The two main approaches to Bayesian inference are sampling and optimisation methods. However many complicated posteriors are difficult to approximate by either. Therefore we propose a novel approach combining features of both. We use a flexible parameterised family of densities, such as a normalising flow. Given a density from this family approximating the posterior we use importance sampling to produce a weighted sample from a more accurate posterior approximation. This sample is then used in optimisation to update the parameters of the approximate density, a process we refer to as "distilling" the importance sampling results. We illustrate our method in a queueing model example.

With the aim of studying the spread of the SARS-CoV-2 infection in the Tuscany region of Italy during the first epidemic wave (February-June 2020), we define a compartmental model that accounts for both detected and undetected infections and assumes that only notified cases can die. We estimate the infection fatality rate, the case fatality rate, and the basic reproduction number, modeled as a time-varying function, by calibrating on the cumulative daily number of observed deaths and notified infected, after fixing to plausible values the other model parameters to assure identifiability. The confidence intervals are estimated by a parametric bootstrap procedure and a Global Sensitivity Analysis is performed to assess the sensitivity of the estimates to changes in the values of the fixed parameters. According to our results, the basic reproduction number drops from an initial value of 6.055 to 0 at the end of the national lockdown, then it grows again, but remaining under 1. At the beginning of the epidemic, the case and the infection fatality rates are estimated to be 13.1% and 2.3%, respectively. Among the parameters considered as fixed, the average time from infection to recovery for the not notified infected appears to be the most impacting one on the model estimates. The probability for an infected to be notified has a relevant impact on the infection fatality rate and on the shape of the epidemic curve. This stresses the need of collecting information on these parameters to better understand the phenomenon and get reliable predictions.

We consider group-based anonymization schemes, 1 a popular approach to data publishing. This approach aims 2 at protecting privacy of the individuals involved in a dataset, 3 by releasing an obfuscated version of the original data, where 4 the exact correspondence between individuals and attribute 5 values is hidden. When publishing data about individuals, one 6 must typically balance the learner's utility against the risk 7 posed by an attacker, potentially targeting individuals in the 8 dataset. Accordingly, we propose a unified Bayesian model of 9 group-based schemes and a related MCMC methodology to learn 10 the population parameters from an anonymized table. This allows 11 one to analyze the risk for any individual in the dataset to be 12 linked to a specific sensitive value, when the attacker knows 13 the individual's nonsensitive attributes, beyond what is implied 14 for the general population. We call this relative threat analysis. 15 Finally, we illustrate the results obtained with the proposed 16 methodology on a real-world dataset.

In forensic science, the rare type match problem arises when the matching characteristic from the suspect and the crime scene is not in the reference database; hence, it is difficult to evaluate the likelihood ratio that compares the defense and prosecution hypotheses. A recent solution consists of modeling the ordered population probabilities according to the two-parameter Poisson-Dirichlet distribution, which is a well-known Bayesian nonparametric prior, and plugging the maximum likelihood estimates of the parameters into the likelihood ratio. We demonstrate that this approximation produces a systematic bias that fully Bayesian inference avoids. Motivated by this forensic application, we consider the need to learn the posterior distribution of the parameters that governs the two-parameter Poisson-Dirichlet using two sampling methods: Markov Chain Monte Carlo and approximate Bayesian computation. These methods are evaluated in terms of accuracy and efficiency. Finally, we compare the likelihood ratio All authors contributed equally to this work.

Model updating procedures based on experimental data are commonly used in case of historic buildings to identify numerical models that are subsequently employed to assess their structural behaviour. The reliability of these models is closely related to their ability to account for all the uncertainties that are involved in the knowledge process. In this regard, to handle these uncertainties and quantify their propagation, Bayesian inference is frequently employed being able to deal with the effects of parameter uncertainty, observation errors and model inadequacy. The computation of the posterior distribution through Bayesian inference needs–however–the evaluation of the likelihood function, which requires solving complex multi-dimensional integration problems. To bridge this shortcoming, the paper compares two Bayesian inference approaches to show how different approximations affect the results of simulated inference: a discrete approach for the likelihood computation in the Bayesian Model Updating (BMU) and a Monte Carlo likelihood-free method known as Approximate Bayesian Computation (ABC) are reported. As reference, the typology of historic masonry towers was considered by using their natural frequencies as experimental data for model updating. The two procedures provide very similar results supporting the validity of both methods despite ABC turns out to be a more flexible approach.