7 research outputs found
Accelerating Parallel Tempering: Quantile Tempering Algorithm (QuanTA)
Using MCMC to sample from a target distribution, on a
-dimensional state space can be a difficult and computationally expensive
problem. Particularly when the target exhibits multimodality, then the
traditional methods can fail to explore the entire state space and this results
in a bias sample output. Methods to overcome this issue include the parallel
tempering algorithm which utilises an augmented state space approach to help
the Markov chain traverse regions of low probability density and reach other
modes. This method suffers from the curse of dimensionality which dramatically
slows the transfer of mixing information from the auxiliary targets to the
target of interest as . This paper introduces a novel
prototype algorithm, QuanTA, that uses a Gaussian motivated transformation in
an attempt to accelerate the mixing through the temperature schedule of a
parallel tempering algorithm. This new algorithm is accompanied by a
comprehensive theoretical analysis quantifying the improved efficiency and
scalability of the approach; concluding that under weak regularity conditions
the new approach gives accelerated mixing through the temperature schedule.
Empirical evidence of the effectiveness of this new algorithm is illustrated on
canonical examples
Weight-Preserving Simulated Tempering
Simulated tempering is popular method of allowing MCMC algorithms to move
between modes of a multimodal target density {\pi}. One problem with simulated
tempering for multimodal targets is that the weights of the various modes
change for different inverse-temperature values, sometimes dramatically so. In
this paper, we provide a fix to overcome this problem, by adjusting the mode
weights to be preserved (i.e., constant) over different inverse-temperature
settings. We then apply simulated tempering algorithms to multimodal targets
using our mode weight correction. We present simulations in which our
weight-preserving algorithm mixes between modes much more successfully than
traditional tempering algorithms. We also prove a diffusion limit for an
version of our algorithm, which shows that under appropriate assumptions, our
algorithm mixes in time O(d [log d]^2)
Skew brownian motion and complexity of the alps algorithm
Simulated tempering is a popular method of allowing Markov chain Monte Carlo algorithms to move between modes of a multimodal target density π . Tawn, Moores and Roberts (2021) introduces the Annealed Leap-Point Sampler (ALPS) to allow for rapid movement between modes. In this paper we prove that, under appropriate assumptions, a suitably scaled version of the ALPS algorithm converges weakly to skew Brownian motion. Our results show that, under appropriate assumptions, the ALPS algorithm mixes in time O(d[logd]2) or O(d), depending on which version is used
Evaluation of prognostic risk models for postoperative pulmonary complications in adult patients undergoing major abdominal surgery: a systematic review and international external validation cohort study
Background Stratifying risk of postoperative pulmonary complications after major abdominal surgery allows clinicians to modify risk through targeted interventions and enhanced monitoring. In this study, we aimed to identify and validate prognostic models against a new consensus definition of postoperative pulmonary complications. Methods We did a systematic review and international external validation cohort study. The systematic review was done in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. We searched MEDLINE and Embase on March 1, 2020, for articles published in English that reported on risk prediction models for postoperative pulmonary complications following abdominal surgery. External validation of existing models was done within a prospective international cohort study of adult patients (≥18 years) undergoing major abdominal surgery. Data were collected between Jan 1, 2019, and April 30, 2019, in the UK, Ireland, and Australia. Discriminative ability and prognostic accuracy summary statistics were compared between models for the 30-day postoperative pulmonary complication rate as defined by the Standardised Endpoints in Perioperative Medicine Core Outcome Measures in Perioperative and Anaesthetic Care (StEP-COMPAC). Model performance was compared using the area under the receiver operating characteristic curve (AUROCC). Findings In total, we identified 2903 records from our literature search; of which, 2514 (86·6%) unique records were screened, 121 (4·8%) of 2514 full texts were assessed for eligibility, and 29 unique prognostic models were identified. Nine (31·0%) of 29 models had score development reported only, 19 (65·5%) had undergone internal validation, and only four (13·8%) had been externally validated. Data to validate six eligible models were collected in the international external validation cohort study. Data from 11 591 patients were available, with an overall postoperative pulmonary complication rate of 7·8% (n=903). None of the six models showed good discrimination (defined as AUROCC ≥0·70) for identifying postoperative pulmonary complications, with the Assess Respiratory Risk in Surgical Patients in Catalonia score showing the best discrimination (AUROCC 0·700 [95% CI 0·683–0·717]). Interpretation In the pre-COVID-19 pandemic data, variability in the risk of pulmonary complications (StEP-COMPAC definition) following major abdominal surgery was poorly described by existing prognostication tools. To improve surgical safety during the COVID-19 pandemic recovery and beyond, novel risk stratification tools are required. Funding British Journal of Surgery Society