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Motivated by an application about interhospital connections, we propose a modelling approach for data referred to a temporal network. The approach may be seen as an extension of the one recently proposed in Bianchi et al. (2020) and, in turn, of the popular p1 and p2 models by Holland and Leinhardt (1981) and van Duijn et al. (2004), on which the latter is built. The proposed extension consists in the introduction of covariates and in the adoption of a hierarchical Bayesian inferential approach that shows advantages in the specific application. For Bayesian inference we rely on a Markov chain Monte Carlo algorithm that produces samples from the posterior distribution of the model parameters. The application is based on original data on patient referral relations among 127 hospitals serving a large regional community of patients in Italy from 2014 to 2018. Results indicate that interhospital collaborative behaviours are primarily local and that collaborative attitudes vary at different time occasions of the considered period and in accordance with the level of competition faced by hospital organisations.

The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures of two competing densities, the null and the alternative distributions. We investigate the use of weighted densities and, in particular, non-local densities as working alternative distributions, to enforce separation from the null and thus refine the screening procedure. We show how these weighted alternatives improve various operating characteristics, such as the Bayesian False Discovery rate, of the resulting tests for a fixed mixture proportion with respect to a local, unweighted likelihood approach. Parametric and nonparametric model specifications are proposed, along with efficient samplers for posterior inference. By means of a simulation study, we exhibit how our model compares with both well-established and state-of-the-art alternatives in terms of various operating characteristics. Finally, to illustrate the versatility of our method, we conduct three differential expression analyses with publicly-available datasets from genomic studies of heterogeneous nature.

When effective vaccines are available, vaccination programs are typically one of the best defences against the spread of an infectious disease. Unfortunately, vaccination rates may be suboptimal for a prolonged duration as a result of slow uptake of vaccines by the public. Key factors driving slow vaccination uptake can be a complex interaction of vaccine roll-out policies and logistics, and vaccine hesitancy behaviours potentially caused by an inflated sense of risk in adverse reactions in some populations or community complacency in communities that have not yet experienced a large outbreak. In the recent COVID-19 pandemic, public health responses around the world began to include vaccination programs from late 2020 to early 2021 with an aim of relaxing non-pharmaceutical interventions such as lockdowns and travel restrictions. For many jurisdictions there have been challenges in getting vaccination rates high enough to enable the relaxation of restrictions based on non-pharmaceutical interventions. A key concern during this time was vaccine hestitancy behaviours potentially caused by vaccine safety concerns fuelled by misinformation and community complacency in jurisdictions that had seen very low COVID-19 case numbers throughout 2020, such as Australia and New Zealand. We develop a novel stochastic epidemiological model of COVID-19 transmission that incorporates changes in population behaviour relating to responses based on non-pharmaceutical interventions and community vaccine uptake as functions of the reported COVID-19 cases, deaths, and vaccination rates. Through a simulation study, we develop a Bayesian analysis approach to demonstrate that different factors inhibiting the uptake of vaccines by the population can be isolated despite key model parameters being subject to substantial uncertainty. In particular, we are able to identify the presence of vaccine hesitancy in a population using reported case, death and vaccination count data alone. Furthermore, our approach provides insight as to whether the dominant concerns driving hesitancy are related to vaccine safety or complacency. While our simulation study is inspired by the COVID-19 pandemic, our tools and techniques are general and could be enable vaccination programs of various infectious diseases to be adapted rapidly in response to community behaviours moving forward into the future.

