Profile Likelihood Analysis Research Articles

Critical look at the cosmological neutrino mass bound

Cosmological neutrino mass bounds are becoming increasingly stringent. The latest limit within ΛCDM from Planck 2018+ACT lensing+DESI is ∑mν<0.072 eV at 95% CL, very close to the minimum possible sum of neutrino masses (∑mν>0.06 eV), hinting at vanishing or even “negative” cosmological neutrino masses. In this context, it is urgent to carefully evaluate the origin of these cosmological constraints. In this paper, we investigate the robustness of these results in three ways: (i) we check the role of potential anomalies in Planck CMB and DESI BAO data; (ii) we compare the results for frequentist and Bayesian techniques, as very close to physical boundaries subtleties in the derivation and interpretation of constraints can arise; (iii) we investigate how deviations from ΛCDM, potentially alleviating these anomalies, can alter the constraints. From a profile likelihood analysis, we derive constraints in agreement at the ∼10% level with Bayesian posteriors. We find that the weak preference for negative neutrino masses is mostly present for Planck 18 data, affected by the well-known “lensing anomaly.” It disappears when the new Planck 2020 HiLLiPoP is used, leading to significantly weaker constraints. Additionally, the pull toward negative masses in DESI data stems from the z=0.7 bin, which contains a BAO measurement in ∼3σ tension with Planck expectations. Without this bin, and in combination with HiLLiPoP, the bound relaxes to ∑mν<0.11 eV at 95% CL. The recent preference for dynamical dark energy alleviates this tension and further weakens the bound. As we are at the dawn of a neutrino mass discovery from cosmology, it will be very exciting to see if this trend is confirmed by future data. Published by the American Physical Society 2024

BO4IO: A Bayesian optimization approach to inverse optimization with uncertainty quantification

Data-driven inverse optimization (IO) aims to estimate unknown parameters in an optimization model from observed decisions. The IO problem is commonly formulated as a large-scale bilevel program that is notoriously difficult to solve. We propose a derivative-free optimization approach based on Bayesian optimization, BO4IO, to solve general IO problems. The main advantages of BO4IO are two-fold: (i) it circumvents the need of complex reformulations or specialized algorithms and can hence enable computational tractability even when the underlying optimization problem is nonconvex or involves discrete variables, and (ii) it allows approximations of the profile likelihood, which provide uncertainty quantification on the IO parameter estimates. Our extensive computational results demonstrate the efficacy and robustness of BO4IO to estimate unknown parameters from small and noisy datasets. In addition, the proposed profile likelihood analysis effectively provides good approximations of the confidence intervals on the parameter estimates and assesses the identifiability of the unknown parameters.

Hints of neutrino dark matter scattering in the CMB? Constraints from the marginalized and profile distributions

We study scatterlike interactions between neutrinos and dark matter in light of different combinations of temperature, polarization and lensing data released by three independent CMB experiments—the Planck satellite, the Atacama Cosmology Telescope (ACT), and the South Pole Telescope (SPT)—in conjunction with baryon acoustic oscillation (BAO) measurements. We apply two different statistical methodologies. Alongside the usual marginalization technique, we cross-check all the results through a profile likelihood analysis. As a first step, working under the assumption of massless neutrinos, we perform a comprehensive (re)analysis aimed at assessing the validity of some recent results hinting at a mild preference for nonvanishing interactions from small-scale CMB data. We find compelling resilience in the results already documented in the literature, confirming that interactions with a strength uνDM∼10−5–10−4 appear to be globally favored by ACT (both alone and in combination with Planck). This result is corroborated by the inclusion of additional data, such as the recent ACT-DR6 lensing likelihood, as well as by the profile likelihood analysis. Interestingly, a fully consistent preference for interactions emerges from SPT, as well, although it is weaker than the one obtained from ACT. As a second step, we repeat the same analysis considering neutrinos as massive particles. Despite the larger parameter space, all the hints pointing towards interactions are confirmed also in this more realistic case. In addition, we report a very mild preference for interactions in Planck+BAO alone (not found in the massless case) which aligns with small-scale data. While this latter result is not fully confirmed by the profile likelihood analysis, the profile distribution does confirm that interactions are not disfavored by Planck. Published by the American Physical Society 2024

Computationally efficient framework for diagnosing, understanding and predicting biphasic population growth.

