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1. A conditional density estimation partition model using logistic Gaussian processes

   https://doi.org/10.1093/biomet/asz064  

   Payne, R D; Guha, N; Ding, Y; Mallick, B K (December 2019, Biometrika)

   Summary Conditional density estimation seeks to model the distribution of a response variable conditional on covariates. We propose a Bayesian partition model using logistic Gaussian processes to perform conditional density estimation. The partition takes the form of a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The methodology models data in which the density changes sharply throughout the covariate space, and can be used to determine where important changes in the density occur. The Markov chain Monte Carlo algorithm involves a Laplace approximation on the latent variables of the logistic Gaussian process model which marginalizes the parameters in each partition element, allowing an efficient search of the approximate posterior distribution of the tessellation. The method is consistent when the density is piecewise constant in the covariate space or when the density is Lipschitz continuous with respect to the covariates. In simulation and application to wind turbine data, the model successfully estimates the partition structure and conditional distribution. 

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2. spOccupancy: An R package for single‐species, multi‐species, and integrated spatial occupancy models

   https://doi.org/10.1111/2041-210X.13897  

   Doser, Jeffrey W.; Finley, Andrew O.; Kéry, Marc; Zipkin, Elise F. (May 2022, Methods in Ecology and Evolution)

   Abstract Occupancy modelling is a common approach to assess species distribution patterns, while explicitly accounting for false absences in detection–nondetection data. Numerous extensions of the basic single‐species occupancy model exist to model multiple species, spatial autocorrelation and to integrate multiple data types. However, development of specialized and computationally efficient software to incorporate such extensions, especially for large datasets, is scarce or absent.We introduce thespOccupancy Rpackage designed to fit single‐species and multi‐species spatially explicit occupancy models. We fit all models within a Bayesian framework using Pólya‐Gamma data augmentation, which results in fast and efficient inference.spOccupancyprovides functionality for data integration of multiple single‐species detection–nondetection datasets via a joint likelihood framework. The package leverages Nearest Neighbour Gaussian Processes to account for spatial autocorrelation, which enables spatially explicit occupancy modelling for potentially massive datasets (e.g. 1,000s–100,000s of sites).spOccupancyprovides user‐friendly functions for data simulation, model fitting, model validation (by posterior predictive checks), model comparison (using information criteria and k‐fold cross‐validation) and out‐of‐sample prediction. We illustrate the package's functionality via a vignette, simulated data analysis and two bird case studies.ThespOccupancypackage provides a user‐friendly platform to fit a variety of single and multi‐species occupancy models, making it straightforward to address detection biases and spatial autocorrelation in species distribution models even for large datasets. 

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3. Predictive Runtime Monitoring for Mobile Robots using Logic-Based Bayesian Intent Inference

   https://doi.org/10.1109/ICRA48506.2021.9561193  

   Yoon, Hansol; Sankaranarayanan, Sriram (May 2021, 2021 IEEE International Conference on Robotics and Automation (ICRA))

   We propose a predictive runtime monitoring framework that forecasts the distribution of future positions of mobile robots in order to detect and avoid impending property violations such as collisions with obstacles or other agents. Our approach uses a restricted class of temporal logic formulas to represent the likely intentions of the agents along with a combination of temporal logic-based optimal cost path planning and Bayesian inference to compute the probability of these intents given the current trajectory of the robot. First, we construct a large but finite hypothesis space of possible intents represented as temporal logic formulas whose atomic propositions are derived from a detailed map of the robot’s workspace. Next, our approach uses real-time observations of the robot’s position to update a distribution over temporal logic formulae that represent its likely intent. This is performed by using a combination of optimal cost path planning and a Boltzmann noisy rationality model. In this manner, we construct a Bayesian approach to evaluating the posterior probability of various hypotheses given the observed states and actions of the robot. Finally, we predict the future position of the robot by drawing posterior predictive samples using a Monte-Carlo method. We evaluate our framework using two different trajectory datasets that contain multiple scenarios implementing various tasks. The results show that our method can predict future positions precisely and efficiently, so that the computation time for generating a prediction is a tiny fraction of the overall time horizon. 

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4. A Bayesian modified Ising model for identifying spatially variable genes from spatial transcriptomics data

   https://doi.org/10.1002/sim.9530  

   Jiang, Xi; Xiao, Guanghua; Li, Qiwei (July 2022, Statistics in Medicine)

   A recent technology breakthrough in spatial molecular profiling (SMP) has enabled the comprehensive molecular characterizations of single cells while preserving spatial information. It provides new opportunities to delineate how cells from different origins form tissues with distinctive structures and functions. One immediate question in SMP data analysis is to identify genes whose expressions exhibit spatially correlated patterns, called spatially variable (SV) genes. Most current methods to identify SV genes are built upon the geostatistical model with Gaussian process to capture the spatial patterns. However, the Gaussian process models rely on ad hoc kernels that could limit the models' ability to identify complex spatial patterns. In order to overcome this challenge and capture more types of spatial patterns, we introduce a Bayesian approach to identify SV genes via a modified Ising model. The key idea is to use the energy interaction parameter of the Ising model to characterize spatial expression patterns. We use auxiliary variable Markov chain Monte Carlo algorithms to sample from the posterior distribution with an intractable normalizing constant in the model. Simulation studies using both simulated and synthetic data showed that the energy‐based modeling approach led to higher accuracy in detecting SV genes than those kernel‐based methods. When applied to two real spatial transcriptomics (ST) datasets, the proposed method discovered novel spatial patterns that shed light on the biological mechanisms. In summary, the proposed method presents a new perspective for analyzing ST data. 

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5. Of traits and trees: probabilistic distances under continuous trait models for dissecting the interplay among phylogeny, model, and data

   https://doi.org/10.1093/sysbio/syab009  

   Adams, Richard H; Blackmon, Heath; DeGiorgio, Michael (February 2021, Systematic Biology)

   null (Ed.)

   Abstract Stochastic models of character trait evolution have become a cornerstone of evolutionary biology in an array of contexts. While probabilistic models have been used extensively for statistical inference, they have largely been ignored for the purpose of measuring distances between phylogeny-aware models. Recent contributions to the problem of phylogenetic distance computation have highlighted the importance of explicitly considering evolutionary model parameters and their impacts on molecular sequence data when quantifying dissimilarity between trees. By comparing two phylogenies in terms of their induced probability distributions that are functions of many model parameters, these distances can be more informative than traditional approaches that rely strictly on differences in topology or branch lengths alone. Currently, however, these approaches are designed for comparing models of nucleotide substitution and gene tree distributions, and thus, are unable to address other classes of traits and associated models that may be of interest to evolutionary biologists. Here we expand the principles of probabilistic phylogenetic distances to compute tree distances under models of continuous trait evolution along a phylogeny. By explicitly considering both the degree of relatedness among species and the evolutionary processes that collectively give rise to character traits, these distances provide a foundation for comparing models and their predictions, and for quantifying the impacts of assuming one phylogenetic background over another while studying the evolution of a particular trait. We demonstrate the properties of these approaches using theory, simulations, and several empirical datasets that highlight potential uses of probabilistic distances in many scenarios. We also introduce an open-source R package named PRDATR for easy application by the scientific community for computing phylogenetic distances under models of character trait evolution. 

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