Non parametric mixture priors based on an exponential random scheme

We propose a general procedure for constructing nonparametric priors for Bayesian inference. Under very general assumptions, the proposed prior selects absolutely continuous distribution functions, hence it can be useful with continuous data. We use the notion ofFeller-type approximation, with a random scheme based on the natural exponential family, in order to construct a large class of distribution functions. We show how one can assign a probability to such a class and discuss the main properties of the proposed prior, namedFeller prior. Feller priors are related to mixture models with unknown number of components or, more generally, to mixtures with unknown weight distribution. Two illustrations relative to the estimation of a density and of a mixing distribution are carried out with respect to well known data-set in order to evaluate the performance of our procedure. Computations are performed using a modified version of an MCMC algorithm which is briefly described.     

Female entrepreneurship: business,marriage and motherhood in England and Wales, 1851–1911

ABSTRACT

This article offers a new perspective on what it meant to be a business proprietor in Victorian Britain. Based on individual census records, it provides an overview of the full population of female business proprietors in England and Wales between 1851 and 1911. These census data show that around 30% of the total business population was female, a considerably higher estimate than the current literature suggests. Female entrepreneurship was not a uniform experience. Certain demographics clustered in specific trades and within those sectors employers and own-account proprietors had strikingly different age, marital status and household profiles. A woman’s life cycle event such as marriage, motherhood and widowhood played an important role in her decision whether to work, the work available to her and the entrepreneurial choices she could make. While marriage and motherhood removed women from the labour force, they had less of an effect on their levels of entrepreneurship. Women who had young children were more entrepreneurial than those who had none, and entrepreneurship rates rose with the arrival of one child and continued to rise the more children were added to the family.     

Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors

Consider a standard conjugate family of prior distributions for a vector-parameter indexing an exponential family. Two distinct model parameterizations may well lead to standard conjugate families which are not consistent, i.e. one family cannot be derived from the other by the usual change-of-variable technique. This raises the problem of finding suitable parameterizations that may lead to enriched conjugate families which are more flexible than the traditional ones. The previous remark motivates the definition of a new property for an exponential family, named conditional reducibility. Features of conditionally-reducible natural exponential families are investigated thoroughly. In particular, we relate this new property to the notion of cut, and show that conditionally-reducible families admit a reparameterization in terms of a vector having likelihood-independent components. A general methodology to obtain enriched conjugate distributions for conditionally-reducible families is described in detail, generalizing previous works and more recent contributions in the area. The theory is illustrated with reference to natural exponential families having simple quadratic variance function.     

Using Expert Models in Human Reliability Analysis—A Dependence Assessment Method Based on Fuzzy Logic

In human reliability analysis (HRA), dependence analysis refers to assessing the influence of the failure of the operators to perform one task on the failure probabilities of subsequent tasks. A commonly used approach is the technique for human error rate prediction (THERP). The assessment of the dependence level in THERP is a highly subjective judgment based on general rules for the influence of five main factors. A frequently used alternative method extends the THERP model with decision trees. Such trees should increase the repeatability of the assessments but they simplify the relationships among the factors and the dependence level. Moreover, the basis for these simplifications and the resulting tree is difficult to trace. The aim of this work is a method for dependence assessment in HRA that captures the rules used by experts to assess dependence levels and incorporates this knowledge into an algorithm and software tool to be used by HRA analysts. A fuzzy expert system (FES) underlies the method. The method and the associated expert elicitation process are demonstrated with a working model. The expert rules are elicited systematically and converted into a traceable, explicit, and computable model. Anchor situations are provided as guidance for the HRA analyst's judgment of the input factors. The expert model and the FES‐based dependence assessment method make the expert rules accessible to the analyst in a usable and repeatable way, with an explicit and traceable basis.     

A Neo-Durkheimian analysis of a new religious movement: The case of Soka Gakkai in Italy

Soka Gakkai is one of the world’s fastest-growing religious movements and Italy figures among the western nations where this religious group has been most successful. This article aims at explaining this success-story: why has Soka Gakkai, and particularly its Italian affiliation, grown so rapidly in recent years? This research question gives the opportunity to assess the applicability of the economic theory of religion to the growth of new religious movements. Hence, in order to explain the expansion of Soka Gakkai, this work begins with an examination of the adaptive strategies developed by a Japanese organization in the Italian religious market. It is claimed, however, that a rational choice explanation cannot stand on its own and that we must take into account the dynamics of pre-contractual solidarity that promote trust, especially when the expected benefits promised by this organization to its adherents do not materialize. Moreover, these solidarity dynamics generate intense emotional gratification that works as a highly motivating incentive to sustain members’ commitment and to prevent them from dropping out. This pre-contractual solidarity is actively produced and continuously reproduced by means of ritual interaction along the lines suggested by Collins’s theory.     

Probability and Possibility‐Based Representations of Uncertainty in Fault Tree Analysis

Expert knowledge is an important source of input to risk analysis. In practice, experts might be reluctant to characterize their knowledge and the related (epistemic) uncertainty using precise probabilities. The theory of possibility allows for imprecision in probability assignments. The associated possibilistic representation of epistemic uncertainty can be combined with, and transformed into, a probabilistic representation; in this article, we show this with reference to a simple fault tree analysis. We apply an integrated (hybrid) probabilistic‐possibilistic computational framework for the joint propagation of the epistemic uncertainty on the values of the (limiting relative frequency) probabilities of the basic events of the fault tree, and we use possibility‐probability (probability‐possibility) transformations for propagating the epistemic uncertainty within purely probabilistic and possibilistic settings. The results of the different approaches (hybrid, probabilistic, and possibilistic) are compared with respect to the representation of uncertainty about the top event (limiting relative frequency) probability. Both the rationale underpinning the approaches and the computational efforts they require are critically examined. We conclude that the approaches relevant in a given setting depend on the purpose of the risk analysis, and that further research is required to make the possibilistic approaches operational in a risk analysis context.     

Uniformly most powerful unbiased test for shoulder condition in point transect sampling

Point transect sampling is a well-known methodology for estimating wildlife population density. In this context, the usual approach is to assume a model for the detection function. Thus, the estimate depends on the shape of the detection function. In particular, the estimation is influenced by the so-called shoulder condition, which guarantees that detection is nearly certain at small distances from the observer. For instance, the half-normal model satisfies this condition, whereas the negative exponential model does not. Testing whether the shoulder condition is consistent with data is a crucial issue. In this paper we propose the uniformly most powerful unbiased test for the shoulder condition in the exponential mixture model of the half-normal and the negative exponential. Critical values of the proposed test are calculated for large samples by means of asymptotic distribution theory and for small samples via Monte Carlo simulations. Finally, a case study is presented.