arXiv subjects

Mikael Kuusela

Publications and source records attributed to Mikael Kuusela.

33 records · Page 2Linked to original sources

arXiv2024

Spatio-temporal methods for estimating subsurface ocean thermal response to tropical cyclones

Tropical cyclones (TCs), driven by heat exchange between the air and sea, pose a substantial risk to many communities around the world. Accurate characterization of the subsurface ocean thermal response to TC passage is crucial for accurate TC intensity forecasts and for an understanding of the role that TCs play in the global climate system. However, that characterization is complicated by the high-noise ocean environment, correlations inherent in spatio-temporal data, relative scarcity of in situ observations, and the entanglement of the TC-induced signal with seasonal signals. We present a general methodological framework that addresses these difficulties, integrating existing techniques in seasonal mean field estimation, Gaussian process modeling, and nonparametric regression into an ANOVA decomposition model. Importantly, we improve upon past work by properly handling seasonality, providing rigorous uncertainty quantification, and treating time as a continuous variable, rather than producing estimates that are binned in time. This ANOVA model is estimated using in situ subsurface temperature profiles from the Argo fleet of autonomous floats through a multi-step procedure, which (1) characterizes the upper ocean seasonal shift during the TC season; (2) models the variability in the temperature observations; (3) fits a thin plate spline using the variability estimates to account for heteroskedasticity and correlation between the observations. This spline fit reveals the ocean thermal response to TC passage. Through this framework, we obtain new scientific insights into the interaction between TCs and the ocean on a global scale, including a three-dimensional characterization of the near-surface and subsurface cooling along the TC storm track and the mixing-induced subsurface warming on the track's right side.

stat.AP↗

arXiv2023

Posterior Uncertainty Estimation via a Monte Carlo Procedure Specialized for Data Assimilation

Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stochastic approximations. In the carbon flux inversion literature, Chevallier et al. proposed a stochastic method capable of approximating posterior variances of linear functionals of the model parameters that is particularly well-suited for large-scale Earth-system data assimilation tasks. This note formalizes this algorithm and clarifies its properties. We provide a formal statement of the algorithm, demonstrate why it converges to the desired posterior variance quantity of interest, and provide additional uncertainty quantification allowing incorporation of the Monte Carlo sampling uncertainty into the method's Bayesian credible intervals. The methodology is demonstrated using toy simulations and a realistic carbon flux inversion observing system simulation experiment.

stat.CO↗

arXiv2023

Simulator-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problems

Prediction algorithms, such as deep neural networks (DNNs), are used in many domain sciences to directly estimate internal parameters of interest in simulator-based models, especially in settings where the observations include images or complex high-dimensional data. In parallel, modern neural density estimators, such as normalizing flows, are becoming increasingly popular for uncertainty quantification, especially when both parameters and observations are high-dimensional. However, parameter inference is an inverse problem and not a prediction task; thus, an open challenge is to construct conditionally valid and precise confidence regions, with a guaranteed probability of covering the true parameters of the data-generating process, no matter what the (unknown) parameter values are, and without relying on large-sample theory. Many simulator-based inference (SBI) methods are indeed known to produce biased or overly confident parameter regions, yielding misleading uncertainty estimates. This paper presents WALDO, a novel method to construct confidence regions with finite-sample conditional validity by leveraging prediction algorithms or posterior estimators that are currently widely adopted in SBI. WALDO reframes the well-known Wald test statistic, and uses a computationally efficient regression-based machinery for classical Neyman inversion of hypothesis tests. We apply our method to a recent high-energy physics problem, where prediction with DNNs has previously led to estimates with prediction bias. We also illustrate how our approach can correct overly confident posterior regions computed with normalizing flows.

stat.ML↗

arXiv2023

Statistical constraints on climate model parameters using a scalable cloud-based inference framework

Atmospheric aerosols influence the Earth's climate, primarily by affecting cloud formation and scattering visible radiation. However, aerosol-related physical processes in climate simulations are highly uncertain. Constraining these processes could help improve model-based climate predictions. We propose a scalable statistical framework for constraining parameters in expensive climate models by comparing model outputs with observations. Using the C3.ai Suite, a cloud computing platform, we use a perturbed parameter ensemble of the UKESM1 climate model to efficiently train a surrogate model. A method for estimating a data-driven model discrepancy term is described. The strict bounds method is applied to quantify parametric uncertainty in a principled way. We demonstrate the scalability of this framework with two weeks' worth of simulated aerosol optical depth data over the South Atlantic and Central African region, written from the model every three hours and matched in time to twice-daily MODIS satellite observations. When constraining the model using real satellite observations, we establish constraints on combinations of two model parameters using much higher time-resolution outputs from the climate model than previous studies. This result suggests that, within the limits imposed by an imperfect climate model, potentially very powerful constraints may be achieved when our framework is scaled to the analysis of more observations and for longer time periods.