Approximate Bayesian computation (ABC) is a simulation-based likelihood-free method applicable to both model selection and parameter estimation. ABC parameter estimation requires the ability to forward simulate datasets from a candidate model, but because the sizes of the observed and simulated datasets usually need to match, this can be computationally expensive. Additionally, since ABC inference is based on comparisons of summary statistics computed on the observed and simulated data, using computationally expensive summary statistics can lead to further losses in efficiency. ABC has recently been applied to the family of mechanistic network models, an area that has traditionally lacked tools for inference and model choice. Mechanistic models of network growth repeatedly add nodes to a network until it reaches the size of the observed network, which may be of the order of millions of nodes. With ABC, this process can quickly become computationally prohibitive due to the resource intensive nature of network simulations and evaluation of summary statistics. We propose two methodological developments to enable the use of ABC for inference in models for large growing networks. First, to save time needed for forward simulating model realizations, we propose a procedure to extrapolate (via both least squares and Gaussian processes) summary statistics from small to large networks. Second, to reduce computation time for evaluating summary statistics, we use sample-based rather than census-based summary statistics. We show that the ABC posterior obtained through this approach, which adds two additional layers of approximation to the standard ABC, is similar to a classic ABC posterior. Although we deal with growing network models, both extrapolated summaries and sampled summaries are expected to be relevant in other ABC settings where the data are generated incrementally., Comment: 28 pages, 16 figures

Dynamic queueing networks (DQN) model queueing systems where demand varies strongly with time, such as airport terminals. With rapidly rising global air passenger traffic placing increasing pressure on airport terminals, efficient allocation of resources is more important than ever. Parameter inference and quantification of uncertainty are key challenges for developing decision support tools. The DQN likelihood function is, in general, intractable and current approaches to simulation make likelihood-free parameter inference methods, such as approximate Bayesian computation (ABC), infeasible since simulating from these models is computationally expensive. By leveraging a recent advance in computationally efficient queueing simulation, we develop the first parameter inference approach for DQNs. We demonstrate our approach with data of passenger flows in a real airport terminal, and we show that our model accurately recreates the behaviour of the system and is useful for decision support. Special care must be taken in developing the distance for ABC since any useful output must vary with time. We use maximum mean discrepancy, a metric on probability measures, as the distance function for ABC. Prediction intervals of performance measures for decision support tools are easily constructed using draws from posterior samples, which we demonstrate with a scenario of a delayed flight.

This paper addresses the risk of fraud in credit card transactions by developing a probabilistic model for the quickest detection of illegitimate purchases. Using optimal stopping theory, the goal is to determine the moment, known as disorder or fraud time, at which the continuously monitored process of a consumer’s transactions exhibits a disorder due to fraud, in order to return the best trade-off between two sources of cost: on the one hand, the disorder time should be detected as soon as possible to counteract illegal activities and minimize the loss that banks, merchants and consumers suffer; on the other hand, the frequency of false alarms should be minimized to avoid generating adverse effects for cardholders and to limit the operational and process costs for the card issuers. The proposed approach allows us to score consumers’ transactions and to determine, in a rigorous, personalized and optimal manner, the threshold with which scores are compared to establish whether a purchase is fraudulent.

We propose a nonparametric Bayesian approach for the estimation of the pricing kernel. Historical stock returns and option market data are combined through the Dirichlet Process (DP) to construct an option-adjusted physical measure. The precision parameter of the DP process is calibrated to the amount of trading activity in deep-out-of-the-money options. We use the option-adjusted physical measure to construct an option-adjusted pricing kernel. An empirical investigation on the S&P 500 Index from 2002 to 2015 shows that the option-adjusted pricing kernel is consistently monotonically decreasing, regardless of the level of volatility, thus providing an explanation to the well known U-shaped pricing kernel puzzle.

Partially exchangeable datasets are characterized by observations grouped into known, heterogeneous units. The recently developed Common Atoms Model (CAM) is a Bayesian nonparametric technique suited for analyzing this type of data. CAM induces a two-layered clustering structure: one across observations and another across units. In particular, the units are clustered according to their distributional similarities. In this article, we illustrate the versatility of CAM with an application to an openly available Spotify dataset. The dataset contains quantitative audio features for a large number of songs grouped by artists. After describing the data preprocessing steps, we employ CAM to group the Spotify artists according to the distributions of the energy of their songs.

We describe two interesting and innovative strands of Murray Aitkin's research publications, dealing with mixture models and with Bayesian inference. Of his considerable publications on mixture models, we focus on a nonparametric random effects approach in generalized linear mixed modelling, which has proven useful in a wide variety of applications. As an early proponent of ways of implementing the Bayesian paradigm, Aitkin proposed an alternative Bayes factor based on a posterior mean likelihood. We discuss these innovative approaches and some research lines motivated by them and also suggest future related methodological implementations.

