Hawkes Processes With Stochastic Exogenous Effects for Continuous-Time Interaction Modelling

Continuous-time interaction data is usually generated under time-evolving environment. Hawkes processes (HP) are commonly used mechanisms for the analysis of such data. However, typical model implementations (such as e.g., stochastic block models) assume that the exogenous (background) interaction rate is constant, and so they are limited in their ability to adequately describe any complex time-evolution in the background rate of a process. In this paper, we introduce a stochastic exogenous rate Hawkes process (SE-HP) which is able to learn time variations in the exogenous rate. The model affiliates each node with a piecewise-constant membership distribution with an unknown number of changepoint locations, and allows these distributions to be related to the membership distributions of interacting nodes. The time-varying background rate function is derived through combinations of these membership functions. We introduce a stochastic gradient MCMC algorithm for efficient, scalable inference. The performance of the SE-HP is explored on real world, continuous-time interaction datasets, where we demonstrate that the SE-HP strongly outperforms comparable state-of-the-art methods.

Trends in methamphetamine use, markets and harms in Australia, 2003-2019

INTRODUCTION

To describe trends in methamphetamine use, markets and harms in Australia from 2003 to 2019.

METHODS

Data comprised patterns of use and price from sentinel samples of people who inject drugs and who use MDMA/other illicit stimulants and population-level amphetamine-related police seizures, arrests, hospitalisations, treatment episodes and deaths from approximately 2003 to 2019. Bayesian autoregressive time-series models were analysed for: no change; constant rate of change; and change over time differing in rate after one to three changepoints. Related indicators were analysed post hoc with identical changepoints.

RESULTS

The percentage of people who inject drugs reporting weekly use increased from 2010 to 2013 onwards, while use among samples of people who regularly use ecstasy and other illicit stimulants decreased. Seizures and arrests rose steeply from around 2009/10 to 2014/15 and subsequently plateaued. Price increased ($15.9 [95% credible interval, CrI $9.9, $28.9] per point of crystal per year) from around 2009 to 2011, plateauing and then declining from around 2017. Hospitalisation rates increased steeply from around 2009/10 until 2015/16, with a small subsequent decline. Treatment also increased (19.8 episodes [95% CrI 13.2, 27.6] with amphetamines as the principal drug of concern per 100 000 persons per year) from 2010/11 onwards. Deaths involving amphetamines increased (0.285 per 100 000 persons per year) from 2012 until 2016.

DISCUSSION AND CONCLUSIONS

These findings suggest that problematic methamphetamine use and harms escalated from 2010 to 2012 in Australia, with continued demand and a sustained market for methamphetamine.

Modeling total predation to avoid perverse outcomes from cat control in a data-poor island ecosystem

Data hungry, complex ecosystem models are often used to predict the consequences of threatened species management, including perverse outcomes. Unfortunately, this approach is impractical in many systems, which have insufficient data to parameterize ecosystem interactions or reliably calibrate or validate such models. Here we demonstrate a different approach, using a minimum realistic model to guide decisions in data- and resource-scarce systems. We illustrate our approach with a case-study in an invaded ecosystem from Christmas Island, Australia, where there are concerns that cat eradication to protect native species, including the red-tailed tropicbird, could release meso-predation by invasive rats. We use biophysical constraints (metabolic demand) and observable parameters (e.g. prey preferences) to assess the combined cat and rat abundances which would threaten the tropicbird population. We find that the population of tropicbirds cannot be sustained if predated by 1607 rats (95% credible interval (CI) [103, 5910]) in the absence of cats, or 21 cats (95% CI [2, 82]) in the absence of rats. For every cat removed from the island, the bird's net population growth rate improves, provided that the rats do not increase by more than 77 individuals (95% CI [30, 174]). Thus, in this context, one cat is equivalent to 30-174 rats. Our methods are especially useful for on-the-ground predator control in the absence of knowledge of predator-predator interactions, to assess whether 1) the current abundance of predators threatens the prey population of interest, 2) managing one predator species alone is sufficient to protect the prey species given potential release of another predator, and 3) control of multiple predator species is needed to meet the conservation goal. Our approach demonstrates how to use limited information for maximum value in data-poor systems, by shifting the focus from predicting future trajectories, to identifying conditions which threaten the conservation goal. This article is protected by copyright. All rights reserved.