stat.AP↗

arXiv2022

Model-Independent Detection of New Physics Signals Using Interpretable Semi-Supervised Classifier Tests

A central goal in experimental high energy physics is to detect new physics signals that are not explained by known physics. In this paper, we aim to search for new signals that appear as deviations from known Standard Model physics in high-dimensional particle physics data. To do this, we determine whether there is any statistically significant difference between the distribution of Standard Model background samples and the distribution of the experimental observations, which are a mixture of the background and a potential new signal. Traditionally, one also assumes access to a sample from a model for the hypothesized signal distribution. Here we instead investigate a model-independent method that does not make any assumptions about the signal and uses a semi-supervised classifier to detect the presence of the signal in the experimental data. We construct three test statistics using the classifier: an estimated likelihood ratio test (LRT) statistic, a test based on the area under the ROC curve (AUC), and a test based on the misclassification error (MCE). Additionally, we propose a method for estimating the signal strength parameter and explore active subspace methods to interpret the proposed semi-supervised classifier in order to understand the properties of the detected signal. We also propose a Score test statistic that can be used in the model-dependent setting. We investigate the performance of the methods on a simulated data set related to the search for the Higgs boson at the Large Hadron Collider at CERN. We demonstrate that the semi-supervised tests have power competitive with the classical supervised methods for a well-specified signal, but much higher power for an unexpected signal which might be entirely missed by the supervised tests.

stat.AP↗

arXiv2022

Spatio-temporal Local Interpolation of Global Ocean Heat Transport using Argo Floats: A Debiased Latent Gaussian Process Approach

The world ocean plays a key role in redistributing heat in the climate system and hence in regulating Earth's climate. Yet statistical analysis of ocean heat transport suffers from partially incomplete large-scale data intertwined with complex spatio-temporal dynamics, as well as from potential model misspecification. We present a comprehensive spatio-temporal statistical framework tailored to interpolating the global ocean heat transport using in-situ Argo profiling float measurements. We formalize the statistical challenges using latent local Gaussian process regression accompanied by a two-stage fitting procedure. We introduce an approximate Expectation-Maximization algorithm to jointly estimate both the mean field and the covariance parameters, and refine the potentially under-specified mean field model with a debiasing procedure. This approach provides data-driven global ocean heat transport fields that vary in both space and time and can provide insights into crucial dynamical phenomena, such as El Ni{ñ}o \& La Ni{ñ}a, as well as the global climatological mean heat transport field, which by itself is of scientific interest. The proposed framework and the Argo-based estimates are thoroughly validated with state-of-the-art multimission satellite products and shown to yield realistic subsurface ocean heat transport estimates.

stat.AP↗

arXiv2022

Objective frequentist uncertainty quantification for atmospheric CO$_2$ retrievals

The steadily increasing amount of atmospheric carbon dioxide (CO$_2$) is affecting the global climate system and threatening the long-term sustainability of Earth's ecosystem. In order to better understand the sources and sinks of CO$_2$, NASA operates the Orbiting Carbon Observatory-2 & 3 satellites to monitor CO$_2$ from space. These satellites make passive radiance measurements of the sunlight reflected off the Earth's surface in different spectral bands, which are then inverted in an ill-posed inverse problem to obtain estimates of the atmospheric CO$_2$ concentration. In this work, we propose a new CO$_2$ retrieval method that uses known physical constraints on the state variables and direct inversion of the target functional of interest to construct well-calibrated frequentist confidence intervals based on convex programming. We compare the method with the current operational retrieval procedure, which uses prior knowledge in the form of probability distributions to regularize the problem. We demonstrate that the proposed intervals consistently achieve the desired frequentist coverage, while the operational uncertainties are poorly calibrated in a frequentist sense both at individual locations and over a spatial region in a realistic simulation experiment. We also study the influence of specific nuisance state variables on the length of the proposed intervals and identify certain key variables that can greatly reduce the final uncertainty given additional deterministic or probabilistic constraints, and develop a principled framework to incorporate such information into our method.

stat.AP↗

arXiv2022

Uncertainty quantification for wide-bin unfolding: one-at-a-time strict bounds and prior-optimized confidence intervals

