Related papers: Teaching Design of Experiments using Hasse diagram…
With the advent of modern statistical software, complex experimental designs are now routinely employed in many areas of research. Failing to correctly identify the structure of the experimental design can lead to incorrect model selection…
Statisticians recommend the Design and Analysis of Experiments (DAE) for evidence-based research but often use tables to present their own simulation studies. Could DAE do better? We outline how DAE methods can be used to plan and analyze…
The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
The design of structural & functional materials for specialized applications is being fueled by rapid advancements in materials synthesis, characterization, manufacturing, with sophisticated computational materials modeling frameworks that…
The undergraduate curriculum in statistics and data science is undergoing changes to accommodate new methods, newly interested students, and the changing role of statistics in society. Because of this, it is more important than ever that…
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.…
We present a simple mathematical framework and API for parallel mesh and data distribution, load balancing, and overlap generation. It relies on viewing the mesh as a Hasse diagram, abstracting away information such as cell shape,…
Using a statistical model-based data generation, we develop an experimental setup for the evaluation of neural networks (NNs). The setup helps to benchmark a set of NNs vis-a-vis minimum-mean-square-error (MMSE) performance bounds. This…
One of the possible objectives when designing experiments is to build or formulate a model for predicting future observations. When the primary objective is prediction, some typical approaches in the planning phase are to use…
Design-based simulations - procedures that hold realized outcomes fixed and generate variation by resampling treatment assignment or shocks - are widely used in both methodological and applied work to assess inference procedures. This paper…
Causal diagrams are logic and graphical tools that depict assumptions about presumed causal relations. Such diagrams have proven effective in tackling a variety of problems in social sciences and epidemiology research yet remain foreign to…
Simulation studies are computer experiments that involve creating data by pseudorandom sampling. The key strength of simulation studies is the ability to understand the behaviour of statistical methods because some 'truth' (usually some…
The unification of statistical (data-driven) and symbolic (knowledge-driven) methods is widely recognised as one of the key challenges of modern AI. Recent years have seen large number of publications on such hybrid neuro-symbolic AI…
Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…
While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Design of experiments (DOE) is playing an essential role in learning and improving a variety of objects and processes. The article discusses the application of unsupervised machine learning to support the pragmatic designs of complex…
The causal assumptions, the study design and the data are the elements required for scientific inference in empirical research. The research is adequately communicated only if all of these elements and their relations are described…