Migration pattern in Bangladesh: a covariate-dependent Markov model

Internal migration is one of the major components of rapid and unplanned growth of towns and cities especially in the developing countries. This paper describes the transition pattern of internal out migration in Bangladesh and some sociodemographic factors influencing such migration in the country using a covariate-dependent Markov model. Four types of migration behavior namely, rural to rural, rural to urban, urban to rural and urban to urban are under consideration of this paper. Defining two discrete states, urban and rural, each of such transition can be characterized by a stochastic process; hence we use a two-state Markov chain for this purpose. We find that age, sex, division and reason of migration are significantly associated with internal migration in Bangladesh. The major findings include that any type of migration, rural to rural, rural to urban, urban to rural and urban to urban, mostly take place at the ages of 15–30 as well as at the ages of 0–15; females have higher odds than males to make a migration; Dhaka, Rajshahi and Chittagong divisions have remarkably higher migration rate as compared to Barisal and Sylhet division; and the professional reason is the main reason for rural to urban migration.     

Time series modelling of childhood diseases: a dynamical systems approach

A key issue in the dynamical modelling of epidemics is the synthesis of complex mathematical models and data by means of time series analysis. We report such an approach, focusing on the particularly well-documented case of measles. We propose the use of a discrete time epidemic model comprising the infected and susceptible class as state variables. The model uses a discrete time version of the susceptible–exposed–infected–recovered type epidemic models, which can be fitted to observed disease incidence time series. We describe a method for reconstructing the dynamics of the susceptible class, which is an unobserved state variable of the dynamical system. The model provides a remarkable fit to the data on case reports of measles in England and Wales from 1944 to 1964. Morever, its systematic part explains the well-documented predominant biennial cyclic pattern. We study the dynamic behaviour of the time series model and show that episodes of annual cyclicity, which have not previously been explained quantitatively, arise as a response to a quicker replenishment of the susceptible class during the baby boom, around 1947.     

Hierarchical space-time modelling of epidemic dynamics: an application to measles outbreaks

How infectious diseases spread in space and time is an important question that has received considerable theoretical attention. There are, however, few empirical studies to support theoretical approaches, because data is scarce. In this paper we propose to model the epidemic spread of measles in the London boroughs between 1960 and 1970 by an extension of the Kriged Kalman filter (Mardia et al. , 1998) to count data. Results show the flexibility of our approach in describing complex spatio-temporal dynamics.     

A random effects model for diseases with heterogeneous rates of infection

One form of data collected in the study of infectious diseases is on the transmission of a disease within households. We consider a model which allows the rate of disease transmission to vary between households. A Bayesian hierarchical approach to fitting the model is proposed and is implemented by the Metropolis–Hastings algorithm, a standard Markov chain Monte Carlo (MCMC) method. Results are presented for both simulated epidemic chain data and the Providence measles data, illustrating the potential that MCMC methods have to dealing with heterogeneity in infectious disease transmission.     

Spatial smoothing of low birth weight rate in Bangladesh using Bayesian hierarchical model

The term low birth weight refers an event where a newborn baby has a weight that is less than 2500?g. This is an essential indicator while the interest is in public health issues such as infant mortality, maternal complications, and antenatal care, etc. of a country, particularly, for a developing country like Bangladesh. The regional development programs are in the current priority list of Bangladesh government and other policy makers. Many of such regional development programs may need the spatial distribution of relative risk for low birth weight that can be obtained by mapping the risks over small area domains like the districts of Bangladesh. This study aims to find whether is there any spatial dependence among the relative risks of low birth weight for the districts of Bangladesh. This has been investigated using Moran's I statistic and a significant spatial dependence in the relative risks was found. Then, attempt has been made to rediscover the spatial distribution based on the idea of spatial smoothing. A Bayesian hierarchical model is used considering percent received antenatal care and female labor force participation as covariates to smooth the observed relative risks of low birth weight in 64 districts of Bangladesh. Revised spatial distribution taking the spatial dependence under consideration through intrinsic conditional autoregressive model is derived and showed in choropleth map along with its different behaviors.     

