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1. GPIRT: A Gaussian Process Model for Item Response Theory

   Duck-Mayr, JBrandon; Garnett, Roman; Montgomery, Jacob (April 2020, Proceedings of Machine Learning Research)

   null (Ed.)

   The goal of item response theoretic (IRT) models is to provide estimates of latent traits from binary observed indicators and at the same time to learn the item response funcitons (IRFs) that map from latent trait to observed response. However, in many cases observed behavior can deviate significantly from the parametric assumptions of traditional IRT models. Nonparametric IRT (NIRT) models overcome these challenges by relaxing assumptions about the form of the IRFs, but standard tools are unable to simultaneously estimate flexible IRFs and recover ability estimates for respondents. We propose a Bayesian nonparametric model that solves this problem by placing Gaussian process priors on the latent functions defining the IRFs. This allows us to simultaneously relax assumptions about the shape of the IRFs while preserving the ability to estimate latent traits. This in turn allows us to easily extend the model to further tasks such as active learning. GPIRT therefore provides a simple and intuitive solution to several longstanding problems in the IRT literature. 

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2. Computational Strategies and Estimation Performance With Bayesian Semiparametric Item Response Theory Models

   https://doi.org/10.3102/10769986221136105  

   Paganin, Sally; Paciorek, Christopher_J; Wehrhahn, Claudia; Rodríguez, Abel; Rabe-Hesketh, Sophia; de_Valpine, Perry (December 2022, Journal of Educational and Behavioral Statistics)

   Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures (DPMs) offer a more flexible representation of the unknown distribution of the latent trait. However, the use of such models in the IRT literature has been extremely limited, in good part because of the lack of comprehensive studies and accessible software tools. This article provides guidance for practitioners on semiparametric IRT models and their implementation. In particular, we rely on NIMBLE, a flexible software system for hierarchical models that enables the use of DPMs. We highlight efficient sampling strategies for model estimation and compare inferential results under parametric and semiparametric models. 

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3. A Bayesian non-parametric mixed-effects model of microbial growth curves

   https://doi.org/10.1371/journal.pcbi.1008366  

   Tonner, Peter D.; Darnell, Cynthia L.; Bushell, Francesca M.; Lund, Peter A.; Schmid, Amy K.; Schmidler, Scott C. (October 2020, PLOS Computational Biology)

   Papin, Jason A. (Ed.)

   Substantive changes in gene expression, metabolism, and the proteome are manifested in overall changes in microbial population growth. Quantifying how microbes grow is therefore fundamental to areas such as genetics, bioengineering, and food safety. Traditional parametric growth curve models capture the population growth behavior through a set of summarizing parameters. However, estimation of these parameters from data is confounded by random effects such as experimental variability, batch effects or differences in experimental material. A systematic statistical method to identify and correct for such confounding effects in population growth data is not currently available. Further, our previous work has demonstrated that parametric models are insufficient to explain and predict microbial response under non-standard growth conditions. Here we develop a hierarchical Bayesian non-parametric model of population growth that identifies the latent growth behavior and response to perturbation, while simultaneously correcting for random effects in the data. This model enables more accurate estimates of the biological effect of interest, while better accounting for the uncertainty due to technical variation. Additionally, modeling hierarchical variation provides estimates of the relative impact of various confounding effects on measured population growth. 

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4. Identifying latent behavioural states in animal movement with M4, a nonparametric Bayesian method

   https://doi.org/10.1111/2041-210X.13745  

   Cullen, Joshua A.; Poli, Caroline L.; Fletcher, Jr., Robert J.; Valle, Denis (October 2021, Methods in Ecology and Evolution)