Trends in cocaine use, markets and harms in Australia, 2003-2019

INTRODUCTION

This paper aims to describe cocaine use, markets and harms in Australia from 2003 to 2019.

METHODS

Outcome indicators comprised prevalence of use from triennial household surveys; patterns of use from annual surveys of sentinel samples who use stimulants; and cocaine-related seizures, arrests, hospitalisations, deaths and treatment episodes. Bayesian autoregressive time-series analyses were conducted to estimate trend over time: Model 1, no change; Model 2, constant rate of change; and Model 3, change over time differing in rate after one change point.

RESULTS

Past-year population prevalence of use increased over time. The percentage reporting recent use in sentinel samples increased by 6.1% (95% credible interval [CrI_95% ] 1.2%,16.9%; Model 3) per year from around 2017 (48%) until the end of the series (2019: 67%). There was a constant annual increase in number of seizures (count ratio: 1.1, CrI_95% 1.1,1.2) and arrests (1.2, CrI_95% 1.1,1.2), and percentage reporting cocaine as easy to obtain in the sentinel samples (percent increase 1.2%, CrI_95% 0.5%,1.8%; Model 2). Cocaine-related hospitalisation rate increased from 5.1 to 15.6 per 100 000 people from around 2011-2012 to 2017-2018: an annual increase of 1.3 per 100 000 people (CrI_95% 0.8,1.8; Model 3). While the death rate was low (0.23 cocaine-related deaths per 100 000 people in 2018; Model 2), treatment episodes increased from 3.2 to 5.9 per 100 000 people from around 2016-2017 to 2017-2018: an annual increase of 2.9 per 100 000 people (CrI_95% 1.6,3.7; Model 3).

DISCUSSION AND CONCLUSIONS

Cocaine use, availability and harm have increased, concentrated in recent years, and accompanied by increased treatment engagement.

Informing management decisions for ecological networks, using dynamic models calibrated to noisy time-series data

Well-intentioned environmental management can backfire, causing unforeseen damage. To avoid this, managers and ecologists seek accurate predictions of the ecosystem-wide impacts of interventions, given small and imprecise datasets, which is an incredibly difficult task. We generated and analysed thousands of ecosystem population time series to investigate whether fitted models can aid decision-makers to select interventions. Using these time-series data (sparse and noisy datasets drawn from deterministic Lotka-Volterra systems with two to nine species, of known network structure), dynamic model forecasts of whether a species' future population will be positively or negatively affected by rapid eradication of another species were correct > 70% of the time. Although 70% correct classifications is only slightly better than an uninformative prediction (50%), this classification accuracy can be feasibly improved by increasing monitoring accuracy and frequency. Our findings suggest that models may not need to produce well-constrained predictions before they can inform decisions that improve environmental outcomes.

Image Denoising Based on Nonlocal Bayesian Singular Value Thresholding and Stein's Unbiased Risk Estimator

Singular value thresholding (SVT)- or nuclear norm minimization (NNM)-based nonlocal image denoising methods often rely on the precise estimation of the noise variance. However, most existing methods either assume that the noise variance is known or require an extra step to estimate it. Under the iterative regularization framework, the error in the noise variance estimate propagates and accumulates with each iteration, ultimately degrading the overall denoising performance. In addition, the essence of these methods is still least squares estimation, which can cause a very high mean-squared error (MSE) and is inadequate for handling missing data or outliers. In order to address these deficiencies, we present a hybrid denoising model based on variational Bayesian inference and Stein's unbiased risk estimator (SURE), which consists of two complementary steps. In the first step, the variational Bayesian SVT performs a low-rank approximation of the nonlocal image patch matrix to simultaneously remove the noise and estimate the noise variance. In the second step, we modify the conventional SURE full-rank SVT and its divergence formulas for rank-reduced eigen-triplets to remove the residual artifacts. The proposed hybrid BSSVT method achieves better performance in recovering the true image compared with state-of-the-art methods.

