Related papers: Bayesian shape modelling of cross-sectional geolog…
The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…
Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and…
In this paper, we describe a novel shape classification method which is embedded in the Bayesian paradigm. We discuss the modelling and the resulting shape classification algorithm for two and three dimensional data shapes. We conclude by…
Spatial documentation is exponentially increasing given the availability of Big IoT Data, enabled by the devices miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence…
Probabilistic graphical models allow us to encode a large probability distribution as a composition of smaller ones. It is oftentimes the case that we are interested in incorporating in the model the idea that some of these smaller…
Models for distributions of shapes contained within images can be widely used in biomedical applications ranging from tumor tracking for targeted radiation therapy to classifying cells in a blood sample. Our focus is on hierarchical…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty…
Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
Spatial connectivity is an important consideration when modelling infectious disease data across a geographical region. Connectivity can arise for many reasons, including shared characteristics between regions, and human or vector movement.…
Normally we judge Topological shapes analytically but they hide significant amount of data in them about coordinate planes and ordered & unordered paris. In this article we will build our intuition and find those datas.
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…