Modern datasets are characterized by numerous features related by complex dependency structures. To deal with these data, dimensionality reduction techniques are essential. Many of these techniques rely on the concept of intrinsic dimension (), a measure of the complexity of the dataset. However, the estimation of this quantity is not trivial: often, the depends rather dramatically on the scale of the distances among data points. At short distances, the can be grossly overestimated due to the presence of noise, becoming smaller and approximately scale-independent only at large distances. An immediate approach to examining the scale dependence consists in decimating the dataset, which unavoidably induces non-negligible statistical errors at large scale. This article introduces a novel statistical method, , that allows estimating the as an explicit function of the scale without performing any decimation. Our approach is based on rigorous distributional results that enable the quantification of uncertainty of the estimates. Moreover, our method is simple and computationally efficient since it relies only on the distances among data points. Through simulation studies, we show that is asymptotically unbiased, provides comparable estimates to other state-of-the-art methods, and is more robust to short-scale noise than other likelihood-based approaches.

Classical and quantum phase transitions (QPTs), with their accompanying concepts of criticality and universality, are a cornerstone of statistical thermodynamics. An exemplary controlled QPT is the field-induced magnetic ordering of a gapped quantum magnet. Although numerous "quasi-one-dimensional" coupled spin-chain and -ladder materials are known whose ordering transition is three-dimensional (3D), quasi-2D systems are special for several physical reasons. Motivated by the ancient pigment Han Purple (BaCuSi$_{2}$O$_{6}$), a quasi-2D material displaying anomalous critical properties, we present a complete analysis of Ba$_{0.9}$Sr$_{0.1}$CuSi$_{2}$O$_{6}$. We measure the zero-field magnetic excitations by neutron spectroscopy and deduce the magnetic Hamiltonian. We probe the field-induced transition by combining magnetization, specific-heat, torque and magnetocalorimetric measurements with low-temperature nuclear magnetic resonance studies near the QPT. By a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Sr-substitution in Han Purple., 19 pages, 5 figures

During the COVID-19 pandemic, many countries implemented international travel restrictions that aimed to contain viral spread while still allowing necessary cross-border travel for social and economic reasons. The relative effectiveness of these approaches for controlling the pandemic has gone largely unstudied. Here we developed a flexible network meta-population model to compare the effectiveness of international travel policies, with a focus on evaluating the benefit of policy coordination. Because country-level epidemiological parameters are unknown, they need to be estimated from data; we accomplished this using approximate Bayesian computation, given the nature of our complex stochastic disease transmission model. Based on simulation and theoretical insights we find that, under our proposed policy, international airline travel may resume up to 58% of the pre-pandemic level with pandemic control comparable to that of a complete shutdown of all airline travel. Our results demonstrate that global coordination is necessary to allow for maximum travel with minimum effect on viral spread.

The use of large datasets for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed for inference on nested datasets, where the observations are assumed to be organized in different units and some sharing of information is required to learn distinctive features of the units. In this manuscript, we propose a nested common atoms model (CAM) that is particularly suited for the analysis of nested datasets where the distributions of the units are expected to differ only over a small fraction of the observations sampled from each unit. The proposed CAM allows a two-layered clustering at the distributional and observational level and is amenable to scalable posterior inference through the use of a computationally efficient nested slice sampler algorithm. We further discuss how to extend the proposed modeling framework to handle discrete measurements, and we conduct posterior inference on a real microbiome dataset from a diet swap study to investigate how the alterations in intestinal microbiota composition are associated with different eating habits. We further investigate the performance of our model in capturing true distributional structures in the population by means of a simulation study.