Throughout the life sciences, biological populations undergo multiple phases of growth, often referred to as biphasic growth for the commonly encountered situation involving two phases. Biphasic population growth occurs over a massive range of spatial and temporal scales, ranging from microscopic growth of tumours over several days, to decades-long regrowth of corals in coral reefs that can extend for hundreds of kilometres. Different mathematical models and statistical methods are used to diagnose, understand and predict biphasic growth. Common approaches can lead to inaccurate predictions of future growth that may result in inappropriate management and intervention strategies being implemented. Here, we develop a very general computationally efficient framework, based on profile likelihood analysis, for diagnosing, understanding and predicting biphasic population growth. The two key components of the framework are as follows: (i) an efficient method to form approximate confidence intervals for the change point of the growth dynamics and model parameters and (ii) parameter-wise profile predictions that systematically reveal the influence of individual model parameters on predictions. To illustrate our framework we explore real-world case studies across the life sciences.

Profile likelihood-based parameter and predictive interval analysis guides model choice for ecological population dynamics

Calibrating mathematical models to describe ecological data provides important insight via parameter estimation that is not possible from analysing data alone. When we undertake a mathematical modelling study of ecological or biological data, we must deal with the trade-off between data availability and model complexity. Dealing with the nexus between data availability and model complexity is an ongoing challenge in mathematical modelling, particularly in mathematical biology and mathematical ecology where data collection is often not standardised, and more broad questions about model selection remain relatively open. Therefore, choosing an appropriate model almost always requires case-by-case consideration. In this work we present a straightforward approach to quantitatively explore this trade-off using a case study exploring mathematical models of coral reef regrowth after some ecological disturbance, such as damage caused by a tropical cyclone. In particular, we compare a simple single species ordinary differential equation (ODE) model approach with a more complicated two-species coupled ODE model. Univariate profile likelihood analysis suggests that the both models are practically identifiable. To provide additional insight we construct and compare approximate prediction intervals using a new parameter-wise prediction approximation, confirming both the simple and complex models perform similarly with regard to making predictions. Our approximate parameter-wise prediction interval analysis provides explicit information about how each parameter affects the predictions of each model. Comparing our approximate prediction intervals with a more rigorous and computationally expensive evaluation of the full likelihood shows that the new approximations are reasonable in this case. All algorithms and software to support this work are freely available as jupyter notebooks on GitHub so that they can be adapted to deal with any other ODE-based models.

Model-based data analysis of tissue growth in thin 3D printed scaffolds

Tissue growth in three-dimensional (3D) printed scaffolds enables exploration and control of cell behaviour in more biologically realistic geometries than that allowed by traditional 2D cell culture. Cell proliferation and migration in these experiments have yet to be explicitly characterised, limiting the ability of experimentalists to determine the effects of various experimental conditions, such as scaffold geometry, on cell behaviour. We consider tissue growth by osteoblastic cells in melt electro-written scaffolds that comprise thin square pores with sizes that were deliberately increased between experiments. We collect highly detailed temporal measurements of the average cell density, tissue coverage, and tissue geometry. To quantify tissue growth in terms of the underlying cell proliferation and migration processes, we introduce and calibrate a mechanistic mathematical model based on the Porous-Fisher reaction–diffusion equation. Parameter estimates and uncertainty quantification through profile likelihood analysis reveal consistency in the rate of cell proliferation and steady-state cell density between pore sizes. This analysis also serves as an important model verification tool: while the use of reaction–diffusion models in biology is widespread, the appropriateness of these models to describe tissue growth in 3D scaffolds has yet to be explored. We find that the Porous-Fisher model is able to capture features relating to the cell density and tissue coverage, but is not able to capture geometric features relating to the circularity of the tissue interface. Our analysis identifies two distinct stages of tissue growth, suggests several areas for model refinement, and provides guidance for future experimental work that explores tissue growth in 3D printed scaffolds.

Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media.

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether these data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second, we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods, we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.

Probing sub-eV Dark Matter decays with PTOLEMY

When the Dark Matter mass is below the eV-scale, its cosmological occupation number exceeds the ones of photons from the cosmic microwave background as well as of relic neutrinos. If such Dark Matter decays to pairs of neutrinos, it implies that experiments that seek the detection of the cosmic neutrino background may as well be sensitive to this additional form of “dark radiation”. Here we study the prospects for detection taking into account various options for the forecasted performance of the future PTOLEMY experiment. From a detailed profile likelihood analysis we find that Dark Matter decays with lifetime as large as 104 Gyr or a sub-% Dark Matter fraction decaying today can be discovered. The prospects are facilitated by the distinct spectral event shape that is introduced from galactic and cosmological neutrino dark radiation fluxes. In the process we also clarify the importance of Pauli-blocking in the Dark Matter decay. The scenarios presented in this work can be considered early physics targets in the development of these instruments with relaxed demands on performance and energy resolution.

A multi-inverse approach for a holistic understanding of applied animal science systems

Technological and mathematical advances have provided opportunities to investigate new approaches for the holistic quantification of complex biological systems. One objective of these approaches, including the multi-inverse deterministic approach proposed in this paper, is to deepen the understanding of biological systems through the structural development of a useful, best-fitted inverse mechanistic model. The objective of the present work was to evaluate the capacity of a deterministic approach, that is, the multi-inverse approach (MIA), to yield meaningful quantitative nutritional information. To this end, a case study addressing the effect of diet composition on sheep weight was performed using data from a previous experiment on saccharina (a sugarcane byproduct), and an inverse deterministic model (named Paracoa) was developed. The MIA successfully revealed an increase in the final weight of sheep with an increase in the percentage of corn in the diet. Although the soluble fraction also increased with increasing corn percentage, the effective nonsoluble degradation increased fourfold, indicating that the increased weight gain resulted from the nonsoluble substrate. A profile likelihood analysis showed that the potential best-fitted model had identifiable parameters, and that the parameter relationships were affected by the type of data, number of parameters and model structure. It is necessary to apply the MIA to larger and/or more complex datasets to obtain a clearer understanding of its potential.

Recognizing Structural Nonidentifiability: When Experiments Do Not Provide Information About Important Parameters and Misleading Models Can Still Have Great Fit.

In the quest to model various phenomena, the foundational importance of parameter identifiability to sound statistical modeling may be less well appreciated than goodness of fit. Identifiability concerns the quality of objective information in data to facilitate estimation of a parameter, while nonidentifiability means there are parameters in a model about which the data provide little or no information. In purely empirical models where parsimonious good fit is the chief concern, nonidentifiability (or parameter redundancy) implies overparameterization of the model. In contrast, nonidentifiability implies underinformativeness of available data in mechanistically derived models where parameters are interpreted as having strong practical meaning. This study explores illustrative examples of structural nonidentifiability and its implications using mechanistically derived models (for repeated presence/absence analyses and dose-response of Escherichia coli O157:H7 and norovirus) drawn from quantitative microbial risk assessment. Following algebraic proof of nonidentifiability in these examples, profile likelihood analysis and Bayesian Markov Chain Monte Carlo with uniform priors are illustrated as tools to help detect model parameters that are not strongly identifiable. It is shown that identifiability should be considered during experimental design and ethics approval to ensure generated data can yield strong objective information about all mechanistic parameters of interest. When Bayesian methods are applied to a nonidentifiable model, the subjective prior effectively fabricates information about any parameters about which the data carry no objective information. Finally, structural nonidentifiability can lead to spurious models that fit data well but can yield severely flawed inferences and predictions when they are interpreted or used inappropriately.

