Sufficient Statistics Research Articles

Tree boosting for learning EFT parameters

We present a new tree boosting algorithm designed for the measurement of parameters in the context of effective field theory (EFT). To construct the algorithm, we interpret the optimized loss function of a traditional decision tree as the maximal Fisher information in Poisson counting experiments. We promote the interpretation to general EFT predictions and develop a suitable boosting method. The resulting “Boosted Information Tree” algorithm approximates the score, the derivative of the log-likelihood function with respect to the parameter. It thus provides a sufficient statistic in the vicinity of a reference point in parameter space where the estimator is trained. The training exploits per-event information of likelihood ratios for different theory parameter values available in the simulated EFT data sets. Program summaryProgram Title: BIT (Boosted Information Trees)CPC Library link to program files:https://doi.org/10.17632/9fjyb5hyxt.1Developer's repository link:https://github.com/HephyAnalysisSW/BITLicensing provisions: GPLv3Programming language: Python2 and Python3Nature of problem: Providing a discriminator for parameter estimation in the context of the standard model effective field theory.Solution method: A tree-based algorithm exploits “augmented” information of the simulated training data set to regress in the score function and thereby provides a sufficient test statistic of an EFT parameter.

A Sufficient Statistics Approach for Macro Policy Evaluation

The evaluation of macroeconomic policy decisions has traditionally relied on the formulation of a specific economic model. In this work, we show that two statistics are sufficient to detect, often even correct, non-optimal policies, i.e., policies that do not minimize the loss function. The two sufficient statistics are (i) the effects of policy shocks on the policy objectives, and (ii) forecasts for the policy objectives conditional on the policy decision. Both statistics can be estimated without relying on a specific model. We illustrate the method by studying US monetary policy decisions.

Analysis of regulatory documents regarding data collection for probability calculations of reinforced concrete structures

Introduction. A sustainable system of risk management in construction is in great demand for both consumers and suppliers of construction products. As one of the main elements of such a system, probability calculations of loader-bearing structures provide a necessary level of reliability and optimality of construction solutions. At the same time, the transition towards risk-oriented design, including the assessment and management of risks, implies the presence of sufficient statistic data, along with the methods of data collection and probability modeling. This study is focused on the issues concerned with collecting data for probability calculations.Aim. To propose suggestions for improving the national regulatory framework as related to probability calculations of reinforced concrete structures and collecting the necessary data.Materials and methods. The main objectives of the study were to investigate and analyze Russian and foreign experience in the field of risk assessment and management in terms of building structures and facilities based on probability calculations. In order to achieve these objectives, an analysis of existing Russian and international documents was carried out. In the course of the study, national regulatory legal acts and standardization documents including codes of rules and GOSTs were considered. In addition, some national regulatory technical documents, which were not included in the lists of both obligatory and non-obligatory applications, were analyzed, as well as other specialized regulatory technical documents. An analysis of foreign regulatory technical documents was conducted, including those regulating the initial data characteristics to perform probability calculations (loads, materials, and calculation models). In general, the methodology for analyzing regulatory technical documents involved a detailed study of the selected documents, an analysis of their positions concerning the issue under consideration, as well as an assessment of the completeness and sufficiency of the positions of the documents concerning the methods for determining the initial data characteristics for probability calculations of reinforced concrete structures regarding loads, materials and calculation models.Conclusions. On the basis of the conducted analysis, specific subject areas for research works are formulated focusing on the development of probability calculations of reinforced concrete structures. A system of regulatory documents is proposed enabling an optimal risk-oriented design of reinforced concrete structures to be implemented.

STATE COERCION AND CITIZENS’ RIGHTS

The paper aims to explore which situations the state can exercise political power over its citizens. The art is to find the fine line between citizens’ rights and state coercion. The best way to present an answer to this issue is by examining the principles when state coercion might be justified. Hence, wewill examine eight following principles: Harm Principle, Offense Principle, Legal Moralism, Legal Paternalism, Collective Benefits Principle, Justice Principle, Need Principle, Sufficiency Principle. In addition to defending liberal principles, wewill argue that Legal Paternalism and The Justice Principle can be adopted but only in specific situations. Finally, we suggest that The Need Principle and The Justice Principle cannot be used as justification to limit one’s freedom but they might be translated and expanded into The Sufficiency Principle.

