Any series of observations ordered along a single dimension, such as time, may be thought of as a time series. The emphasis in time series analysis is on studying the dependence among observations at different points in time. What distinguishes time series analysis from general multivariate analysis is precisely the temporal order imposed on the observations. Many economic variables, such as GNP and its components, price indices, sales, and stock returns are observed over time. In addition to being interested in the contemporaneous relationships among such variables, we are often concerned with relationships between their current and past values, that is, relationships over time.

Time Series Analysis

Dengue is a systemic viral infection transmitted between humans by Aedes mosquitoes. For some patients, dengue is a life-threatening illness. There are currently no licensed vaccines or specific therapeutics, and substantial vector control efforts have not stopped its rapid emergence and global spread. The contemporary worldwide distribution of the risk of dengue virus infection and its public health burden are poorly known. Here we undertake an exhaustive assembly of known records of dengue occurrence worldwide, and use a formal modelling framework to map the global distribution of dengue risk. We then pair the resulting risk map with detailed longitudinal information from dengue cohort studies and population surfaces to infer the public health burden of dengue in 2010. We predict dengue to be ubiquitous throughout the tropics, with local spatial variations in risk influenced strongly by rainfall, temperature and the degree of urbanization. Using cartographic approaches, we estimate there to be 390 million (95% credible interval 284-528) dengue infections per year, of which 96 million (67-136) manifest apparently (any level of disease severity). This infection total is more than three times the dengue burden estimate of the World Health Organization. Stratification of our estimates by country allows comparison with national dengue reporting, after taking into account the probability of an apparent infection being formally reported. The most notable differences are discussed. These new risk maps and infection estimates provide novel insights into the global, regional and national public health burden imposed by dengue. We anticipate that they will provide a starting point for a wider discussion about the global impact of this disease and will help to guide improvements in disease control strategies using vaccine, drug and vector control methods, and in their economic evaluation.

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The global distribution and burden of dengue

Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-confident inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA)provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA have recently emerged. We discuss these methods and present a number of examples.In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue of currently available BMA software.

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Bayesian Model Averaging: A Tutorial

Time series forecasting using a hybrid ARIMA and neural network model

Presents a wide range of forecasting methods useful for undergraduate or graduate students majoring in business management, economics, or engineering. Develops skills for selecting the proper methodology. Integrates forecasting with the planning and decision-making activities within an organization. Methods of forecasting include: decomposition, regression analysis, and econometrics. Stresses the strengths and weaknesses of the individual methods in various types of organizational areas. Numerous examples are included.

Forecasting: Methods and Applications

Two separate sets of forecasts of airline passenger data have been combined to form a composite set of forecasts. The main conclusion is that the composite set of forecasts can yield lower mean-square error than either of the original forecasts. Past errors of each of the original forecasts are used to determine the weights to attach to these two original forecasts in forming the combined forecasts, and different methods of deriving these weights are examined.

The Combination of Forecasts

The combination of forecasts

Data envelopment analysis (a mathematical programming technique) has often been applied to measuring the efficiency with which outputs are produced. The technique derives efficient combinations of outputs for given inputs: constant returns to size may be assumed or one may choose to examine whether decreasing or increasing returns hold true. An analysis of the cost of prescribing drugs for 106 general practices in the Lincolnshire Health Authority for the year 1993/1994 reveals the statistical problems that are encountered in applying this technique.

Measuring the efficiency of prescribing by general practitioners

As with any health care process, the efficiency with which outputs are produced in general practice is of considerable importance. Using data from Lincolnshire, this study utilizes data envelopment analysis to examine the relationships between practice costs and outputs, measured not only as the number of patients treated, but also on the basis of performance indicators. The technique permits the construction of an efficiency ranking, facilitating the accurate targeting of monitoring resources.

J. M. Bates

Papers

The Combination of Forecasts

The combination of forecasts

Measuring the efficiency of prescribing by general practitioners

Assessing Efficiency in General Practice: An Application of Data Envelopment Analysis: