Search results for "Random"
showing 10 items of 3931 documents
On fractional diffusion and continuous time random walks
2003
Abstract A continuous time random walk model is presented with long-tailed waiting time density that approaches a Gaussian distribution in the continuum limit. This example shows that continuous time random walks with long time tails and diffusion equations with a fractional time derivative are in general not asymptotically equivalent.
Bayesian analysis and design for comparison of effect-sizes
2002
Comparison of effect-sizes, or more generally, of non-centrality parameters of non-central t distributions, is a common problem, especially in meta-analysis. The usual simplifying assumptions of either identical or non-related effect-sizes are often too restrictive to be appropriate. In this paper, the effect-sizes are modeled as random effects with t distributions. Bayesian hierarchical models are used both to design and analyze experiments. The main goal is to compare effect-sizes. Sample sizes are chosen so as to make accurate inferences about the difference of effect-sizes and also to convincingly solve the testing of equality of effect-sizes if such is the goal.
Optimal signed-rank tests based on hyperplanes
2005
Abstract For analysing k -variate data sets, Randles (J. Amer. Statist. Assoc. 84 (1989) 1045) considered hyperplanes going through k - 1 data points and the origin. He then introduced an empirical angular distance between two k -variate data vectors based on the number of hyperplanes (the so-called interdirections ) that separate these two points, and proposed a multivariate sign test based on those interdirections. In this paper, we present an analogous concept (namely, lift-interdirections ) to measure the regular distances between data points. The empirical distance between two k -variate data vectors is again determined by the number of hyperplanes that separate these two points; in th…
Time-dependent weak rate of convergence for functions of generalized bounded variation
2016
Let $W$ denote the Brownian motion. For any exponentially bounded Borel function $g$ the function $u$ defined by $u(t,x)= \mathbb{E}[g(x{+}\sigma W_{T-t})]$ is the stochastic solution of the backward heat equation with terminal condition $g$. Let $u^n(t,x)$ denote the corresponding approximation generated by a simple symmetric random walk with time steps $2T/n$ and space steps $\pm \sigma \sqrt{T/n}$ where $\sigma > 0$. For quite irregular terminal conditions $g$ (bounded variation on compact intervals, locally H\"older continuous) the rate of convergence of $u^n(t,x)$ to $u(t,x)$ is considered, and also the behavior of the error $u^n(t,x)-u(t,x)$ as $t$ tends to $T$
Asymptotic optimality of myopic information-based strategies for Bayesian adaptive estimation
2016
This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information gain maximization algorithm for adaptive Bayesian estimation is asymptotically optimal in the sense that the determinant of the posterior covariance in a certain neighborhood of the true parameter value is asymptotically minimal. Using this result, we also obtain an asymptotic expression for the posterior entropy based on a novel definition of almost sure convergence on "most trials" (meaning that the convergence holds on a fraction of trials that converge…
Breaking the curse of dimensionality in quadratic discriminant analysis models with a novel variant of a Bayes classifier enhances automated taxa ide…
2013
Macroinvertebrate samples are commonly used in biomonitoring to study changes on aquatic ecosystems. Traditionally, specimens are identified manually to taxa by human experts being time-consuming and cost intensive. Using the image data of 35 taxa and 64 features, we propose a novel variant of the quadratic discriminant analysis for breaking the curse of dimensionality in quadratic discriminant analysis models. Our variant, called a random Bayes array (RBA), uses bagging and random feature selection similar to random forest. We explore several variations of RBA. We consider three classification (i.e taxa identification) decisions: majority vote, averaged posterior probabilities, and a novel…
A model-based approach to Spotify data analysis: a Beta GLMM
2020
Digital music distribution is increasingly powered by automated mechanisms that continuously capture, sort and analyze large amounts of Web-based data. This paper deals with the management of songs audio features from a statistical point of view. In particular, it explores the data catching mechanisms enabled by Spotify Web API and suggests statistical tools for the analysis of these data. Special attention is devoted to songs popularity and a Beta model, including random effects, is proposed in order to give the first answer to questions like: which are the determinants of popularity? The identification of a model able to describe this relationship, the determination within the set of char…
The linear birth and death process under the influence of independently occurring disasters
1989
A population developing according to a time homogeneous linear birth and death process is subjected to an independently occurring random sequence of disasters. Using an embedded Galton-Watson process with random environments explicit results about the probability of extinction and the asymptotic behavior of the process are obtained.
Power of the Wilcoxon–Mann–Whitney test for non‐inferiority in the presence of death‐censored observations
2017
In clinical trials with patients in a critical state, death may preclude measurement of a quantitative endpoint of interest, and even early measurements, for example for intention-to-treat analysis, may not be available. For example, a non-negligible proportion of patients with acute pulmonary embolism will die before 30 day measurements on the efficacy of thrombolysis can be obtained. As excluding such patients may introduce bias, alternative analyses, and corresponding means for sample size calculation are needed. We specifically consider power analysis in a randomized clinical trial setting in which the goal is to demonstrate noninferiority of a new treatment as compared to a reference t…
Correlated randomness and switching phenomena
2010
One challenge of biology, medicine, and economics is that the systems treated by these serious scientific disciplines have no perfect metronome in time and no perfect spatial architecture—crystalline or otherwise. Nonetheless, as if by magic, out of nothing but randomness one finds remarkably fine-tuned processes in time and remarkably fine-tuned structures in space. Further, many of these processes and structures have the remarkable feature of “switching” from one behavior to another as if by magic. The past century has, philosophically, been concerned with placing aside the human tendency to see the universe as a fine-tuned machine. Here we will address the challenge of uncovering how, th…