ABCpy is a highly modular scientific library for approximate Bayesian computation (ABC) written in Python. The main contribution of this paper is to document a software engineering effort that enables domain scientists to easily apply ABC to their research without being ABC experts; using ABCpy they can easily run large parallel simulations without much knowledge about parallelization. Further, ABCpy enables ABC experts to easily develop new inference schemes and evaluate them in a standardized environment and to extend the library with new algorithms. These benefits come mainly from the modularity of ABCpy. We give an overview of the design of ABCpy and provide a performance evaluation concentrating on parallelization. This points us towards the inherent imbalance in some of the ABC algorithms. We develop a dynamic scheduling MPI implementation to mitigate this issue and evaluate the various ABC algorithms according to their adaptability towards high-performance computing., Journal of Statistical Software, 100 (7), ISSN:1548-7660

One of the basic assumptions in spatial statistic is second-order stationarity, which implies homogeneity and isotropy. However, when using a spatial random field framework to model socio-economical or epidemiological data – just to mention two examples – it is often unreasonable to believe that the relationship between variables could be modelled as a realization of a unique stationary process. In order to provide a more realistic representation, we introduce a latent process which drives the value of the coefficients in a Cliff-Ord-type spatial autoregressive linear model identifying groups of observations with a similar behaviour. The latent process evolves as a Hidden Markov Random Field. This structure allows the topology of the problem to be taken into account when identifying groups. A simulation exercise is performed to investigate the influence of parameter values – estimated via a Markov chain Monte Carlo procedure – on the accuracy of the results. Criteria to perform model comparison in order to establish the optimal number of clusters are also provided. A case study referred to hedonic house prices in Boston illustrates the advantages of the proposed modelling strategy.

Interactions among multiple time series of positive random variables are crucial in diverse financial applications, from spillover effects to volatility interdependence. A popular model in this setting is the vector Multiplicative Error Model (vMEM) which poses a linear iterative structure on the dynamics of the conditional mean, perturbed by a multiplicative innovation term. A main limitation of vMEM is however its restrictive assumption on the distribution of the random innovation term. A Bayesian semiparametric approach that models the innovation vector as an infinite location-scale mixture of multidimensional kernels with support on the positive orthant is used to address this major shortcoming of vMEM. Computational complications arising from the constraints to the positive orthant are avoided through the formulation of a slice sampler on the parameter-extended unconstrained version of the model. The method is applied to simulated and real data and a flexible specification is obtained that outperforms the classical ones in terms of fitting and predictive power.

For the analysis of COVID-19 pandemic data, we propose Bayesian multinomial and Dirichlet-multinomial autoregressive models for time-series of counts of patients in mutually exclusive and exhaustive observational categories, defined according to the severity of the patient status and the required treatment. Categories include hospitalized in regular wards (H) and in intensive care units (ICU), together with deceased (D) and recovered (R). These models explicitly formulate assumptions on the transition probabilities between these categories across time, thanks to a flexible formulation based on parameters that a priori follow normal distributions, possibly truncated to incorporate specific hypotheses having an epidemiological interpretation. The posterior distribution of model parameters and the transition matrices are estimated by a Markov chain Monte Carlo algorithm that also provides predictions and allows us to compute the reproduction number R t . All estimates and predictions are endowed with an accuracy measure obtained thanks to the Bayesian approach. We present results concerning data collected during the first wave of the pandemic in Italy and Lombardy and study the effect of nonpharmaceutical interventions. Suitable discrepancy measures defined to check and compare models show that the Dirichlet-multinomial model has an adequate fit and provides good predictive performance in particular for H and ICU patients.

