A Space—Time Cluster Approach
2013
The purpose of this study is to examine the development of Italian tourist areas ( circoscrizioni turistiche) through a cluster analysis of short time series. The technique is an adaptation of the functional data analysis approach developed by Abraham et al (2003), which combines spline interpolation with k-means clustering. The findings indicate the presence of two patterns (increasing and stable) averagely characterizing groups of territories. Moreover, tests of spatial contiguity suggest the presence of ‘space–time clusters’; that is, areas in the same ‘time cluster’ are also spatially contiguous. These findings appear to be more robust in particular for those series characterized by an…
Stationary and Nontationary Response Probability Density Function of a Beam under Poisson White Noise
2011
In this paper an approximate explicit probability density function for the analysis of external oscillations of a linear and geometric nonlinear simply supported beam driven by random pulses is proposed. The adopted impulsive loading model is the Poisson White Noise , that is a process having Dirac’s delta occurrences with random intensity distributed in time according to Poisson’s law. The response probability density function can be obtained solving the related Kolmogorov-Feller (KF) integro-differential equation. An approximated solution, using path integral method, is derived transforming the KF equation to a first order partial differential equation. The method of characteristic is the…
Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES
2005
In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…
Convergence of Measures
2020
One focus of probability theory is distributions that are the result of an interplay of a large number of random impacts. Often a useful approximation can be obtained by taking a limit of such distributions, for example, a limit where the number of impacts goes to infinity. With the Poisson distribution, we have encountered such a limit distribution that occurs as the number of very rare events when the number of possibilities goes to infinity (see Theorem 3.7). In many cases, it is necessary to rescale the original distributions in order to capture the behavior of the essential fluctuations, e.g., in the central limit theorem. While these theorems work with real random variables, we will a…