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Optimal experimental design (OED) is the general formalism of sensor placement and decisions about the data collection strategy for engineered or natural experiments. This approach is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, and environmental and urban studies. State-of-the-art computational methods for experimental design, however, do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted likelihood and is valid for both finite- and infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.

Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the current candidate in an effort to maximize the chance to select the best. This classical version of the ``Secretary problem'' has been studied in depth using mostly combinatorial approaches, along with numerous other variants. In this work we consider a particular new version where during reviewing one is allowed to query an external expert to improve the probability of making the correct decision. Unlike existing formulations, we consider experts that are not necessarily infallible and may provide suggestions that can be faulty. For the solution of our problem we adopt a probabilistic methodology and view the querying times as consecutive stopping times which we optimize with the help of optimal stopping theory. For each querying time we must also design a mechanism to decide whether we should terminate the search at the querying time or not. This decision is straightforward under the usual assumption of infallible experts but, when experts are faulty, it has a far more intricate structure.

International Classification of Disease (ICD) codes are widely used for encoding diagnoses in electronic health records (EHR). Automated methods have been developed over the years for predicting biomedical responses using EHR that borrow information among diagnostically similar patients. Relatively less attention has been paid to developing patient similarity measures that model the structure of ICD codes and the presence of multiple chronic conditions, where a chronic condition is defined as a set of ICD codes. Motivated by this problem, we first develop a type of string kernel function for measuring similarity between a pair of subsets of ICD codes, which uses the definition of chronic conditions. Second, we extend this similarity measure to define a family of covariance functions on subsets of ICD codes. Using this family, we develop Gaussian process (GP) priors for Bayesian nonparametric regression and classification using diagnoses and other demographic information as covariates. Markov chain Monte Carlo (MCMC) algorithms are used for posterior inference and predictions. The proposed methods are free of any tuning parameters and are well-suited for automated prediction of continuous and categorical biomedical responses that depend on chronic conditions. We evaluate the practical performance of our method on EHR data collected from 1660 patients at the University of Iowa Hospitals and Clinics (UIHC) with six different primary cancer sites. Our method has better sensitivity and specificity than its competitors in classifying different primary cancer sites and estimates the marginal associations between chronic conditions and primary cancer sites.

Discrete choice experiments are frequently used to quantify consumer preferences by having respondents choose between different alternatives. Choice experiments involving mixtures of ingredients have been largely overlooked in the literature, even though many products and services can be described as mixtures of ingredients. As a consequence, little research has been done on the optimal design of choice experiments involving mixtures. The only existing research has focused on D-optimal designs, which means that an estimation-based approach was adopted. However, in experiments with mixtures, it is crucial to obtain models that yield precise predictions for any combination of ingredient proportions. This is because the goal of mixture experiments generally is to find the mixture that optimizes the respondents' utility. As a result, the I-optimality criterion is more suitable for designing choice experiments with mixtures than the D-optimality criterion because the I-optimality criterion focuses on getting precise predictions with the estimated statistical model. In this paper, we study Bayesian I-optimal designs, compare them with their Bayesian D-optimal counterparts, and show that the former designs perform substantially better than the latter in terms of the variance of the predicted utility.

In clinical practice and biomedical research, measurements are often collected sparsely and irregularly in time while the data acquisition is expensive and inconvenient. Examples include measurements of spine bone mineral density, cancer growth through mammography or biopsy, a progression of defective vision, or assessment of gait in patients with neurological disorders. Since the data collection is often costly and inconvenient, estimation of progression from sparse observations is of great interest for practitioners. From the statistical standpoint, such data is often analyzed in the context of a mixed-effect model where time is treated as both a fixed-effect (population progression curve) and a random-effect (individual variability). Alternatively, researchers analyze Gaussian processes or functional data where observations are assumed to be drawn from a certain distribution of processes. These models are flexible but rely on probabilistic assumptions, require very careful implementation, specific to the given problem, and tend to be slow in practice. In this study, we propose an alternative elementary framework for analyzing longitudinal data, relying on matrix completion. Our method yields estimates of progression curves by iterative application of the Singular Value Decomposition. Our framework covers multivariate longitudinal data, regression, and can be easily extended to other settings. As it relies on existing tools for matrix algebra it is efficient and easy to implement. We apply our methods to understand trends of progression of motor impairment in children with Cerebral Palsy. Our model approximates individual progression curves and explains 30% of the variability. Low-rank representation of progression trends enables identification of different progression trends in subtypes of Cerebral Palsy.