Performance Evaluation of Amplitude and Phase Respiratory Gating Methods on Continuous-Bed-Motion Whole-Body PET Studies

Positron emission tomography (PET) scanners with the feature of continuous-bed-motion (CBM) that allows efficient whole-body dynamic scans and customized imaging protocols have been made commercially available in recent years. As the bed motion has to be reasonably slow in order to achieve sufficient count statistics, the blurring effect induced by respiratory motion is inevitable, and adequate gating methods should be applied. The aim of this study is to identify a relatively reliable gating method for CBM whole-body scans with respect to breathing pattern variability. Two methods: 1) equal amplitude gating (EAG) and 2) phase gating (PG) initially developed for the single-bed imaging protocol are evaluated using CBM data for subjects with a regular breathing pattern, irregular breathing pattern with baseline shift, and irregular breathing pattern with prolonged end expiration. The potential influence of the scan duration on the performance of the applied gating methods is taken into account as well. Based on the results, we suggest that the PG method is relatively reliable for all studied breathing patterns, while the EAG method could introduce severe artifacts in the presence of the baseline shift.

Fitting three-dimensional Laguerre tessellations by hierarchical marked point process models

We present a general statistical methodology for analysing a Laguerre tessellation data set viewed as a realization of a marked point process model. In the first step, for the points, we use a nested sequence of multiscale processes which constitute a flexible parametric class of pairwise interaction point process models. In the second step, for the marks/radii conditioned on the points, we consider various exponential family models where the canonical sufficient statistic is based on tessellation characteristics. For each step, parameter estimation based on maximum pseudolikelihood methods is tractable. For model selection, we consider maximized log pseudolikelihood functions for models of the radii conditioned on the points. Model checking is performed using global envelopes and corresponding tests in both steps and moreover by comparing observed and simulated tessellation characteristics in the second step. We apply our methodology for a 3D Laguerre tessellation data set representing the microstructure of a polycrystalline metallic material, where simulations under a fitted model may substitute expensive laboratory experiments.

Morphological Evolution of the Hosts of Far-infrared/Submillimeter Galaxies

Abstract We present a host morphological study of 1266 far-infrared galaxies (FIRGs) and submillimeter galaxies (SMGs) in the Cosmic Evolution Survey field using the F160W and F814W images obtained by the Hubble Space Telescope. The FIRGs and SMGs are selected from the Herschel Multi-tiered Extragalactic Survey and the SCUBA-2 Cosmology Legacy Survey, respectively. Their precise locations are based on the interferometry data from the Atacama Large Millimeter/submillimeter Array and the Very Large Array. These objects are mostly at 0.1 ≲ z ≲ 3. The SMGs can be regarded as the population at the high-redshift tail of the FIRGs. Most of our FIRGs/SMGs have a total infrared luminosity (L IR) in the regimes of luminous and ultraluminous infrared galaxies (LIRGs, L IR = 1011−12 L ⊙; ULIRGs, L IR > 1012 L ⊙). The hosts of the SMG ULIRGs, FIRG ULIRGs, and FIRG LIRGs are of sufficient numbers to allow for detailed analysis, and they are only modestly different in their stellar masses. Their morphological types are predominantly disk galaxies (type D) and irregular/interacting systems (type Irr/Int). There is a morphological transition at z ≈ 1.25 for the FIRG ULIRG hosts, above which the Irr/Int galaxies dominate and below which the D and Irr/Int galaxies have nearly the same contributions. The SMG ULIRG hosts seem to experience a similar transition. This suggests a shift in the relative importance of galaxy mergers/interactions versus secular gas accretions in “normal” disk galaxies as the possible triggering mechanisms of ULIRGs. The FIRG LIRG hosts are predominantly D galaxies over z = 0.25–1.25, where they are of sufficient statistics.

Online Detection and SNR Estimation in Cooperative Spectrum Sensing

Cooperative spectrum sensing has proved to be an effective method to improve the detection performance in cognitive radio systems. This work focuses on centralized cooperative schemes based on the soft fusion of the energy measurements at the cognitive radios (CRs). In these systems, the likelihood ratio test (LRT) is the optimal detection rule, but the sufficient statistic depends on the local signal-to-noise ratio (SNR) at the CRs, which are unknown in most practical cases. Therefore, the detection problem becomes a composite hypothesis test. The generalized LRT is the most popular approach in those cases. Unfortunately, in mobile environments, its performance is well below the LRT because the local energies are measured under varying SNRs. In this work, we present a new algorithm that jointly estimates the instantaneous SNRs and detects the presence of primary signals. Due to its adaptive nature, the algorithm is well suited for mobile scenarios where the local SNRs are time-varying. Simulation results show that its detection performance is close to the LRT in realistic conditions.

