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This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling.

Aggregate measures of family planning are used to monitor demand for and usage of contraceptive methods in populations globally, for example as part of the FP2030 initiative. Family planning measures for low- and middle-income countries are typically based on data collected through cross-sectional household surveys. Recently proposed measures account for sexual activity through assessment of the distribution of time-between-sex (TBS) in the population of interest. In this paper, we propose a statistical approach to estimate the distribution of TBS using data typically available in low- and middle-income countries, while addressing two major challenges. The first challenge is that timing of sex information is typically limited to women's time-since-last-sex (TSLS) data collected in the cross-sectional survey. In our proposed approach, we adopt the current duration method to estimate the distribution of TBS using the available TSLS data, from which the frequency of sex at the population level can be derived. Furthermore, the observed TSLS data are subject to reporting issues because they can be reported in different units and may be rounded off. To apply the current duration approach and account for these data reporting issues, we develop a flexible Bayesian model, and provide a detailed technical description of the proposed modeling approach.

This paper presents a novel mechanism design for multi-item auction settings with uncertain bidders' type distributions. Our proposed approach utilizes nonparametric density estimation to accurately estimate bidders' types from historical bids, and is built upon the Vickrey-Clarke-Groves (VCG) mechanism, ensuring satisfaction of Bayesian incentive compatibility (BIC) and $\delta$-individual rationality (IR). To further enhance the efficiency of our mechanism, we introduce two novel strategies for query reduction: a filtering method that screens potential winners' value regions within the confidence intervals generated by our estimated distribution, and a classification strategy that designates the lower bound of an interval as the estimated type when the length is below a threshold value. Simulation experiments conducted on both small-scale and large-scale data demonstrate that our mechanism consistently outperforms existing methods in terms of revenue maximization and query reduction, particularly in large-scale scenarios. This makes our proposed mechanism a highly desirable and effective option for sellers in the realm of multi-item auctions.

Generalized approximate message passing (GAMP) is a computationally efficient algorithm for estimating an unknown signal \(w_0\in\mathbb{R}^N\) from a random linear measurement \(y= Xw_0 + \epsilon\in\mathbb{R}^M\), where \(X\in\mathbb{R}^{M\times N}\) is a known measurement matrix and \(\epsilon\) is the noise vector. The salient feature of GAMP is that it can provide an unbiased estimator \(\hat{r}^{\rm G}\sim\mathcal{N}(w_0, \hat{s}^2I_N)\), which can be used for various hypothesis-testing methods. In this study, we consider the bootstrap average of an unbiased estimator of GAMP for the elastic net. By numerically analyzing the state evolution of \emph{approximate message passing with resampling}, which has been proposed for computing bootstrap statistics of the elastic net estimator, we investigate when the bootstrap averaging reduces the variance of the unbiased estimator and the effect of optimizing the size of each bootstrap sample and hyperparameter of the elastic net regularization in the asymptotic setting \(M, N\to\infty, M/N\to\alpha\in(0,\infty)\). The results indicate that bootstrap averaging effectively reduces the variance of the unbiased estimator when the actual data generation process is inconsistent with the sparsity assumption of the regularization and the sample size is small. Furthermore, we find that when \(w_0\) is less sparse, and the data size is small, the system undergoes a phase transition. The phase transition indicates the existence of the region where the ensemble average of unbiased estimators of GAMP for the elastic net norm minimization problem yields the unbiased estimator with the minimum variance.

Substandard and falsified pharmaceuticals, prevalent in low- and middle-income countries, substantially increase levels of morbidity, mortality and drug resistance. Regulatory agencies combat this problem using post-market surveillance by collecting and testing samples where consumers purchase products. Existing analysis tools for post-market surveillance data focus attention on the locations of positive samples. This paper looks to expand such analysis through underutilized supply-chain information to provide inference on sources of substandard and falsified products. We first establish the presence of unidentifiability issues when integrating this supply-chain information with surveillance data. We then develop a Bayesian methodology for evaluating substandard and falsified sources that extracts utility from supply-chain information and mitigates unidentifiability while accounting for multiple sources of uncertainty. Using de-identified surveillance data, we show the proposed methodology to be effective in providing valuable inference.

