Making Recursive Bayesian Inference Accessible

Walking Trajectory Estimation Using Multi-Sensor Fusion and a Probabilistic Step Model

This paper presents a framework for accurately and efficiently estimating a walking human's trajectory using a computationally inexpensive non-Gaussian recursive Bayesian estimator. The proposed framework fuses global and inertial measurements with predictions from a kinematically driven step model to provide robustness in localization. A maximum a posteriori-type filter is trained on typical human kinematic parameters and updated based on live measurements. Local step size estimates are generated from inertial measurement units using the zero-velocity update (ZUPT) algorithm, while global measurements come from a wearable GPS. After each fusion event, a gradient ascent optimizer efficiently locates the highest likelihood of the individual's location which then triggers the next estimator iteration.The proposed estimator was compared to a state-of-the-art particle filter in several Monte Carlo simulation scenarios, and the original framework was found to be comparable in accuracy and more efficient at higher resolutions. It is anticipated that the methods proposed in this work could be more useful in general real-time estimation (beyond just personal navigation) than the traditional particle filter, especially if the state is many-dimensional. Applications of this research include but are not limited to: in natura biomechanics measurement, human safety in manual fieldwork environments, and human/robot teaming.

Patient-Preference Diagnostics: Adapting Stated-Preference Methods to Inform Effective Shared Decision Making

BACKGROUND

While clinical practice guidelines underscore the need to incorporate patient preferences in clinical decision making, incorporating meaningful assessment of patient preferences in clinical encounters is challenging. Structured approaches that combine quantitative patient preferences and clinical evidence could facilitate effective patient-provider communication and more patient-centric health care decisions. Adaptive conjoint or stated-preference approaches can identify individual preference parameters, but they can require a relatively large number of choice questions or simplifying assumptions about the error with which preferences are elicited.

METHOD

We propose an approach to efficiently diagnose preferences of patients for outcomes of treatment alternatives by leveraging prior information on patient preferences to generate adaptive choice questions to identify a patient's proximity to known preference phenotypes. This information can be used for measuring sensitivity and specificity, much like any other diagnostic procedure. We simulated responses with varying levels of choice errors for hypothetical patients with specific preference profiles to measure sensitivity and specificity of a 2-question preference diagnostic.

RESULTS

We identified 4 classes representing distinct preference profiles for patients who participated in a previous first-time anterior shoulder dislocation (FTASD) survey. Posterior probabilities of class membership at the end of a 2-question sequence ranged from 87% to 89%. We found that specificity and sensitivity of the 2-question sequences were robust to respondent errors. The questions appeared to have better specificity than sensitivity.

CONCLUSIONS

Our results suggest that this approach could help diagnose patient preferences for treatments for a condition such as FTASD with acceptable precision using as few as 2 choice questions. Such preference-diagnostic tools could be used to improve and document alignment of treatment choices and patient preferences.

HIGHLIGHTS

Approaches that combine patient preferences and clinical evidence can facilitate effective patient-provider communication and more patient-centric healthcare decisions. However, diagnosing individual-level preferences is challenging, and no formal diagnostic tools exist.We propose a structured approach to efficiently diagnose patient preferences based on prior information on the distribution of patient preferences in a population.We generated a 2-question test of preferences for the outcomes associated with the treatment of first-time anterior shoulder dislocation.The diagnosis of preferences can help physicians discuss relevant aspects of the treatment options and proactively address patient concerns during the clinical encounter.

An integrated path for spatial capture-recapture and animal movement modeling

Ecologists and conservation biologists increasingly rely on spatial capture-recapture (SCR) and movement modeling to study animal populations. Historically, SCR has focused on population-level processes (e.g., vital rates, abundance, density, and distribution), whereas animal movement modeling has focused on the behavior of individuals (e.g., activity budgets, resource selection, migration). Even though animal movement is clearly a driver of population-level patterns and dynamics, technical and conceptual developments to date have not forged a firm link between the two fields. Instead, movement modeling has typically focused on the individual level without providing a coherent scaling from individual- to population-level processes, whereas SCR has typically focused on the population level while greatly simplifying the movement processes that give rise to the observations underlying these models. In our view, the integration of SCR and animal movement modeling has tremendous potential for allowing ecologists to scale up from individuals to populations and advancing the types of inferences that can be made at the intersection of population, movement, and landscape ecology. Properly accounting for complex animal movement processes can also potentially reduce bias in estimators of population-level parameters, thereby improving inferences that are critical for species conservation and management. This introductory article to the Special Feature reviews recent advances in SCR and animal movement modeling, establishes a common notation, highlights potential advantages of linking individual-level (Lagrangian) movements to population-level (Eulerian) processes, and outlines a general conceptual framework for the integration of movement and SCR models. We then identify important avenues for future research, including key challenges and potential pitfalls in the developments and applications that lie ahead.