Aggregate implications of financial frictions for unemployment

The Great Recession has witnessed not only a marked disruption in the credit markets and a sharp increase of capital underutilization, but also a severe deterioration of the matching efficiency in the labor market, as evidenced by the historically high unemployment rate and a significant outward shift of the Beveridge curve. Motivated by these facts, I develop a tractable dynamic general equilibrium model to show that financial frictions can manifest themselves as changes in the endogenous matching efficiency in the labor markets. Furthermore, I come up with sufficient statistics to capture the selection and congestion effects of financial frictions on unemployment. The analytical characterization shows that the competing effects crucially depend on interaction between credit imperfections and labor supply elasticity. I then use a calibrated version of the model to show quantitatively that the credit crunch during the financial crisis was a key driving force behind the outward shift of the Beveridge curve, which can explain up to 40% of the rise in the unemployment rate over the business cycles.

Methodological principles of loss of profit assessment

Methodological principles of loss of profit assessment

On sparse high-dimensional graphical model learning for dependent time series

We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso-based frequency-domain formulation of the problem based on frequency-domain sufficient statistic for the observed time series is presented. We investigate an alternating direction method of multipliers (ADMM) approach for optimization of the sparse-group lasso penalized log-likelihood. We provide sufficient conditions for convergence in the Frobenius norm of the inverse PSD estimators to the true value, jointly across all frequencies, where the number of frequencies are allowed to increase with sample size. This result also yields a rate of convergence. We also empirically investigate selection of the tuning parameters based on the Bayesian information criterion, and illustrate our approach using numerical examples utilizing both synthetic and real data.

Phase Transition Analysis for Covariance-Based Massive Random Access With Massive MIMO

This paper considers a massive random access problem in which a large number of sporadically active devices wish to communicate with a base station (BS) equipped with massive multiple-input multiple-output (MIMO) antennas. Each device is preassigned a unique signature sequence, and the BS identifies the active devices by detecting which sequences are transmitted. This device activity detection problem can be formulated as a maximum likelihood estimation (MLE) problem for which the sample covariance matrix of the received signal is a sufficient statistic. The goal of this paper is to characterize the feasible set of problem parameters under which this covariance based approach is able to successfully recover the device activities in the massive MIMO regime. Through an analysis of the asymptotic behaviors of MLE via its associated Fisher information matrix, this paper derives a necessary and sufficient condition on the Fisher information matrix to ensure a vanishing probability of detection error as the number of antennas goes to infinity, based on which a numerical phase transition analysis is obtained. This condition is also examined from a perspective of covariance matching, which relates the phase transition analysis to a recently derived scaling law. Further, we provide a characterization of the distribution of the estimation error in MLE, based on which the error probabilities in device activity detection can be accurately predicted. Finally, this paper studies a random access scheme with joint device activity and data detection and analyzes its performance in a similar way.

Sequential modeling, monitoring, and forecasting of streaming web traffic data

In this paper we introduce strategies for modeling, monitoring, and forecasting sequential web traffic data using flows from the Fox News website. In our analysis we consider a family of Poisson-gamma state space (PGSS) models that can accurately quantify the uncertainty exhibited by web traffic data, can provide fast sequential monitoring and prediction mechanisms for high frequency time intervals, and are computationally feasible when structural breaks are present. As such, we extend the family of PGSS models to include the state augmented (sa-)PGSS model whose state evolution structure is flexible and responsive to sudden changes. Such adaptability is achieved by augmenting the state vector of the PGSS model with an additional state variable for a time-varying discount factor. We develop an efficient particle-based estimation procedure that is suitable for sequential analysis, allowing us to estimate dynamic state variables and static parameters via closed-form conditional sufficient statistics. We compare the performance of the PGSS family of models against viable alternatives from the literature and argue that, especially in the presence of structural breaks, our proposed approach yields superior sequential model fit and predictive performance while preserving computational feasibility. We provide additional insights by designing a simulation study that mimics potential web traffic data patterns.