BackgroundThe global impact of COVID-19 and the country-specific responses to the pandemic provide an unparalleled opportunity to learn about different patterns of the outbreak and interventions. We model the global pattern of trajectories of reported COVID-19 cases during the primary response period, with the aim of learning from the past to prepare for the future.MethodsUsing Bayesian methods, we analyse the response to the COVID-19 outbreak for 158 countries for the period 22 January to 9 June 2020. This encompasses the period in which many countries imposed a variety of response measures and initial relaxation strategies. Instead of modelling specific intervention types and timings for each country explicitly, we adopt a stochastic epidemiological model including a feedback mechanism on virus transmission to capture complex nonlinear dynamics arising from continuous changes in community behaviour in response to rising case numbers. We analyse the overall effect of interventions and community responses across diverse regions. This approach mitigates explicit consideration of issues such as period of infectivity and public adherence to government restrictions.ResultsCountries with the largest cumulative case tallies are characterised by a delayed response, whereas countries that avoid substantial community transmission during the period of study responded quickly. Countries that recovered rapidly also have a higher case identification rate and small numbers of undocumented community transmission at the early stages of the outbreak. We also demonstrate that uncertainty in numbers of undocumented infections dramatically impacts the risk of second waves. Our approach is also effective at pre-empting potential second waves and flare-ups.ConclusionsWe demonstrate the utility of modelling to interpret community behaviour in the early epidemic stages. Two lessons learnt that are important for the future are: i) countries that imposed strict containment measures early in the epidemic fared better with respect to numbers of reported cases; and ii) broader testing is required early in the epidemic to understand the magnitude of undocumented infections and recover rapidly. We conclude that clear patterns of containment are essential prior to relaxation of restrictions and show that modelling can provide insights to this end.

Summary Financial markets are ultimately seen as a collection of dyadic transactions. We study the temporal evolution of dyadic relationships in the European interbank market, as induced by monetary transactions registered in the electronic market for interbank deposits (e-MID) during a period of 10 years (2006–2015). In particular, we keep track of how reciprocal exchange patterns have varied with macro events and exogenous shocks and with the emergence of the Global Financial Crisis in 2008. The approach adopted extends the model of Holland and Leinhardt to a longitudinal setting where individuals’ temporal trajectories for the tendency to connect and reciprocate transactions are explicitly modelled through splines or polynomials, and individual-specific parameters. We estimate the model by an iterative algorithm that maximizes the log-likelihood for every ordered pair of units. The empirical application shows that the methodology proposed may be applied to large networks and represents the process of exchange at a fine-grained level. Further results are available in on-line supplementary material.

The Banana Bunchy Top Virus (BBTV) is one of the most economically important vector-borne banana diseases throughout the Asia-Pacific Basin and presents a significant challenge to the agricultural sector. Current models of BBTV are largely deterministic, limited by an incomplete understanding of interactions in complex natural systems, and the appropriate identification of parameters. A stochastic network-based Susceptible-Infected-Susceptible model has been created which simulates the spread of BBTV across the subsections of a banana plantation, parameterising nodal recovery, neighbouring and distant infectivity across summer and winter. Findings from posterior results achieved through Markov Chain Monte Carlo approach to approximate Bayesian computation suggest seasonality in all parameters, which are influenced by correlated changes in inspection accuracy, temperatures and aphid activity. This paper demonstrates how the model may be used for monitoring and forecasting of various disease management strategies to support policy-level decision making., Author summary The Banana Bunchy Top Virus (BBTV) poses one of the greatest threats to the food security of developing nations and the banana industry throughout the Asia-Pacific Basin. Decision-makers face significant challenges in mitigating BBTV spread in banana plantations due to the vector-borne spread of this disease, which is significantly influenced by a vast array of external environmental factors that are unique to each plantation. We propose a flexible network-based model that describes the spread of BBTV in a real banana plantation through a random process while accounting for individual plantation characteristics and utilise a principled methodology for estimating model parameters. Our models can be used to quantify the effects of seasonal changes and plantation configuration on BBTV spread and can be used to predict high-risk areas in this plantation. We believe that our model might be used by decision-makers to evaluate the effectiveness of current disease management strategies and explore opportunities for improvements.

Parametric specifications in State Space Models (SSMs) are a source of bias in case of mismatch between modeling assumptions and reality. We propose a Bayesian semiparametric SSM that is robust to misspecified emission distributions. The Markovian nature of the latent stochastic process creates a temporal dependence and links the random probability distributions of the observations in a mixture of products of Dirichlet processes (MPDP). The model is shown to be adequate and it is applied to simulated data and to the motivating empirical problem of regime shifts in interest rates with latent state persistence. Bayesian semiparametric State Space model robust to imprecise emission distribution.Application: robustly identify highly persistent regime shifts in interest rates.Adequacy is shown to theoretically justify the model.