A Closed-Form Filter for Binary Time Series

Non-Gaussian state-space models arise in several applications. Within this framework, the binary time series setting is a source of constant interest due to its relevance in many studies. However, unlike Gaussian state-space models, where filtering, predictive and smoothing distributions are available in closed-form, binary state-space models require approximations or sequential Monte Carlo strategies for inference and prediction. This is due to the apparent absence of conjugacy between the Gaussian states and the likelihood induced by the observation equation for the binary data. In this article we prove that the filtering, predictive and smoothing distributions in dynamic probit models with Gaussian state variables are, in fact, available and belong to a class of unified skew-normals (SUN) whose parameters can be updated recursively in time via analytical expressions. Also the functionals of these distributions depend on known functions, but their calculation requires intractable numerical integration. Leveraging the SUN properties, we address this point via new Monte Carlo methods based on independent and identically distributed samples from the smoothing distribution, which can naturally be adapted to the filtering and predictive case, thereby improving state-of-the-art approximate or sequential Monte Carlo inference in small-to-moderate dimensional studies. A scalable and optimal particle filter which exploits the SUN properties is also developed to deal with online inference in high dimensions. Performance gains over competitors are outlined in a real-data financial application

Working women in France, nineteenth and twentieth centuries. Where, when, and which women were in work at marriage?

We look at women's labour force participation for the whole of France in the nineteenth and twentieth centuries. We study to what extent young women were working at the time of their marriage, in which occupations, and how differences in labour force participation might be explained. Using a sample of 53,451 marriage records from the TRA project, we identify regional and temporal differences in rates of female labour force participation and in types of work in France between 1860 and 1986.We observe rather stable levels of female labour force participation between 1860 and 1950 of about 60 per cent, but higher levels in the second half of the twentieth century. Over time, women started to work across virtually all occupational sectors. Regional differences declined over time but continued to exist in the late twentieth century. We formulate a set of hypotheses to explain which women worked, taking into account their resources, as well as their expectations, in a male-breadwinner-dominated society. The results of our hierarchical logistic analysis indicate that women with fewer parental resources were more likely to work