Dark Matter Search Results from a One Ton-Year Exposure of XENON1T.

We report on a search for weakly interacting massive particles (WIMPs) using 278.8days of data collected with the XENON1T experiment at LNGS. XENON1T utilizes a liquid xenon time projection chamber with a fiducial mass of (1.30±0.01) ton, resulting in a 1.0ton yr exposure. The energy region of interest, [1.4,10.6] keV_{ee} ([4.9,40.9] keV_{nr}), exhibits an ultralow electron recoil background rate of [82_{-3}^{+5}(syst)±3(stat)] events/(ton yr keV_{ee}). No significant excess over background is found, and a profile likelihood analysis parametrized in spatial and energy dimensions excludes new parameter space for the WIMP-nucleon spin-independent elastic scatter cross section for WIMP masses above 6 GeV/c^{2}, with a minimum of 4.1×10^{-47} cm^{2} at 30 GeV/c^{2} and a 90%confidence level.

Direct estimation of 17 O MR images (DIESIS) for quantification of oxygen metabolism in the human brain with partial volume correction.

To provide a data post-processing method that corrects for partial volume effects (PVE) and fast decay in dynamic 17 O MRI for the mapping of cerebral metabolic rates of oxygen consumption (CMRO2 ). CMRO2 is altered in neurodegenerative diseases and tumors and can be measured after 17 O gas inhalation using dynamic 17 O MRI. CMRO2 quantification is difficult because of PVE. To correct for PVE, a direct estimation of the MR images (DIESIS) method is proposed and used in 4 dynamic 17 O MRI data sets of a healthy volunteer acquired on a 3T MRI system. With DIESIS, 17 O MR signal time curves in selected regions were directly estimated based on parcellation of a coregistered 1 H MPRAGE image. Profile likelihood analysis of the DIESIS method showed identifiability of CMRO2 . In white matter (WM), DIESES reduced CMRO2 from 0.97 ± 0.25 µmol/gtissue /min with Kaiser-Bessel gridding reconstruction to 0.85 ± 0.21 µmol/gtissue /min, whereas in gray matter (GM) it increases from 1.3 ± 0.31 µmol/gtissue /min to 1.86 ± 0.36 µmol/gtissue /min; both values are closer to the literature values from the 15 O-PET studies. DIESIS provided an increased separation of CMRO2 values in GM and WM brain regions and corrected for partial volume effects in 17 O-MRI inhalation experiments. DIESIS could also be applied to more heterogeneous tissues such as glioblastomas if subregions of the tumor can be represented as additional parcels.

Inverse hygric property determination based on dynamic measurements and swarm-intelligence optimisers

To accelerate the hygric characterisation of porous building materials, dynamic flow and storage measurements in combination with inverse parameter estimation show a lot of promise. Therein though, the processing and interpretation of the experimental output can be challenging. This paper demonstrates the applicability of two swarm-intelligence (SI) optimisers, i.e. the Particle Swarm Optimiser (PSO) and the Grey Wolf Optimiser (GWO), for determining the vapour resistance factor and the sorption isotherm of porous building materials. The methodology is presented for a fictitious dynamic vapour sorption experiment on a calcium silicate insulation sample. The identifiability of the unknown parameters and the reliability of the estimated properties is investigated via a profile likelihood (PL) analysis. By use of the proposed methodology, the measurement time required to determine the hygric properties is reduced strongly compared to standard techniques such as the steady-state cup and sorption tests, and at the same time the uncertainty propagated in the parameter estimation can be characterised. A close agreement with the target values is obtained. Though, to avoid an unreliable parameter estimation it is recommended to not limit the optimisation process to a single run. Furthermore, also the results obtained during the PL analysis can help improving the estimation. Finally, for the current case study, the SI optimisers are found to outperform the Genetic Algorithm (GA) and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES).