Modelling concurrency of events in on-line auctions via spatiotemporal semiparametric models

Summary.  We introduce a semiparametric approach for modelling the effect of concurrent events on an outcome of interest. Concurrency manifests itself as temporal and spatial dependences. By temporal dependence we mean the effect of an event in the past. Modelling this effect is challenging since events arrive at irregularly spaced time intervals. For the spatial part we use an abstract notion of 'feature space' to conceptualize distances among a set of item features. We motivate our model in the context of on-line auctions by modelling the effect of concurrent auctions on an auction's price. Our concurrency model consists of three components: a transaction-related component that accounts for auction design and bidding competition, a spatial component that takes into account similarity between item features and a temporal component that accounts for recently closed auctions. To construct each of these we borrow ideas from spatial and mixed model methodology. The power of this model is illustrated on a large and diverse set of laptop auctions on eBay.com. We show that our model results in superior predictive performance compared with a set of competitor models. The model also allows for new insight into the factors that drive price in on-line auctions and their relationship to bidding competition, auction design, product variety and temporal learning effects.     

Max-stable processes for modeling extremes observed in space and time

Max-stable processes have proved to be useful for the statistical modeling of spatial extremes. For statistical inference it is often assumed that there is no temporal dependence; i.e., that the observations at spatial locations are independent in time. In a first approach we construct max-stable space–time processes as limits of rescaled pointwise maxima of independent Gaussian processes, where the space–time covariance functions satisfy weak regularity conditions. This leads to so-called Brown–Resnick processes. In a second approach, we extend Smith’s storm profile model to a space–time setting. We provide explicit expressions for the bivariate distribution functions, which are equal under appropriate choice of the parameters. We also show how the space–time covariance function of the underlying Gaussian process can be interpreted in terms of the tail dependence function in the limiting max-stable space–time process.     

A Potts‐mixture spatiotemporal joint model for combined magnetoencephalography and electroencephalography data

We develop a new methodology for determining the location and dynamics of brain activity from combined magnetoencephalography (MEG) and electroencephalography (EEG) data. The resulting inverse problem is ill‐posed and is one of the most difficult problems in neuroimaging data analysis. In our development we propose a solution that combines the data from three different modalities, magnetic resonance imaging (MRI), MEG and EEG, together. We propose a new Bayesian spatial finite mixture model that builds on the mesostate‐space model developed by Daunizeau & Friston [Daunizeau and Friston, NeuroImage 2007; 38, 67–81]. Our new model incorporates two major extensions: (i) We combine EEG and MEG data together and formulate a joint model for dealing with the two modalities simultaneously; (ii) we incorporate the Potts model to represent the spatial dependence in an allocation process that partitions the cortical surface into a small number of latent states termed mesostates. The cortical surface is obtained from MRI. We formulate the new spatiotemporal model and derive an efficient procedure for simultaneous point estimation and model selection based on the iterated conditional modes algorithm combined with local polynomial smoothing. The proposed method results in a novel estimator for the number of mixture components and is able to select active brain regions, which correspond to active variables in a high‐dimensional dynamic linear model. The methodology is investigated using synthetic data and simulation studies and then demonstrated on an application examining the neural response to the perception of scrambled faces. R software implementing the methodology along with several sample datasets are available at the following GitHub repository https://github.com/v2south/PottsMix . The Canadian Journal of Statistics 47: 688–711; 2019 © 2019 Statistical Society of Canada     

Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods

The analysis of infectious disease data presents challenges arising from the dependence in the data and the fact that only part of the transmission process is observable. These difficulties are usually overcome by making simplifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and non-temporal information, from outbreaks of measles and influenza. Stochastic epidemic models are used to describe the processes that generate the data. MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithms, such as the Metropolis–Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that standard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in broad agreement with estimates obtained by other methods where they are available. However, we can also provide inferences for parameters which have not been reported in previous analyses.     

Small Area Estimation via Multivariate Fay–Herriot Models with Latent Spatial Dependence

The Fay–Herriot model is a standard model for direct survey estimators in which the true quantity of interest, the superpopulation mean, is latent and its estimation is improved through the use of auxiliary covariates. In the context of small area estimation, these estimates can be further improved by borrowing strength across spatial regions or by considering multiple outcomes simultaneously. We provide here two formulations to perform small area estimation with Fay–Herriot models that include both multivariate outcomes and latent spatial dependence. We consider two model formulations. In one of these formulations the outcome‐by‐space dependence structure is separable. The other accounts for the cross dependence through the use of a generalized multivariate conditional autoregressive (GMCAR) structure. The GMCAR model is shown, in a state‐level example, to produce smaller mean square prediction errors, relative to equivalent census variables, than the separable model and the state‐of‐the‐art multivariate model with unstructured dependence between outcomes and no spatial dependence. In addition, both the GMCAR and the separable models give smaller mean squared prediction error than the state‐of‐the‐art model when conducting small area estimation on county level data from the American Community Survey.     

