We investigate Bayesian and frequentist approaches to resonance searches using a toy model based on an ATLAS search for the Higgs boson in the diphoton channel. We draw pseudo-data from the background only model and background plus signal model at multiple luminosities, from about 0 to 10${}^6$/fb. We chart the change in the Bayesian posterior of the background only model and the global p-value. We find that, as anticipated, the posterior converges to certainty about the model as luminosity increases. The p-value, on the other hand, randomly walks between 0 and 1 under the background only model. After briefly commenting on the frequentist properties of the posterior, we make a direct comparison of the significances obtained in Bayesian and frequentist frameworks. We find that the well-known look-elsewhere effect reduces local significances by about 1$\sigma$. We furthermore find a previously unknown effect: significances from our Bayesian framework are typically about 1 to 2$\sigma$ smaller than the global significances. This suggests that even global significances could significantly overstate the evidence against the background only model. This effect - the Bayes effect - could radically change our interpretation of the evidence for new physics in resonance searches. We checked that the effect was robust with respect to thirteen choices of prior.

We perform frequentist and Bayesian statistical analyses of Higgs- and Z-portal models of dark matter particles with spin 0, ¹⁄₂ and 1. Our analyses incorporate data from direct detection and indirect detection experiments, as well as LHC searches for monojet and monophoton events, and we also analyze the potential impacts of future direct detection experiments. We find acceptable regions of the parameter spaces for Higgs-portal models with real scalar, neutral vector, Majorana or Dirac fermion dark matter particles, and Z-portal models with Majorana or Dirac fermion dark matter particles. In many of these cases, there are interesting prospects for discovering dark matter particles in Higgs or Z decays, as well as dark matter particles weighing 100 GeV. Negative results from planned direct detection experiments would still allow acceptable regions for Higgs- and Z-portal models with Majorana or Dirac fermion dark matter particles.

The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a $\mathbb{Z}_3$ conserving semi-constrained Next-to-Minimal Supersymmetric Standard Model (NMSSM) to the constrained MSSM (CMSSM). We contrast popular fine-tuning measures with naturalness priors, which automatically appear in statistical measures of the plausibility that a given model reproduces the weak scale. Our comparison shows that naturalness priors provide valuable insight into the hierarchy problem and rigorously ground naturalness in Bayesian statistics. For the CMSSM and semi-constrained NMSSM we demonstrate qualitative agreement between naturalness priors and popular fine tuning measures. Thus, we give a clear plausibility argument that favours relatively light superpartners.

Using the DAMA/LIBRA anomaly as an example, we formalise the notion of halo-independence in the context of Bayesian statistics and quantified maximum entropy. We consider an infinite set of possible profiles, weighted by an entropic prior and constrained by a likelihood describing noisy measurements of modulated moments by DAMA/LIBRA. We find the most plausible dark matter (DM) profiles and predictions for unmodulated signal rates at DAMA/LIBRA. The entropic prior contains an a priori unknown regularisation factor, $\beta$, that describes the strength of our conviction that the profile is approximately Maxwellian. By varying $\beta$, we smoothly interpolate between a halo-independent and a halo-dependent analysis, thus exploring the impact of prior information about the DM profile.

A new gauge singlet scalar field can undergo a strongly first-order phase transition (PT) leading to gravitational waves (GW) potentially observable at aLIGO and simultaneously stabilize the electroweak vacuum. aLIGO (O5) is potentially sensitive to cosmological PTs at $10^7$-$10^8$ GeV, which coincides with the requirement that the singlet scale is less than the Standard Model (SM) vacuum instability scale, which is between $10^8$ GeV and $10^{14}$ GeV. After sampling its parameter space, we identify three benchmark points with a PT at about $T \approx 10^7$ GeV in a gauge singlet extension of the SM. We calculate the nucleation temperature, order parameter, characteristic timescale, and peak amplitude and frequency of GW from bubble collisions during the PT for the benchmarks and find that, in an optimistic scenario, GW from such a PT may be in reach of aLIGO (O5). We confirm that the singlet stabilizes the electroweak vacuum whilst remaining consistent with zero-temperature phenomenology as well. Thus, this scenario presents an intriguing possibility that aLIGO may detect traces of fundamental physics motivated by vacuum stability at an energy scale that is well above the reach of any other experiment.