A5069105224- Statistical Methods and Inference
- Gaussian Processes and Bayesian Inference
- Bayesian Methods and Mixture Models
- Fault Detection and Control Systems
- Markov Chains and Monte Carlo Methods
- Financial Risk and Volatility Modeling
- Control Systems and Identification
- Statistical Methods and Bayesian Inference
- Statistical Distribution Estimation and Applications
- Target Tracking and Data Fusion in Sensor Networks
- Parallel Computing and Optimization Techniques
- Machine Learning and Algorithms
- Advanced Statistical Process Monitoring
- Machine Learning in Materials Science
- Machine Learning in Healthcare
- Simulation Techniques and Applications
- Neural Networks and Applications
- Protein Kinase Regulation and GTPase Signaling
- Theoretical and Computational Physics
- Cardiac electrophysiology and arrhythmias
- bioluminescence and chemiluminescence research
- Advanced Memory and Neural Computing
- Blind Source Separation Techniques
- Forecasting Techniques and Applications
- Probabilistic and Robust Engineering Design
King's College London
2019-2022
Turing Institute
2021-2022
The Alan Turing Institute
2020-2022
University of Cambridge
2015-2020
Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific simulations in clinical care will give rise the development virtual cohorts models. These allow capture and quantify inter-patient variability. However, require transformation modelling from small numbers bespoke robust rapid workflows that can create large In this review, we describe state art models, process creating how generate individual cohort member followed by a discussion...
Abstract The use of heuristics to assess the convergence and compress output Markov chain Monte Carlo can be sub-optimal in terms empirical approximations that are produced. Typically a number initial states attributed ‘burn in’ removed, while remainder is ‘thinned’ if compression also required. In this paper, we consider problem retrospectively selecting subset states, fixed cardinality, from sample path such approximation provided by their distribution close optimal. A novel method...
Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun explore adopt UQ methods characterise uncertainty model inputs how that propagates through outputs or predictions. In this perspective piece we draw attention an important under-addressed source our predictions -- the structure equations themselves. difference between imperfect reality termed discrepancy, are often uncertain as size...
Markov chain Monte Carlo (MCMC) is the engine of modern Bayesian statistics, being used to approximate posterior and derived quantities interest. Despite this, issue how output from a post-processed reported often overlooked. Convergence diagnostics can be control bias via burn-in removal, but these do not account for (common) situations where limited computational budget engenders bias-variance trade-off. The aim this article review state-of-the-art techniques post-processing output. Our...
In this paper we extend to the multidimensional case modified Poisson series representation of linear stochastic processes driven by α-stable innovations. The latter has been recently introduced in literature and it involves a Gaussian approximation residuals series, via exact characterization their moments. This allows for Bayesian techniques parameter or state inference that would not be available otherwise, due lack closed-form likelihood function distribution. Simulation results are...
In this paper we introduce a new class of state space models based on shot-noise simulation representations nonGaussian Lévy-driven linear systems, represented as stochastic differential equations. particular conditionally Gaussian version the is proposed that able to capture heavy-tailed non-Gaussianity while retaining tractability for inference procedures. We focus canonical such processes, α-stable Lévy which retain important properties self-similarity and heavy-tails, emphasizing broader...
The results of a series theoretical studies are reported, examining the convergence rate for different approximate representations α-stable distributions. Although they play key role in modelling random processes with jumps and discontinuities, use distributions inference often leads to analytically intractable problems. LePage series, which is probabilistic representation employed this work, used transform an intractable, infinite-dimensional problem into finite-dimensional (conditionally...
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., approximate target distribution by representative point set. We consider sequential algorithms that greedily minimise MMD over discrete candidate propose novel non-myopic algorithm and, in order both improve statistical efficiency and reduce computational cost, we investigate variant applies this technique mini-batch the set at each iteration. When points are...
We report the results of a series numerical studies examining convergence rate for some approximate representations α-stable distributions, which are highly intractable class distributions inference purposes. Our proposed representation turns an infinite-dimensional parameters into (approximately) conditionally Gaussian representation, to standard procedures such as Expectation-Maximization (EM), Markov chain Monte Carlo (MCMC) and Particle Filtering can be readily applied. While we have...
The α-stable distribution is very useful for modelling data with extreme values and skewed behaviour. governed by two key parameters, tail thickness skewness, in addition to scale location. Inferring these parameters difficult due the lack of a closed form expression probability density. We develop Bayesian method, based on pseudo-marginal MCMC approach, that requires only unbiased estimates intractable likelihood. To compute we build an adaptive importance sampler latentvariable-...
The α-stable distribution is highly intractable for inference because of the lack a closed form density function in general case. However, it well-established that admits Poisson series representation (PSR) which terms are arrival times unit rate process. In our previous work, we have shown how to carry out regression models using this representation, leads very convenient conditionally Gaussian framework, amenable tractable procedures. PSR has be truncated finite number practical purposes....
We report the results of several theoretical studies into convergence rate for certain random series representations α -stable variables, which are motivated by and find application in modelling heavy-tailed noise time analysis, inference, stochastic processes. The use distributions generally leads to analytically intractable inference problems. particular version Poisson representation invoked here implies that resulting "conditionally Gaussian," is relatively straightforward, although an...
The use of heuristics to assess the convergence and compress output Markov chain Monte Carlo can be sub-optimal in terms empirical approximations that are produced. Typically a number initial states attributed "burn in" removed, whilst remainder is "thinned" if compression also required. In this paper we consider problem retrospectively selecting subset states, fixed cardinality, from sample path such approximation provided by their distribution close optimal. A novel method proposed, based...
The results of a series theoretical studies are reported, examining the convergence rate for different approximate representations $\alpha$-stable distributions. Although they play key role in modelling random processes with jumps and discontinuities, use distributions inference often leads to analytically intractable problems. LePage series, which is probabilistic representation employed this work, used transform an intractable, infinite-dimensional problem into conditionally Gaussian...
In this paper we introduce a new class of state space models based on shot-noise simulation representations non-Gaussian L\'evy-driven linear systems, represented as stochastic differential equations. particular conditionally Gaussian version the is proposed that able to capture heavy-tailed non-Gaussianity while retaining tractability for inference procedures. We focus canonical such processes, $\alpha$-stable L\'evy which retain important properties self-similarity and heavy-tails,...