Identifying Blaschke-Santal\'o diagrams is an important topic that essentially consists in determining the image $Y=F(X)$ of a map $F:X\to{\mathbb{R}}^d$, where the dimension of the source space $X$ is much larger than the one of the target space. In some cases, that occur for instance in shape optimization problems, $X$ can even be a subset of an infinite-dimensional space. The usual Monte Carlo method, consisting in randomly choosing a number $N$ of points $x_1,\dots,x_N$ in $X$ and plotting them in the target space ${\mathbb{R}}^d$, produces in many cases areas in $Y$ of very high and very low concentration leading to a rather rough numerical identification of the image set. On the contrary, our goal is to choose the points $x_i$ in an appropriate way that produces a uniform distribution in the target space. In this way we may obtain a good representation of the image set $Y$ by a relatively small number $N$ of samples which is very useful when the dimension of the source space $X$ is large (or even infinite) and the evaluation of $F(x_i)$ is costly. Our method consists in a suitable use of {\it Centroidal Voronoi Tessellations} which provides efficient numerical results. Simulations for two and three dimensional examples are shown in the paper.

We consider estimation of generalized additive models using basis expansions with Bayesian model selection. Although Bayesian model selection is an intuitively appealing tool for regression splines by virtue of the flexible knot placement and model-averaged function estimates, its use has traditionally been limited to Gaussian additive regression, as posterior search of the model space requires a tractable form of the marginal model likelihood. We introduce an extension of the method to the exponential family of distributions using the Laplace approximation to the likelihood. Although the Laplace approximation is successful with all Gaussian-type prior distributions in providing a closed-form expression of the marginal likelihood, there is no broad consensus on the best prior distribution to be used for nonparametric regression via model selection. We observe that the classical unit information prior distribution for variable selection may not be suitable for nonparametric regression using basis expansions. Instead, our study reveals that mixtures of g-priors are more suitable. A large family of mixtures of g-priors is considered for a detailed examination of how various mixture priors perform in estimating generalized additive models. Furthermore, we compare several priors of knots for model selection-based spline approaches to determine the most practically effective scheme. The model selection-based estimation methods are also compared with other Bayesian approaches to function estimation. Extensive simulation studies demonstrate the validity of the model selection-based approaches. We provide an R package for the proposed method.

Sensitivity analysis measures the influence of a Bayesian network's parameters on a quantity of interest defined by the network, such as the probability of a variable taking a specific value. Various sensitivity measures have been defined to quantify such influence, most commonly some function of the quantity of interest's partial derivative with respect to the network's conditional probabilities. However, computing these measures in large networks with thousands of parameters can become computationally very expensive. We propose an algorithm combining automatic differentiation and exact inference to efficiently calculate the sensitivity measures in a single pass. It first marginalizes the whole network once, using e.g. variable elimination, and then backpropagates this operation to obtain the gradient with respect to all input parameters. Our method can be used for one-way and multi-way sensitivity analysis and the derivation of admissible regions. Simulation studies highlight the efficiency of our algorithm by scaling it to massive networks with up to 100'000 parameters and investigate the feasibility of generic multi-way analyses. Our routines are also showcased over two medium-sized Bayesian networks: the first modeling the country-risks of a humanitarian crisis, the second studying the relationship between the use of technology and the psychological effects of forced social isolation during the COVID-19 pandemic. An implementation of the methods using the popular machine learning library PyTorch is freely available.

Causal inference on populations embedded in social networks poses technical challenges, since the typical no interference assumption may no longer hold. For instance, in the context of social research, the outcome of a study unit will likely be affected by an intervention or treatment received by close neighbors. While inverse probability-of-treatment weighted (IPW) estimators have been developed for this setting, they are often highly inefficient. In this work, we assume that the network is a union of disjoint components and propose doubly robust (DR) estimators combining models for treatment and outcome that are consistent and asymptotically normal if either model is correctly specified. We present empirical results that illustrate the DR property and the efficiency gain of DR over IPW estimators when both the outcome and treatment models are correctly specified. Simulations are conducted for networks with equal and unequal component sizes and outcome data with and without a multilevel structure. We apply these methods in an illustrative analysis using the Add Health network, examining the impact of maternal college education on adolescent school performance, both direct and indirect.

When estimating causal effects, it is important to assess external validity, i.e., determine how useful a given study is to inform a practical question for a specific target population. One challenge is that the covariate distribution in the population underlying a study may be different from that in the target population. If some covariates are effect modifiers, the average treatment effect (ATE) may not generalize to the target population. To tackle this problem, we propose new methods to generalize or transport the ATE from a source population to a target population, in the case where the source and target populations have different sets of covariates. When the ATE in the target population is identified, we propose new doubly robust estimators and establish their rates of convergence and limiting distributions. Under regularity conditions, the doubly robust estimators provably achieve the efficiency bound and are locally asymptotic minimax optimal. A sensitivity analysis is provided when the identification assumptions fail. Simulation studies show the advantages of the proposed doubly robust estimator over simple plug-in estimators. Importantly, we also provide minimax lower bounds and higher-order estimators of the target functionals. The proposed methods are applied in transporting causal effects of dietary intake on adverse pregnancy outcomes from an observational study to the whole U.S. female population.