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Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at Zenodo.

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at Zenodo.

Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation algorithms that are not yet widely used in particle astrophysics, benchmark them against random sampling and existing techniques, and perform a detailed comparison of their performance on a range of test functions. These include four analytic test functions of varying dimensionality, and a realistic example derived from a recent global fit of weak-scale supersymmetry. Although the best algorithm to use depends on the function being investigated, we are able to present general conclusions about the relative merits of random sampling, Differential Evolution, Particle Swarm Optimisation, the Covariance Matrix Adaptation Evolution Strategy, Bayesian Optimisation, Grey Wolf Optimisation, and the PyGMO Artificial Bee Colony, Gaussian Particle Filter and Adaptive Memory Programming for Global Optimisation algorithms.

We introduce CosmoBit, a module within the open-source GAMBIT software framework for exploring connections between cosmology and particle physics with joint global fits. CosmoBit provides a flexible framework for studying various scenarios beyond ACDM, such as models of inflation, modifications of the effective number of relativistic degrees of freedom, exotic energy injection from annihilating or decaying dark matter, and variations of the properties of elementary particles such as neutrino masses and the lifetime of the neutron. Many observables and likelihoods in CosmoBit are computed via interfaces to AlterBBN, CLASS, DarkAges, MontePython, MultiModeCode, and plc. This makes it possible to apply a wide range of constraints from large-scale structure, Type Ia supernovae, Big Bang Nucleosynthesis and the cosmic microwave background. Parameter scans can be performed using the many different statistical sampling algorithms available within the GAMBIT framework, and results can be combined with calculations from other GAMBIT modules focused on particle physics and dark matter. We include extensive validation plots and a first application to scenarios with non-standard relativistic degrees of freedom and neutrino temperature, showing that the corresponding constraint on the sum of neutrino masses is much weaker than in the standard scenario.

Sky survey telescopes and powerful targeted telescopes play complementary roles in astronomy. In order to investigate the nature and characteristics of the motions of very faint objects, a flexibly-pointed instrument capable of high astrometric accuracy is an ideal complement to current astrometric surveys and a unique tool for precision astrophysics. Such a space-based mission will push the frontier of precision astrometry from evidence of Earth-mass habitable worlds around the nearest stars, to distant Milky Way objects, and out to the Local Group of galaxies. As we enter the era of the James Webb Space Telescope and the new ground-based, adaptive-optics-enabled giant telescopes, by obtaining these high precision measurements on key objects that Gaia could not reach, a mission that focuses on high precision astrometry science can consolidate our theoretical understanding of the local Universe, enable extrapolation of physical processes to remote redshifts, and derive a much more consistent picture of cosmological evolution and the likely fate of our cosmos. Already several missions have been proposed to address the science case of faint objects in motion using high precision astrometry missions: NEAT proposed for the ESA M3 opportunity, micro-NEAT for the S1 opportunity, and Theia for the M4 and M5 opportunities. Additional new mission configurations adapted with technological innovations could be envisioned to pursue accurate measurements of these extremely small motions. The goal of this White Paper is to address the fundamental science questions that are at stake when we focus on the motions of faint sky objects and to briefly review instrumentation and mission profiles.

We present global analyses of effective Higgs portal dark matter models in the frequentist and Bayesian statistical frameworks. Complementing earlier studies of the scalar Higgs portal, we use GAMBIT to determine the preferred mass and coupling ranges for models with vector, Majorana and Dirac fermion dark matter. We also assess the relative plausibility of all four models using Bayesian model comparison. Our analysis includes up-to-date likelihood functions for the dark matter relic density, invisible Higgs decays, and direct and indirect searches for weakly-interacting dark matter including the latest XENON1T data. We also account for important uncertainties arising from the local density and velocity distribution of dark matter, nuclear matrix elements relevant to direct detection, and Standard Model masses and couplings. In all Higgs portal models, we find parameter regions that can explain all of dark matter and give a good fit to all data. The case of vector dark matter requires the most tuning and is therefore slightly disfavoured from a Bayesian point of view. In the case of fermionic dark matter, we find a strong preference for including a CP-violating phase that allows suppression of constraints from direct detection experiments, with odds in favour of CP violation of the order of 100:1. Finally, we present DDCalc2.0.0, a tool for calculating direct detection observables and likelihoods for arbitrary non-relativistic effective operators.

In Ref. (GAMBIT Collaboration: Athron et. al., Eur. Phys. J. C. arXiv: 1705.07908, 2017) we introduced the global-fitting framework GAMBIT. In this addendum, we describe a new minor version increment of this package. GAMBIT 1.1 includes full support for Mathematica backends, which we describe in some detail here. As an example, we backend SUSYHD (Vega and Villadoro, JHEP 07: 159, 2015), which calculates the mass of the Higgs boson in the MSSM from effective field theory. We also describe updated likelihoods in PrecisionBit and DarkBit, and updated decay data included in DecayBit.

We present the GAMBIT modules SpecBit, DecayBit and PrecisionBit. Together they provide a new framework for linking publicly available spectrum generators, decay codes and other precision observable calculations in a physically and statistically consistent manner. This allows users to automatically run various combinations of existing codes as if they are a single package. The modular design allows software packages fulfilling the same role to be exchanged freely at runtime, with the results presented in a common format that can easily be passed to downstream dark matter, collider and flavour codes. These modules constitute an essential part of the broader GAMBIT framework, a major new software package for performing global fits. In this paper we present the observable calculations, data, and likelihood functions implemented in the three modules, as well as the conventions and assumptions used in interfacing them with external codes. We also present 3-BIT-HIT, a command-line utility for computing mass spectra, couplings, decays and precision observables in the MSSM, which shows how the three modules can easily be used independently of GAMBIT.

