Background The spread of SARS-CoV-2 has been studied at unprecedented levels worldwide. In jurisdictions where molecular analysis was performed on large scales, the emergence and competition of numerous SARS-CoV-2lineages have been observed in near real-time. Lineage identification, traditionally performed from clinical samples, can also be determined by sampling wastewater from sewersheds serving populations of interest. Variants of concern (VOCs) and SARS-CoV-2 lineages associated with increased transmissibility and/or severity are of particular interest. Method Here, we consider clinical and wastewater data sources to assess the emergence and spread of VOCs in Canada retrospectively. Results We show that, overall, wastewater-based VOC identification provides similar insights to the surveillance based on clinical samples. Based on clinical data, we observed synchrony in VOC introduction as well as similar emergence speeds across most Canadian provinces despite the large geographical size of the country and differences in provincial public health measures. Conclusion In particular, it took approximately four months for VOC Alpha and Delta to contribute to half of the incidence. In contrast, VOC Omicron achieved the same contribution in less than one month. This study provides significant benchmarks to enhance planning for future VOCs, and to some extent for future pandemics caused by other pathogens, by quantifying the rate of SARS-CoV-2 VOCs invasion in Canada.

Wastewater-based surveillance (WBS) is an important epidemiological and public health tool for tracking pathogens across the scale of a building, neighbourhood, city, or region. WBS gained widespread adoption globally during the SARS-CoV-2 pandemic for estimating community infection levels by qPCR. Sequencing pathogen genes or genomes from wastewater adds information about pathogen genetic diversity, which can be used to identify viral lineages (including variants of concern) that are circulating in a local population. Capturing the genetic diversity by WBS sequencing is not trivial, as wastewater samples often contain a diverse mixture of viral lineages with real mutations and sequencing errors, which must be deconvoluted computationally from short sequencing reads. In this study we assess nine different computational tools that have recently been developed to address this challenge. We simulated 100 wastewater sequence samples consisting of SARS-CoV-2 BA.1, BA.2, and Delta lineages, in various mixtures, as well as a Delta–Omicron recombinant and a synthetic ‘novel’ lineage. Most tools performed well in identifying the true lineages present and estimating their relative abundances and were generally robust to variation in sequencing depth and read length. While many tools identified lineages present down to 1 % frequency, results were more reliable above a 5 % threshold. The presence of an unknown synthetic lineage, which represents an unclassified SARS-CoV-2 lineage, increases the error in relative abundance estimates of other lineages, but the magnitude of this effect was small for most tools. The tools also varied in how they labelled novel synthetic lineages and recombinants. While our simulated dataset represents just one of many possible use cases for these methods, we hope it helps users understand potential sources of error or bias in wastewater sequencing analysis and to appreciate the commonalities and differences across methods.

Genetic sequencing is subject to many different types of errors, but most analyses treat the resultant sequences as if they are known without error. Next generation sequencing methods rely on significantly larger numbers of reads than previous sequencing methods in exchange for a loss of accuracy in each individual read. Still, the coverage of such machines is imperfect and leaves uncertainty in many of the base calls. In this work, we demonstrate that the uncertainty in sequencing techniques will affect downstream analysis and propose a straightforward method to propagate the uncertainty. Our method (which we have dubbed Sequence Uncertainty Propagation, or SUP) uses a probabilistic matrix representation of individual sequences which incorporates base quality scores as a measure of uncertainty that naturally lead to resampling and replication as a framework for uncertainty propagation. With the matrix representation, resampling possible base calls according to quality scores provides a bootstrap- or prior distribution-like first step towards genetic analysis. Analyses based on these re-sampled sequences will include a more complete evaluation of the error involved in such analyses. We demonstrate our resampling method on SARS-CoV-2 data. The resampling procedures add a linear computational cost to the analyses, but the large impact on the variance in downstream estimates makes it clear that ignoring this uncertainty may lead to overly confident conclusions. We show that SARS-CoV-2 lineage designations via Pangolin are much less certain than the bootstrap support reported by Pangolin would imply and the clock rate estimates for SARS-CoV-2 are much more variable than reported.

Research on the occurrence and the final size of wildland fires typically models these two events as two separate processes. In this work, we develop and apply a compound process framework for jointly modelling the frequency and the severity of wildland fires. Separate modelling structures for the frequency and the size of fires are linked through a shared random effect. This allows us to fit an appropriate model for frequency and an appropriate model for size of fires while still having a method to estimate the direction and strength of the relationship (e.g., whether days with more fires are associated with days with large fires). The joint estimation of this random effect shares information between the models without assuming a causal structure. We explore spatial and temporal autocorrelation of the random effects to identify additional variation not explained by the inclusion of weather related covariates. The dependence between frequency and size of lightning-caused fires is found to be negative, indicating that an increase in the number of expected fires is associated with a decrease in the expected size of those fires, possibly due to the rainy conditions necessary for an increase in lightning. Person-caused fires were found to be positively dependent, possibly due to dry weather increasing human activity as well as the amount of dry few. For a test for independence, we perform a power study and find that simply checking whether zero is in the credible interval of the posterior of the linking parameter is as powerful as more complicated tests.