Incentive salience attribution can be understood as a psychobiological process ascribing relevance to potentially rewarding objects and actions. Despite being an important component of the motivational process guiding our everyday behaviour its study in naturalistic contexts is not straightforward. Here we propose a methodology based on artificial neural networks (ANNs) for approximating latent states produced by this process in situations where large volumes of behavioural data are available but no strict experimental control is possible. Leveraging knowledge derived from theoretical and computational accounts of incentive salience attribution we designed an ANN for estimating duration and intensity of future interactions between individuals and a series of video games in a large-scale ($N> 3 \times 10^6$) longitudinal dataset. Through model comparison and inspection we show that our approach outperforms competing ones while also generating a representation that well approximate some of the functions of attributed incentive salience. We discuss our findings with reference to the adopted theoretical and computational frameworks and suggest how our methodology could be an initial step for estimating attributed incentive salience in large scale behavioural studies.

We consider parametric estimation for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main targets are the drift parameter $\alpha$ and the diffusion parameter $\beta$. In this paper, we propose two types of adaptive estimators for $(\alpha,\beta)$ and show their asymptotic properties under $\varepsilon\to0$, $n\to\infty$ and the balance condition that $(\varepsilon n^\rho)^{-1} =O(1)$ for some $\rho\ge 1/2$. In simulation studies, we examine and compare asymptotic behaviors of the two kinds of adaptive estimators. Moreover, we treat the SIR model which describes a simple epidemic spread for a biological application.

Topological Data Analysis (TDA) has emerged recently as a robust tool to extract and compare the structure of datasets. TDA identifies features in data such as connected components and holes and assigns a quantitative measure to these features. Several studies reported that topological features extracted by TDA tools provide unique information about the data, discover new insights, and determine which feature is more related to the outcome. On the other hand, the overwhelming success of deep neural networks in learning patterns and relationships has been proven on a vast array of data applications, images in particular. To capture the characteristics of both powerful tools, we propose \textit{TDA-Net}, a novel ensemble network that fuses topological and deep features for the purpose of enhancing model generalizability and accuracy. We apply the proposed \textit{TDA-Net} to a critical application, which is the automated detection of COVID-19 from CXR images. The experimental results showed that the proposed network achieved excellent performance and suggests the applicability of our method in practice.

Paralytic Ileus (PI) patients are at high risk of death when admitted to the Intensive care unit (ICU), with mortality as high as 40\%. There is minimal research concerning PI patient mortality prediction. There is a need for more accurate prediction modeling for ICU patients diagnosed with PI. This paper demonstrates performance improvements in predicting the mortality of ICU patients diagnosed with PI after 24 hours of being admitted. The proposed framework, PMPI(Process Mining Model to predict mortality of PI patients), is a modification of the work used for prediction of in-hospital mortality for ICU patients with diabetes. PMPI demonstrates similar if not better performance with an Area under the ROC Curve (AUC) score of 0.82 compared to the best results of the existing literature. PMPI uses patient medical history, the time related to the events, and demographic information for prediction. The PMPI prediction framework has the potential to help medical teams in making better decisions for treatment and care for ICU patients with PI to increase their life expectancy.

We analyze repeated cross-sectional survey data collected by the Institute of Global Health Innovation, to characterize the perception and behavior of the Italian population during the Covid-19 pandemic, focusing on the period that spans from April to November 2020. To accomplish this goal, we propose a Bayesian dynamic latent-class regression model, that accounts for the effect of sampling bias including survey weights into the likelihood function. According to the proposed approach, attitudes towards Covid-19 are described via three ideal behaviors that are fixed over time, corresponding to different degrees of compliance with spread-preventive measures. The overall tendency toward a specific profile dynamically changes across survey waves via a latent Gaussian process regression, that adjusts for subject-specific covariates. We illustrate the dynamic evolution of Italians' behaviors during the pandemic, providing insights on how the proportion of ideal behaviors has varied during the phases of the lockdown, while measuring the effect of age, sex, region and employment of the respondents on the attitude toward Covid-19.