Inference for Epidemics with Three Levels of Mixing: Methodology and Application to a Measles Outbreak

Abstract. A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings according to potentially different rates. For this model, we consider how different kinds of data can be used to estimate the infection rate parameters with a view to understanding what can and cannot be inferred. Among other things we find that temporal data can be of considerable inferential benefit compared with final size data, that the degree of heterogeneity in the data can have a considerable effect on inference for non‐household transmission, and that inferences can be materially different from those obtained from a model with only two levels of mixing. We illustrate our findings by analysing a highly detailed dataset concerning a measles outbreak in Hagelloch, Germany.     

Bank Business Models at Zero Interest Rates

We propose a novel observation-driven finite mixture model for the study of banking data. The model accommodates time-varying component means and covariance matrices, normal and Student’s t distributed mixtures, and economic determinants of time-varying parameters. Monte Carlo experiments suggest that units of interest can be classified reliably into distinct components in a variety of settings. In an empirical study of 208 European banks between 2008Q1–2015Q4, we identify six business model components and discuss how their properties evolve over time. Changes in the yield curve predict changes in average business model characteristics.     

Discrete time modelling of disease incidence time series by using Markov chain Monte Carlo methods

Summary.  A stochastic discrete time version of the susceptible–infected–recovered model for infectious diseases is developed. Disease is transmitted within and between communities when infected and susceptible individuals interact. Markov chain Monte Carlo methods are used to make inference about these unobserved populations and the unknown parameters of interest. The algorithm is designed specifically for modelling time series of reported measles cases although it can be adapted for other infectious diseases with permanent immunity. The application to observed measles incidence series motivates extensions to incorporate age structure as well as spatial epidemic coupling between communities.     

Including covariates in a space-time point process with application to seismicity

The paper proposes a spatio-temporal process that improves the assessment of events in space and time, considering a contagion model (branching process) within a regression-like framework to take covariates into account. The proposed approach develops the forward likelihood for prediction method for estimating the ETAS model, including covariates in the model specification of the epidemic component. A simulation study is carried out for analysing the misspecification model effect under several scenarios. Also an application to the Italian seismic catalogue is reported, together with the reference to the developed R package.

     

Bayesian Inference for Contact Networks Given Epidemic Data

Abstract. In this article, we estimate the parameters of a simple random network and a stochastic epidemic on that network using data consisting of recovery times of infected hosts. The SEIR epidemic model we fit has exponentially distributed transmission times with Gamma distributed exposed and infectious periods on a network where every edge exists with the same probability, independent of other edges. We employ a Bayesian framework and Markov chain Monte Carlo (MCMC) integration to make estimates of the joint posterior distribution of the model parameters. We discuss the accuracy of the parameter estimates under various prior assumptions and show that it is possible in many scientifically interesting cases to accurately recover the parameters. We demonstrate our approach by studying a measles outbreak in Hagelloch, Germany, in 1861 consisting of 188 affected individuals. We provide an R package to carry out these analyses, which is available publicly on the Comprehensive R Archive Network.     

A semiparametric multilevel survival model

Summary.  We propose a semiparametric multilevel survival model for clustered duration data in which the effect of a continuous covariate is represented by an unspecified, possibly non-linear, function. This model makes no distributional assumption about the cluster level random effects. The performance of the method is assessed via Monte Carlo simulations. The model is applied in an analysis of first-birth intervals in Bangladesh to examine period effects in the timing of first births, while allowing for clustering within communities; the analysis reveals a non-linear trend in the first-birth interval over time.     

