In this paper limit theorems for the conditional distributions of linear test statistics are proved. The assertions are conditioned by the sigma-field of permutation symmetric sets. Limit theorems are proved both for the conditional distributions under the hypothesis of randomness and under general contiguous alternatives with independent but not identically distributed observations. The proofs are based on results on limit theorems for exchangeable random variables by Strasser and Weber. The limit theorems under contiguous alternatives are consequences of an LAN-result for likelihood ratios of symmetrized product measures. The results of the paper have implications for statistical applications. By example it is shown that minimum variance partitions which are defined by observed data (e.g. by LVQ) lead to asymptotically optimal adaptive tests for the k-sample problem. As another application it is shown that conditional k-sample tests which are based on data-driven partitions lead to simple confidence sets which can be used for the simultaneous analysis of linear contrasts. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

The terminology and ideas involved in the statistical analysis of survival data are explained including the survival function, the probability density function, the hazard function, censored observations, parametric and nonparametric estimations of these functions, the product limit estimation of the survival function, and the proportional hazards estimation of the hazard function with explanatory variables. In Appendix A these ideas are applied to the actual analysis of the survival data for 54 cervical cancer patients.

Several models in econometrics and finance have been proven to be computationally intractable due to their complexity. In this dissertation, we propose an evolutionary-genetic-algorithm for solving these types of problems. We extend the models so that less restrictive assumptions are required and we cope with the increased complexity by using a modified version of the evolutionary algorithm proposed for the simpler cases. More specifically, we study closer the estimation of switching regression models as introduced by Quandt (1958). The applicability of the proposed algorithms is examined through disequilibrium models; models that provide supply and demand functions for markets, when the price is not adjusted so that the quantity supplied equals the quantity demanded. We focus on the computational aspect of the deterministic switching regression models and we suggest a self-evolving genetic algorithm for solving these types of problems. As an illustration, we present results from Monte Carlo simulations and thereafter we apply the algorithm to the disequilibrium model proposed for the gasoline market during the “energy crisis”. We further extend the “general model” for markets in disequilibrium by incorporating dynamic relationships, and we examine the applicability of the proposed genetic algorithm in this more complex and realistic problem. Subsequently, the proposed genetic algorithm for the markets in disequilibrium is applied to financial models, where the structure and computational complexity are comparable with those of the switching regression models. As example, we apply the algorithm to minimizing portfolio tracking error with respect to a pre-specified index. The proposed genetic algorithm possesses unique characteristics that maximize the fitness of the algorithm itself for each individual problem. This is achieved through a Self-Evolving process that teaches the genetic algorithm what internal parameters improve the algorithm's fitness.

A large collection of digital images of natural scenes provides a database for analyzing and modeling small scene patches (e.g., 2 x 2) referred to as natural microimages. A pivotal finding is the stability of the empirical microimage distribution across scene samples and with respect to scaling. With a view toward potential applications (e.g. classification, clutter modeling, segmentation), we present a hierarchy of microimage probability models which capture essential local image statistics. Tools from information theory, algebraic geometry and of course statistical hypothesis testing are employed to assess the “match” between candidate models and the empirical distribution. Geometric symmetries play a key role in the model selection process. One central result is that the microimage distribution exhibits reflection and rotation symmetry and is well-represented by a Gibbs law with only pairwise interactions. However, the acceptance of the up-down reflection symmetry hypothesis is borderline and intensity inversion symmetry is rejected. Finally, possible extensions to larger patches via entropy maximization and to patch classification via vector quantization are briefly discussed.

I report experimental and numerical studies of microparticle motion in a dusty plasma. These microparticles are negatively charged and are levitated in a plasma consisting of electrons, ions and neutral gas atoms. The microparticles repel each other, and are confined by the electric fields in the plasma. The neutral gas damps the microparticle motion, and also exerts random forces on them. I investigate and characterize microparticle motion. In order to do this, I study velocity distributions of microparticles and correlations of their motion. To perform such a study, I develop new experimental and analysis techniques. My thesis consists of four separate projects. In the first project, the battle between deterministic and random motion of microparticles is investigated. Two particle velocity distributions and correlations have previously studied only in theory. I performed an experiment with a very simple one dimensional (1D) system of two microparticles in a plasma. My study of velocity correlations involves just two microparticles which is the simplest system that allows interactions. A study of such a simple system provides insight into the motions of the microparticles. It allowed for the experimental measurement of two-particle distributions and correlations. For such a system, it is shown that the motion of the microparticles is dominated by deterministic or oscillatory effects. In the second project, two experiments with just two microparticles are performed to isolate the effects of ion wakes. The two experiments differ in the alignment of the two microparticles: they are aligned either perpendicular or parallel to the ion flow. To have different alignments, the sheath is shaped differently in the two experiments. I demonstrate that microparticle motion is more correlated when they are aligned along the ion flow, rather than perpendicular to the ion flow. In the third project, I develop a model with some key assumptions to compare with the experiments in the first two projects. My model includes all significant forces: gravity, electrical forces due to curved sheath and interparticle interaction, and gas forces. The model does not agree with both the experiments. In the last project, I study the non-Gaussian statistics by analyzing data for microparticle motion from an experiment performed under microgranity conditions. Microparticle motion is studied in a very thin region of microparticles in a three dimensional dust cloud. The microparticle velocity distributions exhibit non-Gaussian characteristics.