Monitoring partially marked populations using camera and telemetry data

Long-term monitoring is an important component of effective wildlife conservation. However, many methods for estimating density are too costly or difficult to implement over large spatial and temporal extents. Recently developed spatial mark-resight (SMR) models are increasingly being applied as a cost-effective method to estimate density when data include detections of both marked and unmarked individuals. We developed a generalized SMR model that can accommodate long-term camera data and auxiliary telemetry data for improved spatiotemporal inference in monitoring efforts. The model can be applied in two stages, with detection parameters estimated in the first stage using telemetry data and camera detections of instrumented individuals. Density is estimated in the second stage using camera data, with all individuals treated as unmarked. Serial correlation in detection and density parameters is accounted for using time-series models. The two-stage approach reduces computational demands and facilitates the application to large data sets from long-term monitoring initiatives. We applied the model to 3 years (2015-2017) of white-tailed deer (Odocoileus virginianus) data collected in three study areas of the Big Cypress Basin, Florida, USA. In total, 59 females marked with ear tags and fitted with GPS-telemetry collars were detected along with unmarked females on 180 remote cameras. Most of the temporal variation in density was driven by seasonal fluctuations, but one study area exhibited a slight population decline during the monitoring period. Modern technologies such as camera traps provide novel possibilities for long-term monitoring, but the resulting massive data sets, which are subject to unique sources of observation error, have posed analytical challenges. The two-stage spatial mark-resight framework provides a solution with lower computational demands than joint SMR models, allowing for easier implementation in practice. In addition, after detection parameters have been estimated, the model may be used to estimate density even if no synchronous auxiliary information on marked individuals is available, which is often the case in long-term monitoring.

Interoperability of statistical models in pandemic preparedness: principles and reality

We present interoperability as a guiding framework for statistical modelling to assist policy makers asking multiple questions using diverse datasets in the face of an evolving pandemic response. Interoperability provides an important set of principles for future pandemic preparedness, through the joint design and deployment of adaptable systems of statistical models for disease surveillance using probabilistic reasoning. We illustrate this through case studies for inferring and characterising spatial-temporal prevalence and reproduction numbers of SARS-CoV-2 infections in England.

A numerically stable algorithm for integrating Bayesian models using Markov melding

When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the prior for this quantity can be implicit, and its prior density must be estimated. We show that error in this density estimate makes the two-stage Markov chain Monte Carlo sampler employed by Markov melding unstable and unreliable. We propose a robust two-stage algorithm that estimates the required prior marginal self-density ratios using weighted samples, dramatically improving accuracy in the tails of the distribution. The stabilised version of the algorithm is pragmatic and provides reliable inference. We demonstrate our approach using an evidence synthesis for inferring HIV prevalence, and an evidence synthesis of A/H1N1 influenza.

Individual heterogeneity influences the effects of translocation on urban dispersal of an invasive reptile

BACKGROUND

Invasive reptiles pose a serious threat to global biodiversity, but early detection of individuals in an incipient population is often hindered by their cryptic nature, sporadic movements, and variation among individuals. Little is known about the mechanisms that affect the movement of these species, which limits our understanding of their dispersal. Our aim was to determine whether translocation or small-scale landscape features affect movement patterns of brown treesnakes (Boiga irregularis), a destructive invasive predator on the island of Guam.

METHODS

We conducted a field experiment to compare the movements of resident (control) snakes to those of snakes translocated from forests and urban areas into new urban habitats. We developed a Bayesian hierarchical model to analyze snake movement mechanisms and account for attributes unique to invasive reptiles by incorporating multiple behavioral states and individual heterogeneity in movement parameters.

RESULTS

We did not observe strong differences in mechanistic movement parameters (turning angle or step length) among experimental treatment groups. We found some evidence that translocated snakes from both forests and urban areas made longer movements than resident snakes, but variation among individuals within treatment groups weakened this effect. Snakes translocated from forests moved more frequently from pavement than those translocated from urban areas. Snakes translocated from urban areas moved less frequently from buildings than resident snakes. Resident snakes had high individual heterogeneity in movement probability.

CONCLUSIONS

Our approach to modeling movement improved our understanding of invasive reptile dispersal by allowing us to examine the mechanisms that influence their movement. We also demonstrated the importance of accounting for individual heterogeneity in population-level analyses, especially when management goals involve eradication of an invasive species.

Combining chains of Bayesian models with Markov melding

A challenge for practitioners of Bayesian inference is specifying a model that incorporates multiple relevant, heterogeneous data sets. It may be easier to instead specify distinct submodels for each source of data, then join the submodels together. We consider chains of submodels, where submodels directly relate to their neighbours via common quantities which may be parameters or deterministic functions thereof. We propose chained Markov melding, an extension of Markov melding, a generic method to combine chains of submodels into a joint model. One challenge we address is appropriately capturing the prior dependence between common quantities within a submodel, whilst also reconciling differences in priors for the same common quantity between two adjacent submodels. Estimating the posterior of the resulting overall joint model is also challenging, so we describe a sampler that uses the chain structure to incorporate information contained in the submodels in multiple stages, possibly in parallel. We demonstrate our methodology using two examples. The first example considers an ecological integrated population model, where multiple data sets are required to accurately estimate population immigration and reproduction rates. We also consider a joint longitudinal and time-to-event model with uncertain, submodel-derived event times. Chained Markov melding is a conceptually appealing approach to integrating submodels in these settings.