Hierarchical Bayesian bivariate disease mapping: analysis of children and adults asthma visits to hospital

In spatial epidemiology, detecting areas with high ratio of disease is important as it may lead to identifying risk factors associated with disease. This in turn may lead to further epidemiological investigations into the nature of disease. Disease mapping studies have been widely performed with considering only one disease in the estimated models. Simultaneous modelling of different diseases can also be a valuable tool both from the epidemiological and also from the statistical point of view. In particular, when we have several measurements recorded at each spatial location, one can consider multivariate models in order to handle the dependence among the multivariate components and the spatial dependence between locations. In this paper, spatial models that use multivariate conditionally autoregressive smoothing across the spatial dimension are considered. We study the patterns of incidence ratios and identify areas with consistently high ratio estimates as areas for further investigation. A hierarchical Bayesian approach using Markov chain Monte Carlo techniques is employed to simultaneously examine spatial trends of asthma visits by children and adults to hospital in the province of Manitoba, Canada, during 2000–2010.     

Case–control genome-wide joint association study using semiparametric empirical model and approximate Bayes factor

We propose a semiparametric approach for the analysis of case–control genome-wide association study. Parametric components are used to model both the conditional distribution of the case status given the covariates and the distribution of genotype counts, whereas the distribution of the covariates are modelled nonparametrically. This yields a direct and joint modelling of the case status, covariates and genotype counts, and gives a better understanding of the disease mechanism and results in more reliable conclusions. Side information, such as the disease prevalence, can be conveniently incorporated into the model by an empirical likelihood approach and leads to more efficient estimates and a powerful test in the detection of disease-associated SNPs. Profiling is used to eliminate a nuisance nonparametric component, and the resulting profile empirical likelihood estimates are shown to be consistent and asymptotically normal. For the hypothesis test on disease association, we apply the approximate Bayes factor (ABF) which is computationally simple and most desirable in genome-wide association studies where hundreds of thousands to a million genetic markers are tested. We treat the approximate Bayes factor as a hybrid Bayes factor which replaces the full data by the maximum likelihood estimates of the parameters of interest in the full model and derive it under a general setting. The deviation from Hardy–Weinberg Equilibrium (HWE) is also taken into account and the ABF for HWE using cases is shown to provide evidence of association between a disease and a genetic marker. Simulation studies and an application are further provided to illustrate the utility of the proposed methodology.     

Vector-borne infectious disease mapping with stochastic difference equations: an analysis of dengue disease in Malaysia

Few publications consider the estimation of relative risk for vector-borne infectious diseases. Most of these articles involve exploratory analysis that includes the study of covariates and their effects on disease distribution and the study of geographic information systems to integrate patient-related information. The aim of this paper is to introduce an alternative method of relative risk estimation based on discrete time–space stochastic SIR-SI models (susceptible–infective–recovered for human populations; susceptible–infective for vector populations) for the transmission of vector-borne infectious diseases, particularly dengue disease. First, we describe deterministic compartmental SIR-SI models that are suitable for dengue disease transmission. We then adapt these to develop corresponding discrete time–space stochastic SIR-SI models. Finally, we develop an alternative method of estimating the relative risk for dengue disease mapping based on these models and apply them to analyse dengue data from Malaysia. This new approach offers a better model for estimating the relative risk for dengue disease mapping compared with the other common approaches, because it takes into account the transmission process of the disease while allowing for covariates and spatial correlation between risks in adjacent regions.     

A Review of Some Modern Approaches to the Problem of Trend Extraction

This article presents a review of some modern approaches to trend extraction for one-dimensional time series, which is one of the major tasks of time series analysis. The trend of a time series is usually defined as a smooth additive component which contains information about the time series global change, and we discuss this and other definitions of the trend. We do not aim to review all the novel approaches, but rather to observe the problem from different viewpoints and from different areas of expertise. The article contributes to understanding the concept of a trend and the problem of its extraction. We present an overview of advantages and disadvantages of the approaches under consideration, which are: the model-based approach (MBA), nonparametric linear filtering, singular spectrum analysis (SSA), and wavelets. The MBA assumes the specification of a stochastic time series model, which is usually either an autoregressive integrated moving average (ARIMA) model or a state space model. The nonparametric filtering methods do not require specification of model and are popular because of their simplicity in application. We discuss the Henderson, LOESS, and Hodrick–Prescott filters and their versions derived by exploiting the Reproducing Kernel Hilbert Space methodology. In addition to these prominent approaches, we consider SSA and wavelet methods. SSA is widespread in the geosciences; its algorithm is similar to that of principal components analysis, but SSA is applied to time series. Wavelet methods are the de facto standard for denoising in signal procession, and recent works revealed their potential in trend analysis.