Model-informed precision dosing (MIPD) using therapeutic drug/biomarker monitoring offers the opportunity to significantly improve the efficacy and safety of drug therapies. Current strategies comprise model-informed dosing tables or are based on maximum a-posteriori estimates. These approaches, however, lack a quantification of uncertainty and/or consider only part of the available patient-specific information. We propose three novel approaches for MIPD employing Bayesian data assimilation (DA) and/or reinforcement learning (RL) to control neutropenia, the major dose-limiting side effect in anticancer chemotherapy. These approaches have the potential to substantially reduce the incidence of life-threatening grade 4 and subtherapeutic grade 0 neutropenia compared to existing approaches. We further show that RL allows to gain further insights by identifying patient factors that drive dose decisions. Due to its flexibility, the proposed combined DA-RL approach can easily be extended to integrate multiple endpoints or patient-reported outcomes, thereby promising important benefits for future personalized therapies.

Finite mixture models are a widely-used tool for modeling heterogeneous data, consisting of hidden subpopulations with distinct distributions. For applications exhibiting continuous data, location-scale Gaussian mixtures are arguably the most popular family of parametric mixture models. Beyond their broad applications as a modeling and clustering tool in the social, physical and life sciences (McLachlan & Peel 2004), Gaussian mixtures provide a flexible approach to density estimation (Genovese & Wasserman 2000, Ghosal & van der Vaart 2001). Estimating the parameters of a mixture model is crucial for quantifying the underlying heterogeneity of the data. One of the most widely-used approaches is the maximum likelihood estimator (MLE). A Gaussian mixture model with a known number of components K, all of which are well-separated, forms a regular parametric model for which the MLE achieves the standard parametric estimation rate (Ho & Nguyen 2016b, Chen 2017). Such rates are typically understood in terms of convergence of mixing measures, quantified using the Wasserstein distance as a means of avoiding label switching issues inherent in mixture modeling (Nguyen 2013).

Simulators often require calibration inputs estimated from real world data and the quality of the estimate can significantly affect simulation output. Particularly when performing simulation optimisation to find an optimal solution, the uncertainty in the inputs significantly affects the quality of the found solution. One remedy is to search for the solution that has the best performance on average over the uncertain range of inputs yielding an optimal compromise solution. We consider the more general setting where a user may choose between either running simulations or instead collecting real world data. A user may choose an input and a solution and observe the simulation output, or instead query an external data source improving the input estimate enabling the search for a more focused, less compromised solution. We explicitly examine the trade-off between simulation and real data collection in order to find the optimal solution of the simulator with the true inputs. Using a value of information procedure, we propose a novel unified simulation optimisation procedure called Bayesian Information Collection and Optimisation (BICO) that, in each iteration, automatically determines which of the two actions (running simulations or data collection) is more beneficial. Numerical experiments demonstrate that the proposed algorithm is able to automatically determine an appropriate balance between optimisation and data collection.

This paper provides the foundations of a unified cognitive decision-making framework (QulBIT) which is derived from quantum theory. The main advantage of this framework is that it can cater for paradoxical and irrational human decision making. Although quantum approaches for cognition have demonstrated advantages over classical probabilistic approaches and bounded rationality models, they still lack explanatory power. To address this, we introduce a novel explanatory analysis of the decision-maker's belief space. This is achieved by exploiting quantum interference effects as a way of both quantifying and explaining the decision-maker's uncertainty. We detail the main modules of the unified framework, the explanatory analysis method, and illustrate their application in situations violating the Sure Thing Principle.

Deep neural networks have revolutionized medical image analysis and disease diagnosis. Despite their impressive performance, it is difficult to generate well-calibrated probabilistic outputs for such networks, which makes them uninterpretable black boxes. Bayesian neural networks provide a principled approach for modelling uncertainty and increasing patient safety, but they have a large computational overhead and provide limited improvement in calibration. In this work, by taking skin lesion classification as an example task, we show that by shifting Bayesian inference to the functional space we can craft meaningful priors that give better calibrated uncertainty estimates at a much lower computational cost.

This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state observation data. Inverse problems for chaotic systems are numerically challenging as small perturbations in model parameters can cause very large changes in estimated forward trajectories. Bayesian Artificial Neural Networks can be used to simultaneously fit a model and estimate model parameter uncertainty. Knowledge of model parameter uncertainty can then be incorporated into the probabilistic estimates of the inferred system's forward time evolution. The method is demonstrated numerically by analysing the chaotic Sprott B system. Observations of the system are used to estimate a posterior predictive distribution over the weights of a parametric polynomial kernel Artificial Neural Network. It is shown that the proposed method is able to perform accurate time predictions. Further, the proposed method is able to correctly account for model uncertainties and provide useful prediction uncertainty bounds.

Machine learning has seen in the last 5-10 years an explosion in its growth from a research centered area of computer science and mathematics to a driving force for innovation in every aspect of our lives [1, 2, 3]. This was driven mainly by the success of deep learning and the significant investment of big technology firms in open source machine learning research [4, 5, 6]. Real life machine learning based solutions often require a number of models to work together to achieve the business goal of the product(s) [7]. Such models can be trained independently or as part of an optimised training pipeline [8, 9]. Breaking down the product into multiple models has several advantages: I) It allows for parallel model development with model designers focused on solving relatively small and well-defined problems.

Bayesian Networks (BN) are probabilistic graphical models that are widely used for uncertainty modeling, stochastic prediction and probabilistic inference. A Quantum Bayesian Network (QBN) is a quantum version of the Bayesian network that utilizes the principles of quantum mechanical systems to improve the computational performance of various analyses. In this paper, we experimentally evaluate the performance of QBN on various IBM QX hardware against Qiskit simulator and classical analysis. We consider a 4-node BN for stock prediction for our experimental evaluation. We construct a quantum circuit to represent the 4-node BN using Qiskit, and run the circuit on nine IBM quantum devices: Yorktown, Vigo, Ourense, Essex, Burlington, London, Rome, Athens and Melbourne. We will also compare the performance of each device across the four levels of optimization performed by the IBM Transpiler when mapping a given quantum circuit to a given device. We use the root mean square percentage error as the metric for performance comparison of various hardware.

This paper presents a new approach to generate samples from conditional belief functions for a restricted but non trivial subset of conditional belief functions. It assumes the factorization (decomposition) of a belief function along a bayesian network structure. It applies general conditional belief functions. The most profoundly studied measure of uncertainty is the probability. There exist methods of so-called graphoidal representation of joint probability distribution - called Bayesian networks [7] - allowing for expression of qualitative independence, causality, efficient reasoning, explanation, learning from data and sample generation.

Estimation of the number of components (or order) of a finite mixture model is a long standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure---a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods which fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous function of the model parameters. More specifically, given a conservative upper bound on the order, the GSF groups and sorts mixture component parameters to fuse those which are redundant. For a wide range of finite mixture models, we show that the GSF is consistent in estimating the true mixture order and achieves the $n^{-1/2}$ convergence rate for parameter estimation up to polylogarithmic factors. The GSF is implemented for several univariate and multivariate mixture models in the R package GroupSortFuse. Its finite sample performance is supported by a thorough simulation study, and its application is illustrated on two real data examples.