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Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology, borrowing ideas from statistical physics and computational chemistry, for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process. Joint configurations of the underlying process noise and of parameters, mapping onto diffusion paths consistent with observations, form an implicitly defined manifold. Then, by making use of a constrained Hamiltonian Monte Carlo algorithm on the embedded manifold, we are able to perform computationally efficient inference for a class of discretely observed diffusion models. Critically, in contrast with other approaches proposed in the literature, our methodology is highly automated, requiring minimal user intervention and applying alike in a range of settings, including: elliptic or hypo-elliptic systems; observations with or without noise; linear or non-linear observation operators. Exploiting Markovianity, we propose a variant of the method with complexity that scales linearly in the resolution of path discretisation and the number of observation times. Python code reproducing the results is available at //doi.org/10.5281/zenodo.5796148

Randomized experiments (trials) are the gold standard for making causal inferences because randomization removes systematic confounding and the need for assuming any data-generating (super-population) models. However, outcome misclassification (e.g. measurement error or reporting bias in binary outcomes) often exists in practice and even a few misclassified outcomes may distort a causal conclusion drawn from a randomized experiment. All existing approaches to outcome misclassification rely on some data-generating model and therefore may not be applicable to randomized experiments without additional strong assumptions. We propose a model-free and finite-population-exact framework for randomized experiments subject to outcome misclassification, which does not require adding any additional assumptions to a randomized experiment. A central quantity in our framework is "warning accuracy," defined as the threshold such that the causal conclusion drawn from the measured outcomes may differ from that based on the true outcomes if the accuracy of the measured outcomes did not surpass that threshold. We show how learning the warning accuracy and related information and a dual concept can benefit the design, analysis, and validation of a randomized experiment. We show that the warning accuracy can be computed efficiently (even for large datasets) by adaptively reformulating an integer quadratically constrained linear program with respect to the randomization design. Our framework covers both Fisher's sharp null and Neyman's weak null, works for a wide range of randomization designs, and can also be applied to observational studies adopting randomization-based inference. We apply our framework to a large randomized clinical trial of the prevention of prostate cancer.

Sepsis is a life-threatening medical emergency, which is a major cause of death worldwide and the second highest cause of mortality in the United States. Researching the optimal control treatment or intervention strategy on the comprehensive sepsis system is key in reducing mortality. For this purpose, first, this paper improves a complex nonlinear sepsis model proposed in our previous work. Then, bifurcation analyses are conducted for each sepsis subsystem to study the model behaviors under some system parameters. The bifurcation analysis results also further indicate the necessity of control treatment and intervention therapy. If the sepsis system is without adding any control under some parameter and initial system value settings, the system will perform persistent inflammation outcomes as time goes by. Therefore, we develop our complex improved nonlinear sepsis model into a sepsis optimal control model, and then use some effective biomarkers recommended in existing clinic practices as optimization objective function to measure the development of sepsis. Besides that, a Bayesian optimization algorithm by combining Recurrent neural network (RNN-BO algorithm) is introduced to predict the optimal control strategy for the studied sepsis optimal control system. The difference between the RNN-BO algorithm from other optimization algorithms is that once given any new initial system value setting (initial value is associated with the initial conditions of patients), the RNN-BO algorithm is capable of quickly predicting a corresponding time-series optimal control based on the historical optimal control data for any new sepsis patient. To demonstrate the effectiveness and efficiency of the RNN-BO algorithm on solving the optimal control solution on the complex nonlinear sepsis system, some numerical simulations are implemented by comparing with other optimization algorithms in this paper.

Ordinal cumulative probability models (CPMs) -- also known as cumulative link models -- such as the proportional odds regression model are typically used for discrete ordered outcomes, but can accommodate both continuous and mixed discrete/continuous outcomes since these are also ordered. Recent papers describe ordinal CPMs in this setting using non-parametric maximum likelihood estimation. We formulate a Bayesian CPM for continuous or mixed outcome data. Bayesian CPMs inherit many of the benefits of frequentist CPMs and have advantages with regard to interpretation, flexibility, and exact inference (within simulation error) for parameters and functions of parameters. We explore characteristics of the Bayesian CPM through simulations and a case study using HIV biomarker data. In addition, we provide the package 'bayesCPM' which implements Bayesian CPM models using the R interface to the Stan probabilistic programing language. The Bayesian CPM for continuous outcomes can be implemented with only minor modifications to the prior specification and, despite some limitations, has generally good statistical performance with moderate or large sample sizes.

