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1. Phenological patterns in ecology: Problems using circular statistics and solutions based on simulations

   https://doi.org/10.1111/2041-210X.14316  

   Willig, Michael R.; Rojas‐Sandoval, Julissa; Presley, Steven J. (April 2024, Methods in Ecology and Evolution)

   Abstract Quantification of phenological patterns (e.g. migration, hibernation or reproduction) should involve statistical assessments of non‐uniform temporal patterns. Circular statistics (e.g. Rayleigh test or Hermans‐Rasson test) provide useful approaches for doing so based on the number of individuals that exhibit particular activities during a number of time intervals.This study used monthly reproductive activity as an example to illustrate problems in applying circular statistics to data when marginal totals characterize experimental designs (e.g. the number of reproductively active individuals per time interval depends on sampling effort or sampling success). We illustrate the nature of this problem by crafting four exemplar data sets and developing a bootstrapping simulation procedure to overcome complications that arise from the existence of marginal totals. In addition, we apply circular statistics and our bootstrapping simulation to empirical data on the reproductive phenology of six species of Neotropical bats from the Amazon.Because sampling effort or success can differ among time intervals, circular statistics can produce misleading results of two types: those suggesting uniform phenologies when empirical patterns are markedly modal, and those suggesting non‐uniform phenologies when empirical patterns are uniform. The bootstrapping simulation overcomes these limitations: the exemplar phenology in which the percentage of reproductively active individuals is modal is appropriately identified as non‐uniform based on the bootstrapping approach, and the exemplar phenology in which the percentage of reproductively active individuals is invariant is appropriately identified as uniform based on the bootstrapping approach. The reproductive phenology of each of the six empirical examples is non‐uniform based on the bootstrapping approach, and this is true for bats species with unimodal peaks or bimodal peaks.In addition to problems with marginal totals, a review of analyses of phenological patterns in ecology identified two other frequent issues in the application of circular statistics: sampling bias and pseudoreplication. Each of these issues and potential solutions are also discussed. By providing source code for the execution of the Rayleigh test and Hermans‐Rasson test, along with the code for the bootstrapping simulation, we offer a useful tool for assessing non‐random phenologies when marginal totals characterize experimental designs. 

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2. Exact sampling of spanning trees via fast-forwarded random walks

   https://doi.org/10.1093/biomet/asaf031  

   Tam, Edric; Dunson, David B; Duan, Leo L (January 2025, Biometrika)

   Summary Tree graphs are used routinely in statistics. When estimating a Bayesian model with a tree component, sampling the posterior remains a core difficulty. Existing Markov chain Monte Carlo methods tend to rely on local moves, often leading to poor mixing. A promising approach is to instead directly sample spanning trees on an auxiliary graph. Current spanning tree samplers, such as the celebrated Aldous–Broder algorithm, rely predominantly on simulating random walks that are required to visit all the nodes of the graph. Such algorithms are prone to getting stuck in certain subgraphs. We formalize this phenomenon using the bottlenecks in the random walk’s transition probability matrix. We then propose a novel fast-forwarded cover algorithm that can break free from bottlenecks. The core idea is a marginalization argument that leads to a closed-form expression that allows for fast-forwarding to the event of visiting a new node. Unlike many existing approximation algorithms, our algorithm yields exact samples. We demonstrate the enhanced efficiency of the fast-forwarded cover algorithm, and illustrate its application in fitting a Bayesian dendrogram model on a Massachusetts crime and community dataset. 

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3. Easy Variational Inference for Categorical Models via an Independent Binary Approximation

   Michael T Wojnowicz, Shuchin Aeron (January 2022, The 39th International Conference on Machine Learning,)

   We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. GLMs have been difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using conjugate auxiliary variable methods. We define a new class of GLMs for categorical data called categorical-from-binary (CB) models. Each CB model has a likelihood that is bounded by the product of binary likelihoods, suggesting a natural posterior approximation. This approximation makes inference straightforward and fast; using well-known auxiliary variables for probit or logistic regression, the product of binary models admits conjugate closed-form variational inference that is embarrassingly parallel across categories and invariant to category ordering. Moreover, an independent binary model simultaneously approximates multiple CB models. Bayesian model averaging over these can improve the quality of the approximation for any given dataset. We show that our approach scales to thousands of categories, outperforming posterior estimation competitors like Automatic Differentiation Variational Inference (ADVI) and No U-Turn Sampling (NUTS) in the time required to achieve fixed prediction quality. 

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4. Efficient NUFFT backpropagation for stochastic sampling optimization

   Wang, G.; Noll, D.C.; Fessler, J.A. (January 2021, Proceeedings International Society of Magnetic Resonance in Medicine)

   Optimization-based k-space sampling pattern design often involves the Jacobian matrix of non-uniform fast Fourier transform (NUFFT) operations. Previous works relying on auto-differentiation can be time-consuming and less accurate. This work proposes an approximation method using the relationship between exact non-uniform DFT (NDFT) and NUFFT, demonstrating improved results for the sampling pattern optimization problem. 

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5. Improving the Performance of Ambulatory Gait Training System for Rehabilitation by Mechatronics and Design Simulation

   https://doi.org/10.1115/IMECE2021-71487  

   Shetty, Devdas; Thompson, Lara; Sanchez, Pablo; Campana, Claudio (November 2021, ASME 2021 International Mechanical Engineering Congress & Exposition IMECE 2021)

   Abstract This paper addresses the design procedures and simulation results from the mechatronic model of the rehabilitation equipment, which can improve the functionality and precision of the ambulatory gait training system. The distinguishing feature of mechatronic systems is the achievement of system functionality through intensive integration. The paper demonstrates how the mechatronic design modeling has helped improve the design and performance of the new rehabilitation equipment built by the authors and is known as Navigaitor. The Navigaitor is designed to aid the patients who need to improve their balance and walk. The mechatronics aspects allow a better understanding of the dynamic behavior and interactions of the components. Depending on the severity of the patient’s injury (stroke survivor, Parkinson, etc.), the oscillatory motion can range from uniform to non-uniform. The motion needs to be converted from the oscillatory sinusoidal motion of the patient into linear motion that the system can follow the patient with minimum lag and maximum stability. The data acquired during the training stage showing a different rate of recovery and response assists the system designers and thereby provides input to fine-tune the system and upgrade the control requirements. 

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