Related papers: A Useful Algebraic System of Statistical Models
In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
Biological systems are often modelled at different levels of abstraction depending on the particular aims/resources of a study. Such different models often provide qualitatively concordant predictions over specific parametrisations, but it…
This paper presents an automated tool called Morphy for datamorphic testing. It classifies software test artefacts into test entities and test morphisms, which are mappings on testing entities. In addition to datamorphisms, metamorphisms…
Simulations are valuable tools for empirically evaluating the properties of statistical methods and are primarily employed in methodological research to draw general conclusions about methods. In addition, they can often be useful to…
The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes…
Although simulation represents a major advance in the understanding of problems in complex systems, the field currently does not has standards in place that would guide the reporting of the data underlying each model, the process for model…
Simulations play important and diverse roles in statistical workflows, for example, in model specification, checking, validation, and even directly in model inference. Over the past decades, the application areas and overall potential of…
Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation…
Diffusion Models are probabilistic models that create realistic samples by simulating the diffusion process, gradually adding and removing noise from data. These models have gained popularity in domains such as image processing, speech…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data.…
Computer simulations of amphiphilic systems are reviewed. Research areas cover a wide range of length and time scales, and a whole hierarchy of models and methods has been developed to address them all. They range from atomistically…
Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…
Metamodels, or the regression analysis of Monte Carlo simulation results, provide a powerful tool to summarize simulation findings. However, an underutilized approach is the multilevel metamodel (MLMM) that accounts for the dependent data…
Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Probabilistic programming is perfectly suited to reliable and transparent data science, as it allows the user to specify their models in a high-level language without worrying about the complexities of how to fit the models. Static analysis…