It is said that our visual experience is a ‘Grand Illusion’. Our brains can only process a fraction of the total information available in the natural world, and yet our subjective impression of that world appears richly detailed and complete. The apparent disparity between our conscious experience of the visual landscape and the precision of our internal representation has suggested to some that our brains are equipped with specialized mechanisms that surmount the inherent limitations of our perceptual and cognitive systems. One proposed set of mechanisms, called summary statistics, processes information in a scene by representing the regularities that are often shared among groups of similar in terms of descriptive statistics. For example, snowflakes blowing in the wind may be represented in terms of their mean direction and speed. Prevailing views hold that summary statistics may underlie all aspects of our subjective visual experience, inasmuch as such representations are thought to form automatically across multiple visual fields, exhaustively summarizing all available visual features regardless of attention. We challenge this view by showing that summary statistics are mediated by limited-capacity processes and therefore cannot unfold independently across multiple areas of the visual field. We also show that summary statistics require attention and thus cannot account for our sense of visual completeness outside attended visual space. In light of this evidence, we suggest that the application of summary representations to daily perceptual life has been overstated for the past decade. Indeed, many observations interpreted in terms of summary statistics can be accounted for by alternative cognitive processes, such as visual working memory.

Abstract not available

abstract: This research explores tests for statistical suppression. Suppression is a statistical phenomenon whereby the magnitude of an effect becomes larger when another variable is added to the regression equation. From a causal perspective, suppression occurs when there is inconsistent mediation or negative confounding. Several different estimators for suppression are evaluated conceptually and in a statistical simulation study where we impose suppression and non-suppression conditions. For each estimator without an existing standard error formula, one was derived in order to conduct significance tests and build confidence intervals. Overall, two of the estimators were biased and had poor coverage, one worked well but had inflated type-I error rates when the population model was complete mediation. As a result of analyzing these three tests, a fourth was considered in the late stages of the project and showed promising results that address concerns of the other tests. When the tests were applied to real data, they gave similar results and were consistent. / Dissertation/Thesis / Masters Thesis Psychology 2020

Networks are quickly becoming one of the most common data types across diverse disciplines from the biological to the social sciences. Consequently, the study of networks as data objects is fundamental to developing statistical methodology for answering complex scientific questions. In this dissertation, we provide statistical solutions to three tasks related to multiple networks. We first consider the task of prediction given a collection of observed networks. In particular, we provide a Bayesian approach to performing classification, anomaly detection, and survival analysis with network inputs. Our methodology is based on encoding networks as pairwise differences in the kernel of a Gaussian process prior and we are motivated by the goal of predicting preterm delivery using individual microbiome networks. We next consider the task of exploring reaction space in high-throughput chemistry, where the inputs to a reaction are two or more molecules. Our goal is to create a workflow that facilitates quick, low-cost, and effective analysis of reactions. In order to operationalize this goal, we develop a statistical approach that breaks the analysis into several steps based on four unique challenges that we identify. Each of these challenges requires careful consideration in creating our analysis plan. For instance, to address the fact that reactions are run on multiwell plates, we formulate our proposal as a constrained optimization problem; then, we leverage the underlying structure by realizing a plate as a bipartite graph, which allows us to reformulate the problem as a maximal edge biclique problem. These solutions are necessary to optimally navigate a large reaction space given limited resources, which is critical in the application of reaction chemistry, for example, to drug discovery. The final task we consider is the recovery of a network given a sample of noisy unlabeled copies of the network. Toward this end, we make a connection between the noisy network literature and the correlated Erdős–Rényi graph model, which allows us to employ results from graph matching. Research on multiple unlabeled networks has otherwise been underdeveloped but is emerging in areas such as differential privacy and anonymized networks, as well as measurement error in network construction. / 2022-10-25T00:00:00Z

This work solving with the statistical inspection verification of big amounts of products imported to Czech Republic. Work it self is designed as general handbook and it will be possible to use it on other products then the model one. This work was elaborated with company which is importing screws for wood industry. We used common standards to define quality requirements of verificated products, and to design statistical inspection plans. The goal of this work is technical and economical evaluation of designed method, which was used on model product.