Robust evaluation of performance monitoring options for ozone disinfection in water recycling using Bayesian analysis

Ozonation of wastewater has gained popularity because of its effectiveness in removing colour, UV absorbance, trace organic chemicals, and pathogens. Due to the rapid reaction of ozone with organic compounds, dissolved ozone is often not measurable and therefore, the common disinfection controlling parameter, concentration integrated over contact time (CT) cannot be obtained. In such cases, alternative parameters have been shown to be useful as surrogate measures for microbial removal including change in UV₂₅₄ absorbance (ΔUVA), change in total fluorescence (ΔTF), or O₃:TOC (or O₃:DOC). Although these measures have shown promise, a number of caveats remain. These include uncertainties in the associations between these measurements and microbial inactivation. Furthermore, previous use of seeded microorganisms with higher disinfection sensitivity compared to autochthonous microorganisms could lead to overestimation of appropriate log credits. In our study, secondary treated wastewater from a full-scale plant was ozonated in a bench-scale reactor using five increasing ozone doses. During the experiments, removal of four indigenous microbial indicators representing viruses, bacteria and protozoa were monitored concurrent with ΔUVA, ΔTF, O₃:DOC and PARAFAC derived components. Bayesian methods were used to fit linear regression models, and the uncertainty in the posterior predictive distributions and slopes provided a comparison between previously reported results and those reported here. Combined results indicated that all surrogate parameters were useful in predicting the removal of microorganisms, with a better fit to the models using ΔUVA, ΔTF in most cases. Average adjusted determination coefficients for fitted models were high (R²_adjusted>0.47). With ΔUVA, one unit decrease in LRV corresponded with a UVA mean reduction of 15-20% for coliforms, 59% for C. perfringens spores, and 11% for somatic coliphages. With ΔTF, a one unit decrease in LRV corresponded with a TF mean reduction of 18-23% for coliforms, 71% for C. perfringens spores, and 14% for somatic coliphages. Compared to previous studies also analysed, our results suggest that microbial reductions were more conservative for autochthonous than for seeded microorganisms. The findings of our study suggested that site-specific analyses should be conducted to generate models with lower uncertainty and that indigenous microorganisms are useful for the measurement of system performance even when censored observations are obtained.

Virus removal by ultrafiltration: Understanding long-term performance change by application of Bayesian analysis

Ultrafiltration is an effective barrier to waterborne pathogens including viruses. Challenge testing is commonly used to test the inherent reliability of such systems. Performance validation seeks to demonstrate the adequate reliability of the treatment system. Appropriate and rigorous data analysis is an essential aspect of validation testing. In this study we used Bayesian analysis to assess the performance of a full-scale ultrafiltration system which was validated and revalidated after five years of operation. A hierarchical Bayesian model was used to analyse a number of similar ultrafiltration membrane skids working in parallel during the two validation periods. This approach enhanced our ability to obtain accurate estimations of performance variability, especially when the sample size of some system skids was limited. This methodology enabled the quantitative estimation of uncertainty in the performance parameters and generation of predictive distributions incorporating those uncertainties. The results indicated that there was a decrease in the mean skid performance after five years of operation of approximately 1 log reduction value (LRV). Interestingly, variability in the LRV also reduced, with standard deviations from the revalidation data being decreased by a mean 0.37 LRV compared with the original validation data. The model was also useful in comparing the operating performance of the various parallel skids within the same year. Evidence of differences was obtained in 2015 for one of the membrane skids. A hierarchical Bayesian analysis of validation data provides robust estimations of performance and the incorporation of probabilistic analysis which is increasingly important for comprehensive quantitative risk assessment purposes.