We present global analyses of effective Higgs portal dark matter models in the frequentist and Bayesian statistical frameworks. Complementing earlier studies of the scalar Higgs portal, we use GAMBIT to determine the preferred mass and coupling ranges for models with vector, Majorana and Dirac fermion dark matter. We also assess the relative plausibility of all four models using Bayesian model comparison. Our analysis includes up-to-date likelihood functions for the dark matter relic density, invisible Higgs decays, and direct and indirect searches for weakly-interacting dark matter including the latest XENON1T data. We also account for important uncertainties arising from the local density and velocity distribution of dark matter, nuclear matrix elements relevant to direct detection, and Standard Model masses and couplings. In all Higgs portal models, we find parameter regions that can explain all of dark matter and give a good fit to all data. The case of vector dark matter requires the most tuning and is therefore slightly disfavoured from a Bayesian point of view. In the case of fermionic dark matter, we find a strong preference for including a CP-violating phase that allows suppression of constraints from direct detection experiments, with odds in favour of CP violation of the order of 100:1. Finally, we present DDCalc 2.0.0, a tool for calculating direct detection observables and likelihoods for arbitrary non-relativistic effective operators., Comment: 30 pages, 12 figures. v2 matches the published version

We present global fits of cosmologically stable axion-like particle and QCD axion models in the mass range 0.1 neV to 10 eV. We focus on the case where the Peccei-Quinn symmetry is broken before the end of inflation, such that the initial value of the axion field can be considered to be homogeneous throughout the visible Universe. We include detailed likelihood functions from light-shining-through-wall experiments, haloscopes, helioscopes, the axion relic density, horizontal branch stars, supernova 1987A, white dwarf cooling, and gamma-ray observations. We carry out both frequentist and Bayesian analyses, with and without the inclusion of white dwarf cooling. We explore the degree of fine-tuning present in different models and identify parameter regions where it is possible for QCD axion models to account for both the dark matter in the Universe and the cooling hints, comparing them to specific DFSZ- and KSVZ-type models. We find the most credible parameter regions, allowing us to set (prior-dependent) upper and lower bounds on the axion mass. Our analysis also suggests that QCD axions in this scenario most probably make up a non-negligible but sub-dominant component of the dark matter in the Universe., Comment: 77 pages, 29 figures. Version v3: revised version of the paper due to a bug in the code (see Footnote 2); please use GAMBIT 1.3.1 or newer. Updated supplementary material available on Zenodo (version v3) at http://dx.doi.org/10.5281/zenodo.2615235

Searches for supersymmetric electroweakinos have entered a crucial phase, as the integrated luminosity of the Large Hadron Collider is now high enough to compensate for their weak production cross-sections. Working in a framework where the neutralinos and charginos are the only light sparticles in the Minimal Supersymmetric Standard Model, we use gambit to perform a detailed likelihood analysis of the electroweakino sector. We focus on the impacts of recent ATLAS and CMS searches with 36 fb$^{-1}$ of 13 TeV proton-proton collision data. We also include constraints from LEP and invisible decays of the $Z$ and Higgs bosons. Under the background-only hypothesis, we show that current LHC searches do not robustly exclude any range of neutralino or chargino masses. However, a pattern of excesses in several LHC analyses points towards a possible signal, with neutralino masses of $(m_{\tilde{\chi}_1^0}, m_{\tilde{\chi}_2^0}, m_{\tilde{\chi}_3^0}, m_{\tilde{\chi}_4^0})$ = (8-155, 103-260, 130-473, 219-502) GeV and chargino masses of $(m_{\tilde{\chi}_1^{\pm}}, m_{\tilde{\chi}_2^{\pm}})$ = (104-259, 224-507) GeV at the 95% confidence level. The lightest neutralino is mostly bino, with a possible modest Higgsino or wino component. We find that this excess has a combined local significance of $3.3\sigma$, subject to a number of cautions. If one includes LHC searches for charginos and neutralinos conducted with 8 TeV proton-proton collision data, the local significance is lowered to 2.9$\sigma$. We briefly consider the implications for dark matter, finding that the correct relic density can be obtained through the Higgs-funnel and $Z$-funnel mechanisms, even assuming that all other sparticles are decoupled. All samples, gambit input files and best-fit models from this study are available on Zenodo., Comment: 38 pages, 16 figures, v3 is the version accepted by EPJC

The search for the particle nature of dark matter has given rise to a number of experimental, theoretical and statistical challenges. Here, we report on a number of these statistical challenges and new techniques to address them, as discussed in the DMStat workshop held Feb 26 - Mar 3 2018 at the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Alberta., Comment: 32 pages, 8 figures, 331 references

I provide a brief summary of the status of supersymmetric models with parameters defined at either the unification or weak scale, based on global fits using the GAMBIT framework., Comment: 4 pages, 3 figures, proceedings of invited contribution to Rencontres de Moriond QCD 2018

This handbook is designed to provide parents with information about gifted children and the Gifted & Talented Education (G.A.T.E.) Program. An initial section reviews California legislation regarding gifted students. Characteristics of gifted and talented children are described and suggestions are given for parents to enhance young children's development. Common myths about gifted children are explored. Identification efforts focus on students with high intellectual ability and/or high achievement. Among goals of the gifted program are differentiated learning opportunities and opportunities for developing healthy self concepts. Program options are cited for elementary (cluster groups and special day classes) as well as secondary programs. Desirable characteristics for teachers of gifted students are listed. A final section discusses ways in which parents can help their children, including allowing time to daydream and understanding the difference between encouraging and pushing them. Organizations and resources for parents are listed, followed by resources for students. (CL)