14 research outputs found
Multilevel Delayed Acceptance MCMC
We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a
hierarchy of models of increasing complexity to efficiently generate samples
from an unnormalized target distribution. Broadly, the method rewrites the
Multilevel MCMC approach of Dodwell et al. (2015) in terms of the Delayed
Acceptance (DA) MCMC of Christen & Fox (2005). In particular, DA is extended to
use a hierarchy of models of arbitrary depth, and allow subchains of arbitrary
length. We show that the algorithm satisfies detailed balance, hence is ergodic
for the target distribution. Furthermore, multilevel variance reduction is
derived that exploits the multiple levels and subchains, and an adaptive
multilevel correction to coarse-level biases is developed. Three numerical
examples of Bayesian inverse problems are presented that demonstrate the
advantages of these novel methods. The software and examples are available in
PyMC3.Comment: 29 pages, 12 figure
Gaussian Process Regression models for the properties of micro-tearing modes in spherical tokamak
Spherical tokamaks (STs) have many desirable features that make them an
attractive choice for a future fusion power plant. Power plant viability is
intrinsically related to plasma heat and particle confinement and this is often
determined by the level of micro-instability driven turbulence. Accurate
calculation of the properties of turbulent micro-instabilities is therefore
critical for tokamak design, however, the evaluation of these properties is
computationally expensive. The considerable number of geometric and
thermodynamic parameters and the high resolutions required to accurately
resolve these instabilities makes repeated use of direct numerical simulations
in integrated modelling workflows extremely computationally challenging and
creates the need for fast, accurate, reduced-order models.
This paper outlines the development of a data-driven reduced-order model,
often termed a {\it surrogate model} for the properties of micro-tearing modes
(MTMs) across a spherical tokamak reactor-relevant parameter space utilising
Gaussian Process Regression (GPR) and classification; techniques from machine
learning. These two components are used in an active learning loop to maximise
the efficiency of data acquisition thus minimising computational cost. The
high-fidelity gyrokinetic code GS2 is used to calculate the linear properties
of the MTMs: the mode growth rate, frequency and normalised electron heat flux;
core components of a quasi-linear transport model. Five-fold cross-validation
and direct validation on unseen data is used to ascertain the performance of
the resulting surrogate models
Self-management including exercise, education and activity modification compared to usual care for adolescents with Osgood-Schlatter (the SOGOOD trial):protocol of a randomized controlled superiority trial
BACKGROUND: Osgood-Schlatter is the most frequent growth-related injury affecting about 10% of physically active adolescents. It can cause long-term pain and limitations in sports and physical activity, with potential sequela well into adulthood. The management of Osgood-Schlatter is very heterogeneous. Recent systematic reviews have found low level evidence for surgical intervention and injection therapies, and an absence of studies on conservative management. Recently, a novel self-management approach with exercise, education, and activity modification, demonstrated favorable outcomes for adolescents with patellofemoral pain and Osgood-Schlatter in prospective cohort studies.AIM: The aim of this trial is to assess the effectiveness of the novel self-management approach compared to usual care in improving self-reported knee-related function in sport (measured using the KOOS-child 'Sport/play' subscale) after a 5-month period.METHODS: This trial is a pragmatic, assessor-blinded, randomized controlled trial with a two-group parallel arm design, including participants aged 10-16 years diagnosed with Osgood-Schlatter. Participants will receive 3 months of treatment, consisting of either usual care or the self-management approach including exercise, education, and activity modification, followed by 2 months of self-management. Primary endpoint is the KOOS-child 'Sport/play' score at 5 months. This protocol details the planned methods and procedures.DISCUSSION: The novel approach has already shown promise in previous cohort studies. This trial will potentially provide much-needed level 1 evidence for the effectiveness of the self-management approach, representing a crucial step towards addressing the long-term pain and limitations associated with Osgood-Schlatter.TRIAL REGISTRATION: Clinicaltrials.gov: NCT05174182. Prospectively registered December 30th 2021. Date of first recruitment: January 3rd 2022. Target sample size: 130 participants.</p
Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3
Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be
prohibitively expensive for target probability densities with expensive
likelihood functions, for instance when the evaluation it involves solving a
Partial Differential Equation (PDE), as is the case in a wide range of
engineering applications. Multilevel Delayed Acceptance (MLDA) with an Adaptive
Error Model (AEM) is a novel approach, which alleviates this problem by
exploiting a hierarchy of models, with increasing complexity and cost, and
correcting the inexpensive models on-the-fly. The method has been integrated
within the open-source probabilistic programming package PyMC3 and is available
in the latest development version. In this paper, the algorithm is presented
along with an illustrative example.Comment: 8 pages, 4 figures, accepted for Machine Learning for Engineering
Modeling, Simulation, and Design Workshop at Neural Information Processing
Systems 202