Unfolding is an ill-posed inverse problem in particle physics aiming to infer a true particle-level spectrum from smeared detector-level data. For computational and practical reasons, these spaces are typically discretized using histograms, and the smearing is modeled through a response matrix corresponding to a discretized smearing kernel of the particle detector. This response matrix depends on the unknown shape of the true spectrum, leading to a fundamental systematic uncertainty in the unfolding problem. To handle the ill-posed nature of the problem, common approaches regularize the problem either directly via methods such as Tikhonov regularization, or implicitly by using wide-bins in the true space that match the resolution of the detector. Unfortunately, both of these methods lead to a non-trivial bias in the unfolded estimator, thereby hampering frequentist coverage guarantees for confidence intervals constructed from these methods. We propose two new approaches to addressing the bias in the wide-bin setting through methods called One-at-a-time Strict Bounds (OSB) and Prior-Optimized (PO) intervals. The OSB intervals are a bin-wise modification of an existing guaranteed-coverage procedure, while the PO intervals are based on a decision-theoretic view of the problem. Importantly, both approaches provide well-calibrated frequentist confidence intervals even in constrained and rank-deficient settings. These methods are built upon a more general answer to the wide-bin bias problem, involving unfolding with fine bins first, followed by constructing confidence intervals for linear functionals of the fine-bin counts. We test and compare these methods to other available methodologies in a wide-bin deconvolution example and a realistic particle physics simulation of unfolding a steeply falling particle spectrum.

stat.AP↗

arXiv2018

Locally stationary spatio-temporal interpolation of Argo profiling float data

Argo floats measure seawater temperature and salinity in the upper 2,000 m of the global ocean. Statistical analysis of the resulting spatio-temporal dataset is challenging due to its nonstationary structure and large size. We propose mapping these data using locally stationary Gaussian process regression where covariance parameter estimation and spatio-temporal prediction are carried out in a moving-window fashion. This yields computationally tractable nonstationary anomaly fields without the need to explicitly model the nonstationary covariance structure. We also investigate Student-$t$ distributed fine-scale variation as a means to account for non-Gaussian heavy tails in ocean temperature data. Cross-validation studies comparing the proposed approach with the existing state-of-the-art demonstrate clear improvements in point predictions and show that accounting for the nonstationarity and non-Gaussianity is crucial for obtaining well-calibrated uncertainties. This approach also provides data-driven local estimates of the spatial and temporal dependence scales for the global ocean which are of scientific interest in their own right.

stat.AP↗

arXiv2017

Shape-constrained uncertainty quantification in unfolding steeply falling elementary particle spectra

The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from measurements smeared by the finite resolution of the particle detectors. Previous unfolding methods use ad hoc discretization and regularization, resulting in confidence intervals that can have significantly lower coverage than their nominal level. Instead of regularizing using a roughness penalty or stopping iterative methods early, we impose physically motivated shape constraints: positivity, monotonicity, and convexity. We quantify the uncertainty by constructing a nonparametric confidence set for the true spectrum, consisting of all those spectra that satisfy the shape constraints and that predict the observations within an appropriately calibrated level of fit. Projecting that set produces simultaneous confidence intervals for all functionals of the spectrum, including averages within bins. The confidence intervals have guaranteed conservative frequentist finite-sample coverage in the important and challenging class of unfolding problems for steeply falling particle spectra. We demonstrate the method using simulations that mimic unfolding the inclusive jet transverse momentum spectrum at the LHC. The shape-constrained intervals provide usefully tight conservative inferences, while the conventional methods suffer from severe undercoverage.

stat.AP↗

arXiv2015

Statistical unfolding of elementary particle spectra: Empirical Bayes estimation and bias-corrected uncertainty quantification

We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse problem arising in data analysis at the Large Hadron Collider at CERN consists in estimating the intensity function of an indirectly observed Poisson point process. Unfolding typically proceeds in two steps: one first produces a regularized point estimate of the unknown intensity and then uses the variability of this estimator to form frequentist confidence intervals that quantify the uncertainty of the solution. In this paper, we propose forming the point estimate using empirical Bayes estimation which enables a data-driven choice of the regularization strength through marginal maximum likelihood estimation. Observing that neither Bayesian credible intervals nor standard bootstrap confidence intervals succeed in achieving good frequentist coverage in this problem due to the inherent bias of the regularized point estimate, we introduce an iteratively bias-corrected bootstrap technique for constructing improved confidence intervals. We show using simulations that this enables us to achieve nearly nominal frequentist coverage with only a modest increase in interval length. The proposed methodology is applied to unfolding the $Z$ boson invariant mass spectrum as measured in the CMS experiment at the Large Hadron Collider.