A continued learning approach for model-informed precision dosing: updating models in clinical practice

Model-informed precision dosing (MIPD) is a quantitative dosing framework that combines prior knowledge on the drug-disease-patient system with patient data from therapeutic drug/biomarker monitoring (TDM) to support individualized dosing in ongoing treatment. Structural models and prior parameter distributions used in MIPD approaches typically build on prior clinical trials that involve only a limited number of patients selected according to some exclusion/inclusion criteria. Compared to the prior clinical trial population, the patient population in clinical practice can be expected to include also altered behavior and/or increased interindividual variability, the extent of which, however, is typically unknown. Here, we address the question of how to adapt and refine models on the level of the model parameters to better reflect this real-world diversity. We propose an approach for continued learning across patients during MIPD using a sequential hierarchical Bayesian framework. The approach builds on two stages to separate the update of the individual patient parameters from updating the population parameters. Consequently, it enables continued learning across hospitals or study centers, since only summary patient data (on the level of model parameters) need to be shared, but no individual TDM data. We illustrate this continued learning approach with neutrophil-guided dosing of paclitaxel. The present study constitutes an important step towards building confidence in MIPD and eventually establishing MIPD increasingly in everyday therapeutic use.

Recursive Bayesian computation facilitates adaptive optimal design in ecological studies

Optimal design procedures provide a framework to leverage the learning generated by ecological models to flexibly and efficiently deploy future monitoring efforts. At the same time, Bayesian hierarchical models have become widespread in ecology and offer a rich set of tools for ecological learning and inference. However, coupling these methods with an optimal design framework can become computationally intractable. Recursive Bayesian computation offers a way to substantially reduce this computational burden, making optimal design accessible for modern Bayesian ecological models. We demonstrate the application of so-called prior-proposal recursive Bayes to optimal design using a simulated data binary regression and the real-world example of monitoring and modeling sea otters in Glacier Bay, Alaska. These examples highlight the computational gains offered by recursive Bayesian methods and the tighter fusion of monitoring and science that those computational gains enable.

Variance Propagation for Density Surface Models

Spatially explicit estimates of population density, together with appropriate estimates of uncertainty, are required in many management contexts. Density surface models (DSMs) are a two-stage approach for estimating spatially varying density from distance sampling data. First, detection probabilities—perhaps depending on covariates—are estimated based on details of individual encounters; next, local densities are estimated using a GAM, by fitting local encounter rates to location and/or spatially varying covariates while allowing for the estimated detectabilities. One criticism of DSMs has been that uncertainty from the two stages is not usually propagated correctly into the final variance estimates. We show how to reformulate a DSM so that the uncertainty in detection probability from the distance sampling stage (regardless of its complexity) is captured as an extra random effect in the GAM stage. In effect, we refit an approximation to the detection function model at the same time as fitting the spatial model. This allows straightforward computation of the overall variance via exactly the same software already needed to fit the GAM. A further extension allows for spatial variation in group size, which can be an important covariate for detectability as well as directly affecting abundance. We illustrate these models using point transect survey data of Island Scrub-Jays on Santa Cruz Island, CA, and harbour porpoise from the SCANS-II line transect survey of European waters. Supplementary materials accompanying this paper appear on-line.

Statistical Implementations of Agent-Based Demographic Models

A variety of demographic statistical models exist for studying population dynamics when individuals can be tracked over time. In cases where data are missing due to imperfect detection of individuals, the associated measurement error can be accommodated under certain study designs (e.g. those that involve multiple surveys or replication). However, the interaction of the measurement error and the underlying dynamic process can complicate the implementation of statistical agent-based models (ABMs) for population demography. In a Bayesian setting, traditional computational algorithms for fitting hierarchical demographic models can be prohibitively cumbersome to construct. Thus, we discuss a variety of approaches for fitting statistical ABMs to data and demonstrate how to use multi-stage recursive Bayesian computing and statistical emulators to fit models in such a way that alleviates the need to have analytical knowledge of the ABM likelihood. Using two examples, a demographic model for survival and a compartment model for COVID-19, we illustrate statistical procedures for implementing ABMs. The approaches we describe are intuitive and accessible for practitioners and can be parallelised easily for additional computational efficiency.

Accumulating evidence in ecology: Once is not enough

Many published studies in ecological science are viewed as stand-alone investigations that purport to provide new insights into how ecological systems behave based on single analyses. But it is rare for results of single studies to provide definitive results, as evidenced in current discussions of the "reproducibility crisis" in science. The key step in science is the comparison of hypothesis-based predictions with observations, where the predictions are typically generated by hypothesis-specific models. Repeating this step allows us to gain confidence in the predictive ability of a model, and its corresponding hypothesis, and thus to accumulate evidence and eventually knowledge. This accumulation may occur via an ad hoc approach, via meta-analyses, or via a more systematic approach based on the anticipated evolution of an information state. We argue the merits of this latter approach, provide an example, and discuss implications for designing sequences of studies focused on a particular question. We conclude by discussing current data collection programs that are preadapted to use this approach and argue that expanded use would increase the rate of learning in ecology, as well as our confidence in what is learned.