Estimation of multivariate normal covariance and precision matrices in a star-shape model with missing data

AbstractIn this paper, we study the problem of estimating the covariance matrix Σ and the precision matrix Ω (the inverse of the covariance matrix) in a star-shape model with missing data. By considering a type of Cholesky decomposition of the precision matrix Ω=Ψ′Ψ, where Ψ is a lower triangular matrix with positive diagonal elements, we get the MLEs of the covariance matrix and precision matrix and prove that both of them are biased. Based on the MLEs, unbiased estimators of the covariance matrix and precision matrix are obtained. A special group G, which is a subgroup of the group consisting all lower triangular matrices, is introduced. By choosing the left invariant Haar measure on G as a prior, we obtain the closed forms of the best equivariant estimates of Ω under any of the Stein loss, the entropy loss, and the symmetric loss. Consequently, the MLE of the precision matrix (covariance matrix) is inadmissible under any of the above three loss functions. Some simulation results are given for illustration

Causation and effectuation in the context of product development process in a large-sized established company

Effectuation represents entrepreneurial way of thinking and it is commonly applied to new ventures. Causation, as the inverse logic to effectuation, represents traditional way of thinking, and it is commonly used among large existing organizations. Recent research on effectuation shows that causation and effectuation are two relative logics, and effectuation can be extended to the existing organizations. The purpose of this research is to study relationship between causation and effectuation and to reveal how causation and effectuation influence each other during the product development process of Stage-Gate in the context of a large existing organization

MONITORING AND ANALYSIS OF CANTILEVER JACKING OF HIGH SLOPE PRESTRESSED CONCRETE CONTINUOUS BOX GIRDER

Due to the rapid development of the transportation industry and economy, an increasing number of bridges have been unable to meet the demands of traffic. Demolishing and rebuilding bridges can lengthen the construction period, waste a lot of resources, and increase construction costs. Based on the lifting renovation project of the old Harbin Dongsan Ring Expressway viaduct, this paper combines finite element analysis and on-site testing to analyze the construction process. The bridge alignment, elevation, and deviations were monitored during the construction process, and a correction system was developed to address such issues. Structural analysis was conducted to evaluate the internal forces when uneven jacking occurred. The construction process described in this paper can effectively solve the jacking problems of urban continuous bridges with large tonnage, high slopes, and heights. The successful implementation of the jacking retrofitting project has verified the reliability of the measures taken

Symbol-LLM: Leverage Language Models for Symbolic System in Visual Human Activity Reasoning

Human reasoning can be understood as a cooperation between the intuitive, associative "System-1" and the deliberative, logical "System-2". For existing System-1-like methods in visual activity understanding, it is crucial to integrate System-2 processing to improve explainability, generalization, and data efficiency. One possible path of activity reasoning is building a symbolic system composed of symbols and rules, where one rule connects multiple symbols, implying human knowledge and reasoning abilities. Previous methods have made progress, but are defective with limited symbols from handcraft and limited rules from visual-based annotations, failing to cover the complex patterns of activities and lacking compositional generalization. To overcome the defects, we propose a new symbolic system with two ideal important properties: broad-coverage symbols and rational rules. Collecting massive human knowledge via manual annotations is expensive to instantiate this symbolic system. Instead, we leverage the recent advancement of LLMs (Large Language Models) as an approximation of the two ideal properties, i.e., Symbols from Large Language Models (Symbol-LLM). Then, given an image, visual contents from the images are extracted and checked as symbols and activity semantics are reasoned out based on rules via fuzzy logic calculation. Our method shows superiority in extensive activity understanding tasks. Code and data are available at https://mvig-rhos.com/symbol_llm.Comment: Accepted by NeurIPS 202

Bayesian spatial data analysis with application to the Missouri Ozark forest ecosystem project

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file viewed on (May 1, 2007)Vita.Thesis (Ph.D.) University of Missouri-Columbia 2006.The first part studies the problem of estimating the covariance matrix in a star-shaped model with missing data. By introducing a class of priors based on a type of Cholesky decomposition of the precision matrix, we then obtain the closed forms of Bayesian estimators under several invariant loss functions. In the second part, we first propose an efficient algorithm for Bayesian spatial analysis via the generalized Ratio-of-Uniforms method, which generates independent samples from the resulting posterior distribution. We then present a Bayesian spatial methodology for analyzing the site index data from the Missouri Ozark Forest Ecosystem Project (MOFEP). Our results show that aspect class and soil depth are both significant while land type association is less significant. In the third part, we present a new spatial model that takes into account the special data structure and treats a cluster of measurements as repeated measurements in one location. The model is applied to the analysis of the total vegetation coverage data in the MOFEP. Our results show that the soil depth is an important factor while the aspect class is less important. We also show that the strong spatial effect exists in the data discussed and the measurements in four quadrats of a subplot are not strongly correlated but are not independent.Includes bibliographical reference