stat.AP↗

arXiv2014

Empirical Bayes unfolding of elementary particle spectra at the Large Hadron Collider

We consider the so-called unfolding problem in experimental high energy physics, where the goal is to estimate the true spectrum of elementary particles given observations distorted by measurement error due to the limited resolution of a particle detector. This an important statistical inverse problem arising in the analysis of data at the Large Hadron Collider at CERN. Mathematically, the problem is formalized as one of estimating the intensity function of an indirectly observed Poisson point process. Particle physicists are particularly keen on unfolding methods that feature a principled way of choosing the regularization strength and allow for the quantification of the uncertainty inherent in the solution. Though there are many approaches that have been considered by experimental physicists, it can be argued that few -- if any -- of these deal with these two key issues in a satisfactory manner. In this paper, we propose to attack the unfolding problem within the framework of empirical Bayes estimation: we consider Bayes estimators of the coefficients of a basis expansion of the unknown intensity, using a regularizing prior; and employ a Monte Carlo expectation-maximization algorithm to find the marginal maximum likelihood estimate of the hyperparameter controlling the strength of the regularization. Due to the data-driven choice of the hyperparameter, credible intervals derived using the empirical Bayes posterior lose their subjective Bayesian interpretation. Since the properties and meaning of such intervals are poorly understood, we explore instead the use of bootstrap resampling for constructing purely frequentist confidence bands for the true intensity. The performance of the proposed methodology is demonstrated using both simulations and real data from the Large Hadron Collider.

stat.AP↗

arXiv2012

Semi-Supervised Anomaly Detection - Towards Model-Independent Searches of New Physics

Most classification algorithms used in high energy physics fall under the category of supervised machine learning. Such methods require a training set containing both signal and background events and are prone to classification errors should this training data be systematically inaccurate for example due to the assumed MC model. To complement such model-dependent searches, we propose an algorithm based on semi-supervised anomaly detection techniques, which does not require a MC training sample for the signal data. We first model the background using a multivariate Gaussian mixture model. We then search for deviations from this model by fitting to the observations a mixture of the background model and a number of additional Gaussians. This allows us to perform pattern recognition of any anomalous excess over the background. We show by a comparison to neural network classifiers that such an approach is a lot more robust against misspecification of the signal MC than supervised classification. In cases where there is an unexpected signal, a neural network might fail to correctly identify it, while anomaly detection does not suffer from such a limitation. On the other hand, when there are no systematic errors in the training data, both methods perform comparably.

physics.data-an↗

arXiv2010

Soft Classification of Diffractive Interactions at the LHC

Multivariate machine learning techniques provide an alternative to the rapidity gap method for event-by-event identification and classification of diffraction in hadron-hadron collisions. Traditionally, such methods assign each event exclusively to a single class producing classification errors in overlap regions of data space. As an alternative to this so called hard classification approach, we propose estimating posterior probabilities of each diffractive class and using these estimates to weigh event contributions to physical observables. It is shown with a Monte Carlo study that such a soft classification scheme is able to reproduce observables such as multiplicity distributions and relative event rates with a much higher accuracy than hard classification.

hep-ex↗

arXiv2009

Multivariate Techniques for Identifying Diffractive Interactions at the LHC

Close to one half of the LHC events are expected to be due to elastic or inelastic diffractive scattering. Still, predictions based on extrapolations of experimental data at lower energies differ by large factors in estimating the relative rate of diffractive event categories at the LHC energies. By identifying diffractive events, detailed studies on proton structure can be carried out. The combined forward physics objects: rapidity gaps, forward multiplicity and transverse energy flows can be used to efficiently classify proton-proton collisions. Data samples recorded by the forward detectors, with a simple extension, will allow first estimates of the single diffractive (SD), double diffractive (DD), central diffractive (CD), and non-diffractive (ND) cross sections. The approach, which uses the measurement of inelastic activity in forward and central detector systems, is complementary to the detection and measurement of leading beam-like protons. In this investigation, three different multivariate analysis approaches are assessed in classifying forward physics processes at the LHC. It is shown that with gene expression programming, neural networks and support vector machines, diffraction can be efficiently identified within a large sample of simulated proton-proton scattering events. The event characteristics are visualized by using the self-organizing map algorithm.

hep-ex↗