Optimal experimental design (OED) plays an important role in the problem of identifying uncertainty with limited experimental data. In many applications, we seek to minimize the uncertainty of a predicted quantity of interest (QoI) based on the solution of the inverse problem, rather than the inversion model parameter itself. In these scenarios, we develop an efficient method for goal-oriented optimal experimental design (GOOED) for large-scale Bayesian linear inverse problem that finds sensor locations to maximize the expected information gain (EIG) for a predicted QoI. By deriving a new formula to compute the EIG, exploiting low-rank structures of two appropriate operators, we are able to employ an online-offline decomposition scheme and a swapping greedy algorithm to maximize the EIG at a cost measured in model solutions that is independent of the problem dimensions. We provide detailed error analysis of the approximated EIG, and demonstrate the efficiency, accuracy, and both data- and parameter-dimension independence of the proposed algorithm for a contaminant transport inverse problem with infinite-dimensional parameter field.

We perform a systematic analysis of the quality of fit of the stochastic block model (SBM) for 275 empirical networks spanning a wide range of domains and orders of size magnitude. We employ posterior predictive model checking as a criterion to assess the quality of fit, which involves comparing networks generated by the inferred model with the empirical network, according to a set of network descriptors. We observe that the SBM is capable of providing an accurate description for the majority of networks considered, but falls short of saturating all modeling requirements. In particular, networks possessing a large diameter and slow-mixing random walks tend to be badly described by the SBM. However, contrary to what is often assumed, networks with a high abundance of triangles can be well described by the SBM in many cases. We demonstrate that simple network descriptors can be used to evaluate whether or not the SBM can provide a sufficiently accurate representation, potentially pointing to possible model extensions that can systematically improve the expressiveness of this class of models.

Estimating the effects of interventions on patient outcome is one of the key aspects of personalized medicine. Their inference is often challenged by the fact that the training data comprises only the outcome for the administered treatment, and not for alternative treatments (the so-called counterfactual outcomes). Several methods were suggested for this scenario based on observational data, i.e.~data where the intervention was not applied randomly, for both continuous and binary outcome variables. However, patient outcome is often recorded in terms of time-to-event data, comprising right-censored event times if an event does not occur within the observation period. Albeit their enormous importance, time-to-event data is rarely used for treatment optimization. We suggest an approach named BITES (Balanced Individual Treatment Effect for Survival data), which combines a treatment-specific semi-parametric Cox loss with a treatment-balanced deep neural network; i.e.~we regularize differences between treated and non-treated patients using Integral Probability Metrics (IPM). We show in simulation studies that this approach outperforms the state of the art. Further, we demonstrate in an application to a cohort of breast cancer patients that hormone treatment can be optimized based on six routine parameters. We successfully validated this finding in an independent cohort. BITES is provided as an easy-to-use python implementation.

Estimation of heterogeneous treatment effects is an active area of research in causal inference. Most of the existing methods, however, focus on estimating the conditional average treatment effects of a single, binary treatment given a set of pre-treatment covariates. In this paper, we propose a method to estimate the heterogeneous causal effects of high-dimensional treatments, which poses unique challenges in terms of estimation and interpretation. The proposed approach is based on a Bayesian mixture of regularized regressions to identify groups of units who exhibit similar patterns of treatment effects. By directly modeling cluster membership with covariates, the proposed methodology allows one to explore the unit characteristics that are associated with different patterns of treatment effects. Our motivating application is conjoint analysis, which is a popular survey experiment in social science and marketing research and is based on a high-dimensional factorial design. We apply the proposed methodology to the conjoint data, where survey respondents are asked to select one of two immigrant profiles with randomly selected attributes. We find that a group of respondents with a relatively high degree of prejudice appears to discriminate against immigrants from non-European countries like Iraq. An open-source software package is available for implementing the proposed methodology.

This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many applications in statistics, applied mathematics, signal processing and machine learning. This article provides a comprehensive study of the state-of-the-art of the topic. We highlight limitations, benefits, connections and differences among the different techniques. Problems and possible solutions with the use of improper priors are also described. Some of the most relevant methodologies are compared through theoretical comparisons and numerical experiments.

The positive definiteness of discrete time-fractional derivatives is fundamental to the numerical stability (in the energy sense) for time-fractional phase-field models. A novel technique is proposed to estimate the minimum eigenvalue of discrete convolution kernels generated by the nonuniform L1, half-grid based L1 and time-averaged L1 formulas of the fractional Caputo's derivative. The main discrete tools are the discrete orthogonal convolution kernels and discrete complementary convolution kernels. Certain variational energy dissipation laws at discrete levels of the variable-step L1-type methods are then established for time-fractional Cahn-Hilliard model.They are shown to be asymptotically compatible, in the fractional order limit $\alpha\rightarrow1$, with the associated energy dissipation law for the classical Cahn-Hilliard equation. Numerical examples together with an adaptive time-stepping procedure are provided to demonstrate the effectiveness of the proposed methods.