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The expected-posterior prior (EPP) and the power-expected-posterior (PEP) prior are based on random imaginary observations and offer several advantages in objective Bayesian hypothesis testing. The use of sufficient statistics, when these exist, as a way to redefine the EPP and PEP prior is investigated. In this way the dimensionality of the problem can be reduced, by generating samples of sufficient statistics instead of generating full sets of imaginary data. On the theoretical side it is proved that the new EPP and PEP definitions based on imaginary training samples of sufficient statistics are equivalent with the standard definitions based on individual training samples. This equivalence provides a strong justification and generalization of the definition of both EPP and PEP prior, since from the individual samples or from the sufficient samples the criteria coincide. This avoids potential inconsistencies or paradoxes when only sufficient statistics are available. The applicability of the new definitions in different hypotheses testing problems is explored, including the case of an irregular model. Calculations are simplified; and it is shown that when testing the mean of a normal distribution the EPP and PEP prior can be expressed as a beta mixture of normal priors. The paper concludes with a discussion about the interpretation and the benefits of the proposed approach.

Power-expected-posterior (PEP) priors have been recently introduced as generalized versions of the expected-posterior-priors (EPPs) for variable selection in Gaussian linear models. They are minimally-informative priors that reduce the effect of training samples under the EPP approach, by combining ideas from the power-prior and unit-information-prior methodologies. In this paper we prove the information consistency of the PEP methodology, when using the independence Jeffreys as a baseline prior, for the variable selection problem in normal linear models.

In this work, the problem of transformation and simultaneous variable selection is thoroughly treated via objective Bayesian approaches by the use of default Bayes factor variants. Four uniparametric families of transformations (Box–Cox, Modulus, Yeo-Johnson and Dual), denoted by T, are evaluated and compared. The subjective prior elicitation for the transformation parameter $$\lambda _T$$ , for each T, is not a straightforward task. Additionally, little prior information for $$\lambda _T$$ is expected to be available, and therefore, an objective method is required. The intrinsic Bayes factors and the fractional Bayes factors allow us to incorporate default improper priors for $$\lambda _T$$ . We study the behaviour of each approach using a simulated reference example as well as two real-life examples.

In this paper, we focus on the variable selection problem in normal regression models using the expected-posterior prior methodology. We provide a straightforward MCMC scheme for the derivation of the posterior distribution, as well as Monte Carlo estimates for the computation of the marginal likelihood and posterior model probabilities. Additionally, for large spaces, a model search algorithm based on $\mathit{MC}^{3}$ is constructed. The proposed methodology is applied in two real life examples, already used in the relevant literature of objective variable selection. In both examples, uncertainty over different training samples is taken into consideration.

Data holders, such as statistical institutions and financial organizations, have a very serious and demanding task when producing data for official and public use. It's about controlling the risk of identity disclosure and protecting sensitive information when they communicate data-sets among themselves, to governmental agencies and to the public. One of the techniques applied is that of micro-aggregation. In a Bayesian setting, micro-aggregation can be viewed as the optimal partitioning of the original data-set based on the minimization of an appropriate measure of discrepancy, or distance, between two posterior distributions, one of which is conditional on the original data-set and the other conditional on the aggregated data-set. Assuming d-variate normal data-sets and using several measures of discrepancy, it is shown that the asymptotically optimal equal probability m-partition of $ \mathbb{R}^{d} $ , with m 1/d ? $ \mathbb{N} $ , is the convex one which is provided by hypercubes whose sides are formed by hyperplanes perpendicular to the canonical axes, no matter which discrepancy measure has been used. On the basis of the above result, a method that produces a sub-optimal partition with a very small computational cost is presented.

To describe the dietary patterns of 10 European countries and their socio-demographic determinants, using the comparable between-countries DAFNE data. Analysis of standardized and postharmonized data collected through the national household budget surveys. Nationally representative surveys undertaken in 10 European countries, generally in the second half of the 1990s. The differences in the fruit and vegetable consumption previously identified between Mediterranean and Northern European countries seem to be leveling out, particularly in relation to fruit consumption. Pulses, however, still characterize the diet of the Mediterraneans. Straying from their traditional food choices, Mediterraneans recorded high availability of unprocessed red meat, while Central and Northern Europeans preferably consumed meat products. The household availability of beverages (alcoholic and non-alcoholic) is generally higher among Central and Northern European populations. Principal component (PC) analysis led to the identification of two dietary patterns in each of the 10 countries. The first was similar in all countries and indicated ‘wide-range’ food buyers. The second was slightly more varied and described ‘beverage and convenience’ food buyers. PC1 was common among households of retired and elderly members, while PC2 was common among households located in urban or semi-urban areas and among adult Scandinavians living alone. The dietary patterns identified point towards a progressive narrowing of dietary differences between North and South European countries. The comparable between-countries DAFNE data could prove useful in ecological studies, in the formulation of dietary guidelines and public health initiatives addressing specific population groups. European Commission.

We use Bayesian decision theory to address a variable selection problem arising in attempts to indirectly measure the quality of hospital care, by comparing observed mortality rates to expected values based on patient sickness at admission. Our method weighs data collection costs against predictive accuracy to find an optimal subset of the available admission sickness variables. The approach involves maximizing expected utility across possible subsets, using Monte Carlo methods based on random division of the available data into N modeling and validation splits to approximate the expectation. After exploring the geometry of the solution space, we compare a variety of stochastic optimization methods –- including genetic algorithms (GA), simulated annealing (SA), tabu search (TS), threshold acceptance (TA), and messy simulated annealing (MSA) –- on their performance in finding good subsets of variables, and we clarify the role of N in the optimization. Preliminary results indicate that TS is somewhat better than TA and SA in this problem, with MSA and GA well behind the other three methods. Sensitivity analysis reveals broad stability of our conclusions.