Bayesian belief network modelling of chlorine disinfection for human pathogenic viruses in municipal wastewater

Chlorine disinfection of biologically treated wastewater is practiced in many locations prior to environmental discharge or beneficial reuse. The effectiveness of chlorine disinfection processes may be influenced by several factors, such as pH, temperature, ionic strength, organic carbon concentration, and suspended solids. We investigated the use of Bayesian multilayer perceptron (BMLP) models as efficient and practical tools for compiling and analysing free chlorine and monochloramine virus disinfection performance as a multivariate problem. Corresponding to their relative susceptibility, Adenovirus 2 was used to assess disinfection by monochloramine and Coxsackievirus B5 was used for free chlorine. A BMLP model was constructed to relate key disinfection conditions (CT, pH, turbidity) to observed Log Reduction Values (LRVs) for these viruses at constant temperature. The models proved to be valuable for incorporating uncertainty in the chlor(am)ination performance estimation and interpolating between operating conditions. Various types of queries could be performed with this model including the identification of target CT for a particular combination of LRV, pH and turbidity. Similarly, it was possible to derive achievable LRVs for combinations of CT, pH and turbidity. These queries yielded probability density functions for the target variable reflecting the uncertainty in the model parameters and variability of the input variables. The disinfection efficacy was greatly impacted by pH and to a lesser extent by turbidity for both types of disinfections. Non-linear relationships were observed between pH and target CT, and turbidity and target CT, with compound effects on target CT also evidenced. This work demonstrated that the use of BMLP models had considerable ability to improve the resolution and understanding of the multivariate relationships between operational parameters and disinfection outcomes for wastewater treatment.

Modelling pathogen log10 reduction values achieved by activated sludge treatment using naïve and semi naïve Bayes network models

Risk management for wastewater treatment and reuse have led to growing interest in understanding and optimising pathogen reduction during biological treatment processes. However, modelling pathogen reduction is often limited by poor characterization of the relationships between variables and incomplete knowledge of removal mechanisms. The aim of this paper was to assess the applicability of Bayesian belief network models to represent associations between pathogen reduction, and operating conditions and monitoring parameters and predict AS performance. Naïve Bayes and semi-naïve Bayes networks were constructed from an activated sludge dataset including operating and monitoring parameters, and removal efficiencies for two pathogens (native Giardia lamblia and seeded Cryptosporidium parvum) and five native microbial indicators (F-RNA bacteriophage, Clostridium perfringens, Escherichia coli, coliforms and enterococci). First we defined the Bayesian network structures for the two pathogen log10 reduction values (LRVs) class nodes discretized into two states (< and ≥ 1 LRV) using two different learning algorithms. Eight metrics, such as Prediction Accuracy (PA) and Area Under the receiver operating Curve (AUC), provided a comparison of model prediction performance, certainty and goodness of fit. This comparison was used to select the optimum models. The optimum Tree Augmented naïve models predicted removal efficiency with high AUC when all system parameters were used simultaneously (AUCs for C. parvum and G. lamblia LRVs of 0.95 and 0.87 respectively). However, metrics for individual system parameters showed only the C. parvum model was reliable. By contrast individual parameters for G. lamblia LRV prediction typically obtained low AUC scores (AUC < 0.81). Useful predictors for C. parvum LRV included solids retention time, turbidity and total coliform LRV. The methodology developed appears applicable for predicting pathogen removal efficiency in water treatment systems generally.

Modeling extreme risks in ecology

Extreme risks in ecology are typified by circumstances in which data are sporadic or unavailable, understanding is poor, and decisions are urgently needed. Expert judgments are pervasive and disagreements among experts are commonplace. We outline approaches to evaluating extreme risks in ecology that rely on stochastic simulation, with a particular focus on methods to evaluate the likelihood of extinction and quasi-extinction of threatened species, and the likelihood of establishment and spread of invasive pests. We evaluate the importance of assumptions in these assessments and the potential of some new approaches to account for these uncertainties, including hierarchical estimation procedures and generalized extreme value distributions. We conclude by examining the treatment of consequences in extreme risk analysis in ecology and how expert judgment may better be harnessed to evaluate extreme risks.

