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Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
The virtues of an effective field theory (EFT) approach to many-body problems are illustrated by deriving the expansion for the energy of an homogeneous, interacting Fermi gas at low density and zero temperature. A renormalization scheme…
We present a Bayesian analysis of renormalization-group invariant nucleon-nucleon interactions at leading order in chiral effective field theory ($\chi$EFT) with momentum cutoffs in the range 400--4000 MeV. We use history matching to…
Accurate ab initio modelling of surfaces and interfaces, especially under an applied external potential bias, is important for describing and characterizing various phenomena that occur in electronic, catalytic, and energy storage devices.…
Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…
This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…
The current Bayesian FFT algorithm relies on direct differentiation to obtain the posterior covariance matrix (PCM), which is time-consuming, memory-intensive, and hard to code, especially for the multi-setup operational modal analysis…
I summarise a method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories which are non-perturbative at leading order. It uses the fact that the Renormalisation Group evolution of an observable…
We treat low-energy $^3$He-$\alpha$ elastic scattering in an Effective Field Theory (EFT) that exploits the separation of scales in this reaction. We compute the amplitude up to Next-to-Next-to-Leading Order (NNLO), developing a hierarchy…
Assuming the presence of physics beyond the Standard Model (SM) with a characteristic scale M ~ O(10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the…
In this dissertation, I introduce the principles and methods of effective field theory and describe my work in three EFTs: First, in the perturbative QCD region, I use soft collinear effective theory (SCET) to prove that strong interaction…
In the absence of a theory of everything, modern physicists need to rely on other predictive tools and turned to Effective Field Theories (EFTs) in a number of fields, including but not limited to statistical mechanics, condensed matter,…
Constraining the equation of state (EOS) of strongly interacting, dense matter is the focus of intense experimental, observational, and theoretical effort. Chiral effective field theory ($\chi$EFT) can describe the EOS between the typical…
Effective field theories (EFT) are commonly used to parameterize effects of BSM physics in vector boson scattering (VBS). For Wilson coefficients which are large enough to produce presently observable effects, the validity range of the EFT…
We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint…
The characteristics of a meaningful effective field theory (EFT) analysis are discussed and compared with traditional approaches to NN scattering. A key feature of an EFT treatment is a systematic expansion in powers of momentum, which is…
This paper studies an entropy-based multi-objective Bayesian optimization (MBO). The entropy search is successful approach to Bayesian optimization. However, for MBO, existing entropy-based methods ignore trade-off among objectives or…
We discuss an effective field theory (EFT) approach to the computation of fluctuation-induced interactions between particles bound to a thermally fluctuating fluid surface controlled by surface tension. By describing particles as points,…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
We show that perturbative techniques inspired by effective field theory (EFT) can be used to "paint on" the 21~cm field during reionization using only the underlying linear density field. This procedure is accurate to within O(10%) on large…