Search for bosonic super-WIMP interactions with the XENON100 experiment

We present results of searches for vector and pseudo-scalar bosonic super-WIMPs, which are dark matter candidates with masses at the keV-scale, with the XENON100 experiment. XENON100 is a dual-phase xenon time projection chamber operated at the Laboratori Nazionali del Gran Sasso. A profile likelihood analysis of data with an exposure of 224.6 live days $\times$ 34\,kg showed no evidence for a signal above the expected background. We thus obtain new and stringent upper limits in the $(8-125)$\,keV/c$^2$ mass range, excluding couplings to electrons with coupling constants of $g_{ae} > 3\times10^{-13}$ for pseudo-scalar and $\alpha'/\alpha > 2\times10^{-28}$ for vector super-WIMPs, respectively. These limits are derived under the assumption that super-WIMPs constitute all of the dark matter in our galaxy.

Comparison of statistical sampling methods with ScannerBit, the GAMBIT scanning module

We introduce ScannerBit, the statistics and sampling module of the public, open-source global fitting framework GAMBIT. ScannerBit provides a standardised interface to different sampling algorithms, enabling the use and comparison of multiple computational methods for inferring profile likelihoods, Bayesian posteriors, and other statistical quantities. The current version offers random, grid, raster, nested sampling, differential evolution, Markov Chain Monte Carlo (MCMC) and ensemble Monte Carlo samplers. We also announce the release of a new standalone differential evolution sampler, Diver, and describe its design, usage and interface to ScannerBit. We subject Diver and three other samplers (the nested sampler MultiNest, the MCMC GreAT, and the native ScannerBit implementation of the ensemble Monte Carlo algorithm T-Walk) to a battery of statistical tests. For this we use a realistic physical likelihood function, based on the scalar singlet model of dark matter. We examine the performance of each sampler as a function of its adjustable settings, and the dimensionality of the sampling problem. We evaluate performance on four metrics: optimality of the best fit found, completeness in exploring the best-fit region, number of likelihood evaluations, and total runtime. For Bayesian posterior estimation at high resolution, T-Walk provides the most accurate and timely mapping of the full parameter space. For profile likelihood analysis in less than about ten dimensions, we find that Diver and MultiNest score similarly in terms of best fit and speed, outperforming GreAT and T-Walk; in ten or more dimensions, Diver substantially outperforms the other three samplers on all metrics.

First Dark Matter Search Results from the XENON1T Experiment.

We report the first dark matter search results from XENON1T, a ∼2000-kg-target-mass dual-phase (liquid-gas) xenon time projection chamber in operation at the Laboratori Nazionali del Gran Sasso in Italy and the first ton-scale detector of this kind. The blinded search used 34.2 live days of data acquired between November 2016 and January 2017. Inside the (1042±12)-kg fiducial mass and in the [5,40] keV_{nr} energy range of interest for weakly interacting massive particle (WIMP) dark matter searches, the electronic recoil background was (1.93±0.25)×10^{-4} events/(kg×day×keV_{ee}), the lowest ever achieved in such a dark matter detector. A profile likelihood analysis shows that the data are consistent with the background-only hypothesis. We derive the most stringent exclusion limits on the spin-independent WIMP-nucleon interaction cross section for WIMP masses above 10 GeV/c^{2}, with a minimum of 7.7×10^{-47} cm^{2} for 35-GeV/c^{2} WIMPs at 90%C.L.

Hygric property determination based on dynamic measurement techniques and metaheuristic strategies

To speed up the hygric characterization of building materials dynamic measurements can be applied; the data-processing of their experimental output can however be challenging. This paper presents the applicability of a metaheuristic, in the current study the Grey Wolf Optimizer, for the estimation of the vapour transport properties based on a fictitious dynamic sorption experiment. A profile likelihood analysis is applied to check the identifiability of the parameters and to define the likelihood-based confidence intervals. For the estimation, two approaches are followed: (1) the estimation of physical parameters and (2) the estimation of non-physical parameters in a parametric function. Both approaches result in a close agreement with the target values. Though, not all parameters in the parametric function are practically identifiable and correlation is detected. Furthermore, the definition of the search space for the parameters in the parametric function may require some knowledge on the typical course of such a function.

