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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. 相似文献
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Carry van Lieshout Harry Smith Piero Montebruno Robert J. Bennett 《Social history》2013,38(4):440-468
ABSTRACTThis 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. 相似文献
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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. 相似文献
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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. 相似文献
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Luca Podofillini Vinh Dang Enrico Zio Piero Baraldi Massimo Librizzi 《Risk analysis》2010,30(8):1277-1297
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. 相似文献
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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. 相似文献
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Piero Demetrio Falorsi Giorgio Alleva Fabio Bacchini Roberto Iannaccone 《Statistical Methods and Applications》2005,14(1):83-99
Various approaches to obtaining estimates based on preliminary data are outlined. A case is then considered which frequently
arises when selecting a subsample of units, the information for which is collected within a deadline that allows preliminary
estimates to be produced. At the moment when these estimates have to be produced it often occurs that, although the collection
of data on subsample units is still not complete, information is available on a set of units which does not belong to the
sample selected for the production of the preliminary estimates. An estimation method is proposed which allows all the data
available on a given date to be used to the full-and the expression of the expectation and variance are derived. The proposal
is based on two-phase sampling theory and on the hypothesis that the response mechanism is the result of random processes
whose parameters can be suitably estimated. An empirical analysis of the performance of the estimator on the Italian Survey
on building permits concludes the work.
The Sects. 1,2,3,4 and the technical appendixes have been developed by Giorgio Alleva and Piero Demetrio Falorsi; Sect. 5
has been done by Fabio Bacchini and Roberto Iannaccone.
Piero Demetrio Falorsi is chief statisticians at Italian National Institute of Statistics (ISTAT); Giorgio Alleva is Professor
of Statistics at University “La Sapienza” of Rome, Fabio Bacchini and Roberto Iannaccone are researchers at ISTAT. 相似文献
10.
Bayesian analysis of dynamic magnetic resonance breast images 总被引:2,自引:0,他引:2
Francesco de Pasquale Piero Barone Giovanni Sebastiani Julian Stander 《Journal of the Royal Statistical Society. Series C, Applied statistics》2004,53(3):475-493
Summary. We describe an integrated methodology for analysing dynamic magnetic resonance images of the breast. The problems that motivate this methodology arise from a collaborative study with a tumour institute. The methods are developed within the Bayesian framework and comprise image restoration and classification steps. Two different approaches are proposed for the restoration. Bayesian inference is performed by means of Markov chain Monte Carlo algorithms. We make use of a Metropolis algorithm with a specially chosen proposal distribution that performs better than more commonly used proposals. The classification step is based on a few attribute images yielded by the restoration step that describe the essential features of the contrast agent variation over time. Procedures for hyperparameter estimation are provided, so making our method automatic. The results show the potential of the methodology to extract useful information from acquired dynamic magnetic resonance imaging data about tumour morphology and internal pathophysiological features. 相似文献