A model-based Bayesian estimation of the rate of evolution of VNTR loci in Mycobacterium tuberculosis

Variable numbers of tandem repeats (VNTR) typing is widely used for studying the bacterial cause of tuberculosis. Knowledge of the rate of mutation of VNTR loci facilitates the study of the evolution and epidemiology of Mycobacterium tuberculosis. Previous studies have applied population genetic models to estimate the mutation rate, leading to estimates varying widely from around to per locus per year. Resolving this issue using more detailed models and statistical methods would lead to improved inference in the molecular epidemiology of tuberculosis. Here, we use a model-based approach that incorporates two alternative forms of a stepwise mutation process for VNTR evolution within an epidemiological model of disease transmission. Using this model in a Bayesian framework we estimate the mutation rate of VNTR in M. tuberculosis from four published data sets of VNTR profiles from Albania, Iran, Morocco and Venezuela. In the first variant, the mutation rate increases linearly with respect to repeat numbers (linear model); in the second, the mutation rate is constant across repeat numbers (constant model). We find that under the constant model, the mean mutation rate per locus is (95% CI: ,)and under the linear model, the mean mutation rate per locus per repeat unit is (95% CI: ,). These new estimates represent a high rate of mutation at VNTR loci compared to previous estimates. To compare the two models we use posterior predictive checks to ascertain which of the two models is better able to reproduce the observed data. From this procedure we find that the linear model performs better than the constant model. The general framework we use allows the possibility of extending the analysis to more complex models in the future.

Genetically typing the bacterium responsible for tuberculosis is useful for understanding the evolutionary and epidemiological characteristics of the disease. Typing methods based on variable number tandem repeat (VNTR) loci are increasingly being used. These loci, which are composed of repeated units, mutate by increasing or decreasing in the number of these repeats. Knowledge of the mutation rate of molecular markers facilitates the epidemiological interpretation of the observed genetic variation in a sample of bacterial isolates. Few studies have examined the rate of mutation at these markers and estimates to date have varied considerably. To address this problem we develop a stochastic model of evolution of these markers and then estimate their mutation rate using approximate Bayesian computation. We examine two alternative forms of the mutation process. The observed data are from four published data sets of tuberculosis bacterial isolates sampled in Albania, Iran, Morocco and Venezuela. We find that these markers have fairly high rates of mutation compared with estimates from previous studies.

Bayesian analysis of animal movements related to factors at herd and between herd levels: Implications for disease spread modeling

A method to assess the influence of between herd distances, production types and herd sizes on patterns of between herd contacts is presented. It was applied on pig movement data from a central database of the Swedish Board of Agriculture. To determine the influence of these factors on the contact between holdings we used a Bayesian model and Markov chain Monte Carlo (MCMC) methods to estimate the posterior distribution of model parameters. The analysis showed that the contact pattern via animal movements is highly heterogeneous and influenced by all three factors, production type, herd size, and distance between holdings. Most production types showed a positive relationship between maximum capacity and the probability of both incoming and outgoing movements. In agreement with previous studies, holdings also differed in both the number of contacts as well as with what holding types contact occurred with. Also, the scale and shape of distance dependence in contact probability was shown to differ depending on the production types of holdings.To demonstrate how the methodology may be used for risk assessment, disease transmissions via animal movements were simulated with the model used for analysis of contacts, and parameterized by the analyzed posterior distribution. A Generalized Linear Model showed that herds with production types Sow pool center, Multiplying herd and Nucleus herd have higher risk of generating a large number of new infections. Multiplying herds are also expected to generate many long distance transmissions, while transmissions generated by Sow pool centers are confined to more local areas. We argue that the methodology presented may be a useful tool for improvement of risk assessment based on data found in central databases.