Constraining Lorentz Invariance Violation Using the Crab Pulsar Emission Observed up to TeV Energies by MAGIC

Abstract Spontaneous breaking of Lorentz symmetry at energies on the order of the Planck energy or lower is predicted by many quantum gravity theories, implying non-trivial dispersion relations for the photon in vacuum. Consequently, gamma-rays of different energies, emitted simultaneously from astrophysical sources, could accumulate measurable differences in their time of flight until they reach the Earth. Such tests have been carried out in the past using fast variations of gamma-ray flux from pulsars, and more recently from active galactic nuclei and gamma-ray bursts. We present new constraints studying the gamma-ray emission of the galactic Crab Pulsar, recently observed up to TeV energies by the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) collaboration. A profile likelihood analysis of pulsar events reconstructed for energies above 400 GeV finds no significant variation in arrival time as their energy increases. Ninety-five percent CL limits are obtained on the effective Lorentz invariance violating energy scale at the level of ( ) for a linear, and ( ) for a quadratic scenario, for the subluminal and the superluminal cases, respectively. A substantial part of this study is dedicated to calibration of the test statistic, with respect to bias and coverage properties. Moreover, the limits take into account systematic uncertainties, which are found to worsen the statistical limits by about 36%–42%. Our constraints would have been much more stringent if the intrinsic pulse shape of the pulsar between 200 GeV and 400 GeV was understood in sufficient detail and allowed inclusion of events well below 400 GeV.

Halo-independent determination of the unmodulated WIMP signal in DAMA: the isotropic case

We present a halo-independent determination of the unmodulated signal corresponding to the DAMA modulation if interpreted as due to dark matter weakly interacting massive particles (WIMPs). First we show how a modulated signal gives information on the WIMP velocity distribution function in the Galactic rest frame from which the unmodulated signal descends. Then we describe a mathematically-sound profile likelihood analysis in which the likelihood is profiled over a continuum of nuisance parameters (namely, the WIMP velocity distribution). As a first application of the method, which is very general and valid for any class of velocity distributions, we restrict the analysis to velocity distributions that are isotropic in the Galactic frame. In this way we obtain halo-independent maximum-likelihood estimates and confidence intervals for the DAMA unmodulated signal. We find that the estimated unmodulated signal is in line with expectations for a WIMP-induced modulation and is compatible with the DAMA background+signal rate. Specifically, for the isotropic case we find that the modulated amplitude ranges between a few percent and about 25% of the unmodulated amplitude, depending on the WIMP mass.

Search for WIMP inelastic scattering off xenon nuclei with XENON100

We present the first constraints on the spin-dependent, inelastic scattering cross section of Weakly Interacting Massive Particles (WIMPs) on nucleons from XENON100 data with an exposure of 7.64$\times$10$^3$\,kg\,day. XENON100 is a dual-phase xenon time projection chamber with 62\,kg of active mass, operated at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy and designed to search for nuclear recoils from WIMP-nucleus interactions. Here we explore inelastic scattering, where a transition to a low-lying excited nuclear state of $^{129}$Xe is induced. The experimental signature is a nuclear recoil observed together with the prompt de-excitation photon. We see no evidence for such inelastic WIMP-$^{129}$Xe interactions. A profile likelihood analysis allows us to set a 90\% C.L. upper limit on the inelastic, spin-dependent WIMP-nucleon cross section of $3.3 \times 10^{-38}$\,cm$^{2}$ at 100\,GeV/c$^2$. This is the most constraining result to date, and sets the pathway for an analysis of this interaction channel in upcoming, larger dual-phase xenon detectors.