Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.     

A robust coefficient of determination for regression

To assess the quality of the fit in a multiple linear regression, the coefficient of determination or R² is a very simple tool, yet the most used by practitioners. Indeed, it is reported in most statistical analyzes, and although it is not recommended as a final model selection tool, it provides an indication of the suitability of the chosen explanatory variables in predicting the response. In the classical setting, it is well known that the least-squares fit and coefficient of determination can be arbitrary and/or misleading in the presence of a single outlier. In many applied settings, the assumption of normality of the errors and the absence of outliers are difficult to establish. In these cases, robust procedures for estimation and inference in linear regression are available and provide a suitable alternative.     

Celebrity capital: redefining celebrity using field theory

This article proposes to redefine celebrity as a kind of capital, thereby extending Bourdieu’s field theory. This redefinition is necessary, it is argued, because one of the main limitations shared by current definitions of celebrity is their lack of explanatory power of the convertibility of celebrity into other resources, such as economic or political capital. Celebrity capital, or broadly recognizability, is conceptualized as accumulated media visibility that results from recurrent media representations. In that sense, it is a substantial kind of capital and not a subset or special category of social or symbolic capital, the latter being defined as legitimate recognition by other agents in a social field. Rather than adding another definition of celebrity next to many others, the notion of celebrity capital proposed here should be seen as an attempt to integrate the existing approaches of celebrity into a single comprehensive conceptualization that can enable us to grasp this societal and cultural phenomenon better.     

ISO 45001 and controversial transnational private regulation for occupational health and safety

This article analyses the genesis of the ISO 45001 standard on occupational health and safety, a new initiative of transnational private regulation. The authors draw a picture of controversy from interviews with stakeholders involved in its design, approval and initial dissemination, and from a qualitative content analysis of the internal documentation of the committee responsible for its approval. Like its predecessors relating to environmental management – ISO 14001 – and corporate social responsibility – ISO 26000 – this new standard raises serious concerns among stakeholders given that it deals with substantive political, social and legal issues.     

Consumption Over the Life Cycle

This paper estimates a structural model of optimal life‐cycle consumption expenditures in the presence of realistic labor income uncertainty. We employ synthetic cohort techniques and Consumer Expenditure Survey data to construct average age‐profiles of consumption and income over the working lives of typical households across different education and occupation groups. The model fits the profiles quite well. In addition to providing reasonable estimates of the discount rate and risk aversion, we find that consumer behavior changes strikingly over the life cycle. Young consumers behave as buffer‐stock agents. Around age 40, the typical household starts accumulating liquid assets for retirement and its behavior mimics more closely that of a certainty equivalent consumer. Our methodology provides a natural decomposition of saving and wealth into its precautionary and life‐cycle components.     

Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets

We develop an econometric methodology to infer the path of risk premia from a large unbalanced panel of individual stock returns. We estimate the time‐varying risk premia implied by conditional linear asset pricing models where the conditioning includes both instruments common to all assets and asset‐specific instruments. The estimator uses simple weighted two‐pass cross‐sectional regressions, and we show its consistency and asymptotic normality under increasing cross‐sectional and time series dimensions. We address consistent estimation of the asymptotic variance by hard thresholding, and testing for asset pricing restrictions induced by the no‐arbitrage assumption. We derive the restrictions given by a continuum of assets in a multi‐period economy under an approximate factor structure robust to asset repackaging. The empirical analysis on returns for about ten thousand U.S. stocks from July 1964 to December 2009 shows that risk premia are large and volatile in crisis periods. They exhibit large positive and negative strays from time‐invariant estimates, follow the macroeconomic cycles, and do not match risk premia estimates on standard sets of portfolios. The asset pricing restrictions are rejected for a conditional four‐factor model capturing market, size, value, and momentum effects.     

Detection and correction of artificial shifts in climate series

Summary.  Many long instrumental climate records are available and might provide useful information in climate research. These series are usually affected by artificial shifts, due to changes in the conditions of measurement and various kinds of spurious data. A comparison with surrounding weather-stations by means of a suitable two-factor model allows us to check the reliability of the series. An adapted penalized log-likelihood procedure is used to detect an unknown number of breaks and outliers. An example concerning temperature series from France confirms that a systematic comparison of the series together is valuable and allows us to correct the data even when no reliable series can be taken as a reference.     

Data-driven Kriging models based on FANOVA-decomposition

Kriging models have been widely used in computer experiments for the analysis of time-consuming computer codes. Based on kernels, they are flexible and can be tuned to many situations. In this paper, we construct kernels that reproduce the computer code complexity by mimicking its interaction structure. While the standard tensor-product kernel implicitly assumes that all interactions are active, the new kernels are suited for a general interaction structure, and will take advantage of the absence of interaction between some inputs. The methodology is twofold. First, the interaction structure is estimated from the data, using a first initial standard Kriging model, and represented by a so-called FANOVA graph. New FANOVA-based sensitivity indices are introduced to detect active interactions. Then this graph is used to derive the form of the kernel, and the corresponding Kriging model is estimated by maximum likelihood. The performance of the overall procedure is illustrated by several 3-dimensional and 6-dimensional simulated and real examples. A substantial improvement is observed when the computer code has a relatively high level of complexity.     

Risk Assessment for Hospital-Acquired Diseases: A Risk-Theory Approach

We introduce a new approach to hospital-acquired disease risk assessment from public health databases. In a spirit similar to actuarial risk theory, we define an adjustment coefficient that can quantify the risk associated with a hospital department, allowing comparisons of similar departments. The adjustment coefficient characterizes the tail of the distribution of the total patient length of stay in a department before the first disease event occurs. We show that this coefficient is the solution of a Lundberg-like equation, and we provide a nonparametric estimation procedure for this measure, based on a Cramér-Lundberg approximation for the tail of the distribution. Using simulations, we provide evidence of the robustness of the approximation to various individual risk models. In addition, we illustrate the relevance of this approach by evaluating the risk associated with a standard patient safety indicator in 20 hospitals of southeastern France.