Multilevel Delayed Acceptance MCMC with Applications to Hydrogeological Inverse Problems

Quantifying the uncertainty of model predictions is a critical task for engineering decision support systems. This is a particularly challenging effort in the context of statistical inverse problems, where the model parameters are unknown or poorly constrained, and where the data is often scarce. Many such problems emerge in the fields of hydrology and hydro--environmental engineering in general, and in hydrogeology in particular. While methods for rigorously quantifying the uncertainty of such problems exist, they are often prohibitively computationally expensive, particularly when the forward model is high--dimensional and expensive to evaluate. In this thesis, I present a Metropolis--Hastings algorithm, namely the Multilevel Delayed Acceptance (MLDA) algorithm, which exploits a hierarchy of forward models of increasing computational cost to significantly reduce the total cost of quantifying the uncertainty of high--dimensional, expensive forward models. The algorithm is shown to be in detailed balance with the posterior distribution of parameters, and the computational gains of the algorithm is demonstrated on multiple examples. Additionally, I present an approach for exploiting a deep neural network as an ultra--fast model approximation in an MLDA model hierarchy. This method is demonstrated in the context of both 2D and 3D groundwater flow modelling. Finally, I present a novel approach to adaptive optimal design of groundwater surveying, in which MLDA is employed to construct the posterior Monte Carlo estimates. This method utilises the posterior uncertainty of the primary problem in conjunction with the expected solution to an adjoint problem to sequentially determine the optimal location of the next datapoint.Engineering and Physical Sciences Research Council (EPSRC)Alan Turing InstituteEngineering and Physical Sciences Research Council (EPSRC

Is the Prognosis of Osgood-Schlatter Poorer Than Anticipated?:A Prospective Cohort Study With 24-Month Follow-up

BACKGROUND: Osgood-Schlatter disease (OSD), an apophyseal injury of the tibial tuberosity, affects up to 1 in 10 adolescents. This condition has previously been assumed to be innocuous and to self-resolve with limited intervention. PURPOSE: To investigate the 24-month prognosis of OSD and examine if ultrasound (US) classification is associated with outcomes. STUDY DESIGN: Case series; Level of evidence, 4. METHODS: This study included a preregistered prospective cohort of 51 adolescents (aged 10-14 years) diagnosed with OSD who were evaluated for 24 months. The primary outcome at 24-month follow-up was whether participants continued to experience OSD-related knee pain. Baseline US scans were collected and characterized by OSD type (De Flaviis classification) as well as maturation of the tibial tuberosity. Secondary outcomes included sports participation, Knee injury and Osteoarthritis Outcome Score (KOOS) Sport/Recreation subscale, and health-related quality of life (European Quality of Life–5 Dimensions–Youth [EQ-5D-Y]). All participants were invited for re-examination by US at follow-up. RESULTS: A total of 51 patients preregistered for the study, with 90% (n = 46) available at follow-up. Of these 46 participants, 37% (n = 17) still reported knee pain due to OSD. In this subgroup, the median duration since symptom onset was 42 months (interquartile range, 38-51 months). More than 1 in 5 participants reported stopping sport due to knee pain, and those who continued to experience knee pain reported significantly worse KOOS Sport/Recreation scores at follow-up compared with patients with no knee pain (mean 74 [95% CI, 63-84] vs 91 [95% CI, 85-97]). Participants with continued OSD-related pain also had lower health-related quality of life (mean difference in EQ-5D-Y, 0.11 [95% CI, 0.06-0.13]). Higher De Flaviis classification at baseline was significantly associated with an increased risk of knee pain at 2 years. Diagnostic US at follow-up demonstrated primarily tendon changes (thickening, positive Doppler signal), as well as an ununited ossicle in 32% of participants who underwent US scanning at follow-up. CONCLUSION: Over one-third of the study participants had knee pain at 2-year follow-up, which was associated with lower sports related function and health related quality of life. This questions the assumption that all patients with OSD experience quick recovery. Participants without any changes on imaging at baseline were less likely to report pain at follow-up

Care-seeking behaviour of adolescents with patellofemoral pain: a retrospective cohort study [version 1; peer review: 2 approved]

Aim: The aim of this study was to assess the care-seeking behaviour among adolescents with patellofemoral pain (PFP). Methods: This retrospective study included data on 121 adolescents with PFP enrolled in a randomized controlled trial. A questionnaire was sent to the general practitioner (GP) of each adolescent, assessing information on the consultation dates for knee pain, potential diagnoses, and treatment provided. Results: 106/121 adolescents had been in contact with their GP, and 95 medical records of adolescents were available. Of the 95 adolescents with available medical records 60 had consulted their GP for knee pain. The median number of contacts was 1.5 (range 1-7). The GPs initiated treatment for 48 of the 60 adolescents and in most cases it was information and advice (36/48) or pain medication to a minor extent (6/48). Out of the 60 adolescents who consulted their GP 26 were subsequently referred to different types of health care professionals, in 11 out of 26 to physiotherapy, but also to the department of rheumatology or orthopaedics. Conclusions: 63% of adolescents diagnosed with PFP had previously consulted their GP due to knee pain. Several types of treatments were initiated by the GP, but most commonly advice and information were given. Standardized and evidence-based treatment guidelines for adolescent knee pain in general practice are neede

Antiangiogenic therapy for breast cancer

Angiogenesis is an important component of cancer growth, invasion and metastasis. Therefore, inhibition of angiogenesis is an attractive strategy for treatment of cancer. We describe existing clinical trials of antiangiogenic agents and the challenges facing the clinical development and optimal use of these agents for the treatment of breast cancer. Currently, the most promising approach has been the use of bevacizumab, a humanized monoclonal antibody directed against the most potent pro-angiogenic factor, vascular endothelial growth factor (VEGF). Small molecular inhibitors of VEGF tyrosine kinase activity, such as sorafenib, appear promising. While, the role of sunitinib and inhibitors of mammalian target of rapamycin (mTOR) in breast cancer has to be defined. Several unanswered questions remain, such as choice of drug(s), optimal duration of therapy and patient selection criteria

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Code to reproduce results from "Where to Drill Next? A Dual-Weighted Approach to Adaptive Optimal Design of Groundwater Surveys"

Python code which sets up a synthetic groundwater flow example, extracts data from 8 random locations and then runs an MCMC sampler to quantify the uncertainty. After completing the initial run, it will choose 8 additional sampling locations based on the "Vanilla" and "Dual-Weighted" criteria described in the paper. The script is set up to work in batches because of memory constraints. Each run of the code will repeat the procedure described above 5 times and save the results in the "results" folder. The batch number (0-5) must be given as a command line argument: "python3 run_batch.py "This is the code used for the Lykkegaard & Dodwell (2022) article "Where to Drill Next? A Dual-Weighted Approach to Adaptive Optimal Design of Groundwater Surveys".Engineering and Physical Sciences Research Council (EPSRC)Alan Turing Institut