Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response

A fundamental issue when predicting structural response by using mathematical models is how to treat both modeling and excitation uncertainty. A general framework for this is presented which uses probability as a multi-valued conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The fundamental probability models that represent the structure’s uncertain behavior are specified by the choice of a stochastic system model class: a set of input-output probability models for the structure and a prior probability distribution over this set that quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic structural model by stochastic embedding utilizing Jaynes’ Principle of Maximum Information Entropy. Robust predictive analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if structural response data is available, by its posterior probability from Bayes’ Theorem for the model class. Additional robustness to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates weighted by the prior or posterior probability of the model class, the latter being computed from Bayes’ Theorem. This higherlevel application of Bayes’ Theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more complex model classes that extract more information from the data. Robust predictive analyses involve integrals over highdimensional spaces that usually must be evaluated numerically. Published applications have used Laplace's method of asymptotic approximation or Markov Chain Monte Carlo algorithms

Maximal information component analysis: a novel non-linear network analysis method.

BackgroundNetwork construction and analysis algorithms provide scientists with the ability to sift through high-throughput biological outputs, such as transcription microarrays, for small groups of genes (modules) that are relevant for further research. Most of these algorithms ignore the important role of non-linear interactions in the data, and the ability for genes to operate in multiple functional groups at once, despite clear evidence for both of these phenomena in observed biological systems.ResultsWe have created a novel co-expression network analysis algorithm that incorporates both of these principles by combining the information-theoretic association measure of the maximal information coefficient (MIC) with an Interaction Component Model. We evaluate the performance of this approach on two datasets collected from a large panel of mice, one from macrophages and the other from liver by comparing the two measures based on a measure of module entropy, Gene Ontology (GO) enrichment, and scale-free topology (SFT) fit. Our algorithm outperforms a widely used co-expression analysis method, weighted gene co-expression network analysis (WGCNA), in the macrophage data, while returning comparable results in the liver dataset when using these criteria. We demonstrate that the macrophage data has more non-linear interactions than the liver dataset, which may explain the increased performance of our method, termed Maximal Information Component Analysis (MICA) in that case.ConclusionsIn making our network algorithm more accurately reflect known biological principles, we are able to generate modules with improved relevance, particularly in networks with confounding factors such as gene by environment interactions

Enhancement of dronogram aid to visual interpretation of target objects via intuitionistic fuzzy hesitant sets

In this paper, we address the hesitant information in enhancement task often caused by differences in image contrast. Enhancement approaches generally use certain filters which generate artifacts or are unable to recover all the objects details in images. Typically, the contrast of an image quantifies a unique ratio between the amounts of black and white through a single pixel. However, contrast is better represented by a group of pix- els. We have proposed a novel image enhancement scheme based on intuitionistic hesi- tant fuzzy sets (IHFSs) for drone images (dronogram) to facilitate better interpretations of target objects. First, a given dronogram is divided into foreground and background areas based on an estimated threshold from which the proposed model measures the amount of black/white intensity levels. Next, we fuzzify both of them and determine the hesitant score indicated by the distance between the two areas for each point in the fuzzy plane. Finally, a hyperbolic operator is adopted for each membership grade to improve the pho- tographic quality leading to enhanced results via defuzzification. The proposed method is tested on a large drone image database. Results demonstrate better contrast enhancement, improved visual quality, and better recognition compared to the state-of-the-art methods.Web of Science500866