Many spatial statistics applications result in a collection of spatial estimates, especially if a different (but possibly correlated) estimate is produced for a sequence of time epochs. For a small collection of epochs, the connections or trends between estimates and the prominent or common features can be found via inspection of the spatial estimates. As the number of spatial estimates grows, this task becomes much more difficult. We present a method of summarizing a sequence of estimates using an image recognition technique called Non-Negative Matrix Factorization which results in a meaningful decomposition of the source images into basis functions and coefficients. This visualization technique allows for investigation of trends over time as well as common spatial features of the estimates without needing to fit a temporal model or use pre-specified spatial regions. We apply this technique to a sequence of models that jointly model the spatial location of wildland fires with the total burn area of each of the fires. We discuss the extensions of the visualization technique to the joint modelling framework and are able to draw new insights about the connection between the location and size of the fires.

Genetic sequencing is subject to many different types of errors, but most analyses treat the resultant sequences as if they are known without error. Next generation sequencing methods rely on significantly larger numbers of reads than previous sequencing methods in exchange for a loss of accuracy in each individual read. Still, the coverage of such machines is imperfect and leaves uncertainty in many of the base calls. On top of this machine-level uncertainty, there is uncertainty induced by human error, such as errors in data entry or incorrect parameter settings. In this work, we demonstrate that the uncertainty in sequencing techniques will affect downstream analysis and propose a straightforward method to propagate the uncertainty. Our method uses a probabilistic matrix representation of individual sequences which incorporates base quality scores as a measure of uncertainty that naturally lead to resampling and replication as a framework for uncertainty propagation. With the matrix representation, resampling possible base calls according to quality scores provides a bootstrap- or prior distribution-like first step towards genetic analysis. Analyses based on these re-sampled sequences will include a more complete evaluation of the error involved in such analyses. We demonstrate our resampling method on SARS-CoV-2 data. The resampling procedures adds a linear computational cost to the analyses, but the large impact on the variance in downstream estimates makes it clear that ignoring this uncertainty may lead to overly confident conclusions. We show that SARS-CoV-2 lineage designations via Pangolin are much less certain than the bootstrap support reported by Pangolin would imply and the clock rate estimates for SARS-CoV-2 are much more variable than reported.

Abstract Spatial point processes have been successfully used to model the relative efficiency of shot locations for each player in professional basketball games. Those analyses were possible because each player makes enough baskets to reliably fit a point process model. Goals in hockey are rare enough that a point process cannot be fit to each player’s goal locations, so novel techniques are needed to obtain measures of shot efficiency for each player. A Log-Gaussian Cox Process (LGCP) is used to model all shot locations, including goals, of each NHL player who took at least 500 shots during the 2011–2018 seasons. Each player’s LGCP surface is treated as an image and these images are then used in an unsupervised statistical learning algorithm that decomposes the pictures into a linear combination of spatial basis functions. The coefficients of these basis functions are shown to be a very useful tool to compare players. To incorporate goals, the locations of all shots that resulted in a goal are treated as a “perfect player” and used in the same algorithm (goals are further split into perfect forwards, perfect centres and perfect defence). These perfect players are compared to other players as a measure of shot efficiency. This analysis provides a map of common shooting locations, identifies regions with the most goals relative to the number of shots and demonstrates how each player’s shot location differs from scoring locations.

Spatial point processes have been successfully used to model the relative efficiency of shot locations for each player in professional basketball games. These analyses are possible because each player makes enough baskets to reliably fit a point process model. Goals in hockey are rare enough that a point process cannot be fit to each player’s goal locations, so we must employ novel techniques to obtain measures of shot efficiency for each player.

Aerial wildland fire fighters have a unique challenge. They are able to fill their tank with water via a nearby body of water, drop this water on a fire, then return to repeat this process. For a given fire, the replications of the fills and drops are multivariate time series measured in space, and this data structure allows us to compare replications over space and time. We use control chart methodologies to determine which time series were unlike the others, then examine the data from both a univariate and a multivariate viewpoint to determine potential causes.

ABSTRACT In this paper, we extend Choi and Hall's [Data sharpening as a prelude to density estimation. Biometrika. 1999;86(4):941–947] data sharpening algorithm for kernel density estimation to interval-censored data. Data sharpening has several advantages, including bias and mean integrated squared error (MISE) reduction as well as increased robustness to bandwidth misspecification. Several interval metrics are explored for use with the kernel function in the data sharpening transformation. A simulation study based on randomly generated data is conducted to assess and compare the performance of each interval metric. It is found that the bias is reduced by sharpening, often with little effect on the variance, thus maintaining or reducing overall MISE. Applications involving time to onset of HIV and running distances subject to measurement error are used for illustration.