In defence of model-based inference in phylogeography

Recent papers have promoted the view that model-based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested Clade Phylogeographic Analysis (NCPA) offers the best approach in statistical phylogeography. In order to remove the confusion and misconceptions introduced by these papers, we justify and explain the reasoning behind model-based inference. We argue that ABC is a statistically valid approach, alongside other computational statistical techniques that have been successfully used to infer parameters and compare models in population genetics. We also examine the NCPA method and highlight numerous deficiencies, either when used with single or multiple loci. We further show that the ages of clades are carelessly used to infer ages of demographic events, that these ages are estimated under a simple model of panmixia and population stationarity but are then used under different and unspecified models to test hypotheses, a usage the invalidates these testing procedures. We conclude by encouraging researchers to study and use model-based inference in population genetics.

High affinity extremes in combinatorial libraries and repertoires

By generating a large diversity of molecules, the immune system selects antibodies that bind antigens. Sharing the same approach, combinatorial biotechnologies use a large library of compounds to screen for molecules of high affinity to a given target. Understanding the properties of the best binders in the pool aids the design of the library. In particular, how does the maximum affinity increase with the size of the library or repertoire? We consider two alternative models to examine the properties of extreme affinities. In the first model, affinities are distributed lognormally, while in the second, affinities are determined by the number of matches to a target sequence. The second model more explicitly models nucleic acids (DNA or RNA) and proteins such as antibodies. Using extreme value theory we show that the logarithm of the mean of the highest affinity in a combinatorial library grows linearly with the square root of the log of the library size. When there is an upper bound to affinity, this "absolute maximum" is also approached approximately linearly with root log library size, reaching the upper limit abruptly. The design of libraries may benefit from considering how this plateau is reached as the library size is increased.

Sequential Monte Carlo without likelihoods

Recent new methods in Bayesian simulation have provided ways of evaluating posterior distributions in the presence of analytically or computationally intractable likelihood functions. Despite representing a substantial methodological advance, existing methods based on rejection sampling or Markov chain Monte Carlo can be highly inefficient and accordingly require far more iterations than may be practical to implement. Here we propose a sequential Monte Carlo sampler that convincingly overcomes these inefficiencies. We demonstrate its implementation through an epidemiological study of the transmission rate of tuberculosis.

Using approximate Bayesian computation to estimate tuberculosis transmission parameters from genotype data

Tuberculosis can be studied at the population level by genotyping strains of Mycobacterium tuberculosis isolated from patients. We use an approximate Bayesian computational method in combination with a stochastic model of tuberculosis transmission and mutation of a molecular marker to estimate the net transmission rate, the doubling time, and the reproductive value of the pathogen. This method is applied to a published data set from San Francisco of tuberculosis genotypes based on the marker IS6110. The mutation rate of this marker has previously been studied, and we use those estimates to form a prior distribution of mutation rates in the inference procedure. The posterior point estimates of the key parameters of interest for these data are as follows: net transmission rate, 0.69/year [95% credibility interval (C.I.) 0.38, 1.08]; doubling time, 1.08 years (95% C.I. 0.64, 1.82); and reproductive value 3.4 (95% C.I. 1.4, 79.7). These figures suggest a rapidly spreading epidemic, consistent with observations of the resurgence of tuberculosis in the United States in the 1980s and 1990s.

Bayesian Point Estimation of Quantitative Trait Loci

In this article, we consider the problem of the estimation of quantitative trait loci (QTL), those chromosomal regions at which genetic information affecting some quantitative trait is encoded. Generally the number of such encoding sites is unknown, and associations between neutral molecular marker genotypes and observed trait phenotypes are sought to locate them. We consider a Bayesian model for simple experimental designs, and discuss the existing approaches to inference for this problem. In particular, we focus on locating positions of the best candidate markers segregating for the trait, a situation which is of primary interest in comparative mapping. We introduce a loss function for estimating both the number of QTL and their location, and we illustrate its application via simulated and real data.