   Abstract Understanding animal movement often relies upon telemetry and biologging devices. These data are frequently used to estimate latent behavioural states to help understand why animals move across the landscape. While there are a variety of methods that make behavioural inferences from biotelemetry data, some features of these methods (e.g. analysis of a single data stream, use of parametric distributions) may limit their generality to reliably discriminate among behavioural states.To address some of the limitations of existing behavioural state estimation models, we introduce a nonparametric Bayesian framework called the mixed‐membership method for movement (M4), which is available within the open‐sourcebayesmoveR package. This framework can analyse multiple data streams (e.g. step length, turning angle, acceleration) without relying on parametric distributions, which may capture complex behaviours more successfully than current methods. We tested our Bayesian framework using simulated trajectories and compared model performance against two segmentation methods (behavioural change point analysis (BCPA) and segclust2d), one machine learning method [expectation‐maximization binary clustering (EMbC)] and one type of state‐space model [hidden Markov model (HMM)]. We also illustrated this Bayesian framework using movements of juvenile snail kitesRostrhamus sociabilisin Florida, USA.The Bayesian framework estimated breakpoints more accurately than the other segmentation methods for tracks of different lengths. Likewise, the Bayesian framework provided more accurate estimates of behaviour than the other state estimation methods when simulations were generated from less frequently considered distributions (e.g. truncated normal, beta, uniform). Three behavioural states were estimated from snail kite movements, which were labelled as ‘encamped’, ‘area‐restricted search’ and ‘transit’. Changes in these behaviours over time were associated with known dispersal events from the nest site, as well as movements to and from possible breeding locations.Our nonparametric Bayesian framework estimated behavioural states with comparable or superior accuracy compared to the other methods when step lengths and turning angles of simulations were generated from less frequently considered distributions. Since the most appropriate parametric distributions may not be obvious a priori, methods (such as M4) that are agnostic to the underlying distributions can provide powerful alternatives to address questions in movement ecology. 

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5. Identifying direct and indirect associations among traits by merging phylogenetic comparative methods and structural equation models

   https://doi.org/10.1111/2041-210X.14076  

   Thorson, James T.; Maureaud, Aurore A.; Frelat, Romain; Mérigot, Bastien; Bigman, Jennifer S.; Friedman, Sarah T.; Palomares, Maria Lourdes D.; Pinsky, Malin L.; Price, Samantha A.; Wainwright, Peter (March 2023, Methods in Ecology and Evolution)

   Abstract Traits underlie organismal responses to their environment and are essential to predict community responses to environmental conditions under global change. Species differ in life‐history traits, morphometrics, diet type, reproductive characteristics and habitat utilization.Trait associations are widely analysed using phylogenetic comparative methods (PCM) to account for correlations among related species. Similarly, traits are measured for some but not all species, and missing continuous traits (e.g. growth rate) can be imputed using ‘phylogenetic trait imputation’ (PTI), based on evolutionary relatedness and trait covariance. However, PTI has not been available for categorical traits, and estimating covariance among traits without ecological constraints risks inferring implausible evolutionary mechanisms.Here, we extend previous PCM and PTI methods by (1) specifying covariance among traits as a structural equation model (SEM), and (2) incorporating associations among both continuous and categorical traits. Fitting a SEM replaces the covariance among traits with a set of linear path coefficients specifying potential evolutionary mechanisms. Estimated parameters then represent regression slopes (i.e. the average change in trait Y given an exogenous change in trait X) that can be used to calculate both direct effects (X impacts Y) and indirect effects (X impacts Z and Z impacts Y).We demonstrate phylogenetic structural‐equation mixed‐trait imputation using 33 variables representing life history, reproductive, morphological, and behavioural traits for all >32,000 described fishes worldwide. SEM coefficients suggest that one degree Celsius increase in habitat is associated with an average 3.5% increase in natural mortality (including a 1.4% indirect impact that acts via temperature effects on the growth coefficient), and an average 3.0% decrease in fecundity (via indirect impacts on maximum age and length). Cross‐validation indicates that the model explains 54%–89% of variance for withheld measurements of continuous traits and has an area under the receiver‐operator‐characteristics curve of 0.86–0.99 for categorical traits.We use imputed traits to classify all fishes into life‐history types, and confirm a phylogenetic signal in three dominant life‐history strategies in fishes. PTI using phylogenetic SEMs ensures that estimated parameters are interpretable as regression slopes, such that the inferred evolutionary relationships can be compared with long‐term evolutionary and rearing experiments. 

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