Summary. We present theoretical results on the random wavelet coef®cients covariance structure. We use simple properties of the coef®cients to derive a recursive way to compute the within-and across-scale covariances. We point out a useful link between the algorithm proposed and the twodimensional discrete wavelet transform. We then focus on Bayesian wavelet shrinkage for estimating a function from noisy data. A prior distribution is imposed on the coef®cients of the unknown function. We show how our ®ndings on the covariance structure make it possible to specify priors that take into account the full correlation between coef®cients through a parsimonious number of hyperparameters. We use Markov chain Monte Carlo methods to estimate the parameters and illustrate our method on bench-mark simulated signals.

Background: The role of antibiotic therapy on Salmonella faecal excretion is controversial. Acute Salmonella gastroenteritis induces long‐lasting digestive symptoms in up to one‐third of subjects. The role of antimicrobial therapy on persistent post‐infectious symptoms is unknown. Aim: To investigate the role of antibiotic therapy on long‐term germ faecal excretion and digestive symptoms after Salmonella infection. Subjects and methods: 1543 subjects [518 aged between 3 and 5 years (35.3%); 950 between 6 and 10 years (64.7%) and 75 adults (4.9%)] involved in a single outbreak of Salmonella enteritis fulfilled the study criteria by repeating stool cultures and answering a symptom questionnaire 3 months post‐infection. Results: 327 subjects (21.2%) were treated with antibiotics during the acute infection [121 children aged 3–5 years (23.4%), 175 children aged 6–10 years (18.4%) and 31 adults (41.3%)]. Antibiotic treatment did not affect Salmonella excretion at any of the time points studied up to three months post‐infection in any age group as compared to age‐matched untreated controls. Persistent digestive symptoms were more common among the patients treated with antibiotics (9.5% vs. 2.9%; P=0.003). Conclusions: Antibiotic therapy does not affect Salmonella enteritis excretion. Digestive symptoms after clearance of the infectious agent are significantly higher in patients treated with antibiotics during acute gastroenteritis.

:  This study introduces a method to classify individuals according to an age threshold, given sex and third molars’ dental maturity measured on the Demirjian scale by expressing uncertainty on dental evidence (soft evidence). We introduced a procedure to learn the parameters of the Naïve Bayes model, and we discussed two classification rules. The model was estimated and tested on 559 Italians aged 16–22. Two experts provided the dental evaluations, and the model was estimated for each of them. We evaluated the coherence of the evidence provided by the experts. Some indexes have been proposed to evaluate the effectiveness of the models, emphasizing how the experts’ ability and the technology affect the results. We introduced two benchmarks, one based on the sample distribution per sex and age: in this case, probability of correct classification increases 22% and the proportion of false adults impressively decreases 80.2%; the other benchmark, obtained by simulating hard evidence, shows how the use of soft evidence increases the proportion of correct classification 3.1% and decreases the crucial proportion of false adults about 20%. Similarly, the proportion of false minors decreases about 5.3%.

After a review of several studies concerning the age classification of young individuals by using dental evidence, we must conclude that it is almost impossible to make a comparison among them. To rank the effectiveness of different methods is to challenge them with the same problem and data, looking at the results measured by the same accepted scoring rule. It could also be interesting to repeat the experiment in different conditions varying the reference population and considering if some important covariates, like sex and health status, influence the model performances.

In this paper we evaluate the characteristics observed both on a crime sample and on individuals included in a database to assess the probability of alternative hypotheses concerning identification. The problem is first addressed by considering a generic characteristic and we demonstrate the problem via a computationally efficient Bayesian network. Then we turn our attention to a heritable  trait to show how to evaluate the hypotheses that some individuals, genetically related to the members of the database, are the donors of the crime sample. Then the network is extended to cope with many loci. Applications of the method are provided as well as details of computational requirements.