Risk, informal institutions, and index insurance

The question of how informal institutions interact with formal markets is a central economic question, particularly in developing countries. We analyze this issue for the demand of an innovative weather insurance product. Specifically, when does informal risk-sharing act as barrier or support to the take-up of index-based insurance? The presence of an individual in a risk-sharing arrangement reduces her risk aversion, termed “Effective Risk Aversion”— a sufficient statistic for index decision making. Our analysis establishes that such reduction in risk aversion can lead to either reduced or increased take up of index insurance. These results provide alternative explanations for two empirical puzzles: unexpectedly low takeup for index insurance and demand being particularly low for the most risk averse. From a policy perspective, our results highlight how the combination of premium subsidies and informal networks might promote take-up and how this might eventually facilitate better protection against weather risks.

Towards machine learning aided real-time range imaging in proton therapy

Compton imaging represents a promising technique for range verification in proton therapy treatments. In this work, we report on the advantageous aspects of the i-TED detector for proton-range monitoring, based on the results of the first Monte Carlo study of its applicability to this field. i-TED is an array of Compton cameras, that have been specifically designed for neutron-capture nuclear physics experiments, which are characterized by gamma -ray energies spanning up to 5–6 MeV, rather low gamma -ray emission yields and very intense neutron induced gamma -ray backgrounds. Our developments to cope with these three aspects are concomitant with those required in the field of hadron therapy, especially in terms of high efficiency for real-time monitoring, low sensitivity to neutron backgrounds and reliable performance at the high gamma -ray energies. We find that signal-to-background ratios can be appreciably improved with i-TED thanks to its light-weight design and the low neutron-capture cross sections of its LaCl_{3} crystals, when compared to other similar systems based on LYSO, CdZnTe or LaBr_{3}. Its high time-resolution (CRT sim 500 ps) represents an additional advantage for background suppression when operated in pulsed HT mode. Each i-TED Compton module features two detection planes of very large LaCl_{3} monolithic crystals, thereby achieving a high efficiency in coincidence of 0.2% for a point-like 1 MeV gamma -ray source at 5 cm distance. This leads to sufficient statistics for reliable image reconstruction with an array of four i-TED detectors assuming clinical intensities of 10^{8} protons per treatment point. The use of a two-plane design instead of three-planes has been preferred owing to the higher attainable efficiency for double time-coincidences than for threefold events. The loss of full-energy events for high energy gamma -rays is compensated by means of machine-learning based algorithms, which allow one to enhance the signal-to-total ratio up to a factor of 2.

Deep Bayesian Unsupervised Lifelong Learning

Lifelong Learning (LL) refers to the ability to continually learn and solve new problems with incremental available information over time while retaining previous knowledge. Much attention has been given lately to Supervised Lifelong Learning (SLL) with a stream of labelled data. In contrast, we focus on resolving challenges in Unsupervised Lifelong Learning (ULL) with streaming unlabelled data when the data distribution and the unknown class labels evolve over time. Bayesian framework is natural to incorporate past knowledge and sequentially update the belief with new data. We develop a fully Bayesian inference framework for ULL with a novel end-to-end Deep Bayesian Unsupervised Lifelong Learning (DBULL) algorithm, which can progressively discover new clusters without forgetting the past with unlabelled data while learning latent representations. To efficiently maintain past knowledge, we develop a novel knowledge preservation mechanism via sufficient statistics of the latent representation for raw data. To detect the potential new clusters on the fly, we develop an automatic cluster discovery and redundancy removal strategy in our inference inspired by Nonparametric Bayesian statistics techniques. We demonstrate the effectiveness of our approach using image and text corpora benchmark datasets in both LL and batch settings.

Development of triaxial compressive apparatus for neutron experiments with rocks.

Underground engineering for processes such as geological disposal of high-level nuclear waste, CO2 capture and storage, and mining and drilling for resources requires an understanding of the mechanical behavior of rocks at subsurface stress states, i.e., triaxial compressive stress. Strain measurement using neutron diffraction can be applied to rocks to analyze strain accumulation mechanisms at the microscopic scale. This study reports the development of triaxial compressive apparatus for strain measurement using neutron diffraction. The apparatus can analyze rock specimens (diameter, 25mm; length, 50mm) and apply a maximum confining pressure of 50 MPa. Materials for the components of the apparatus were investigated theoretically based on neutron beam transmission and experimentally using neutron diffraction experiments. The feasibility of the apparatus was verified by measuring strain at hydrostatic pressure under the application of confining pressure and triaxial compression. The theoretical and experimental results show that the apparatus could obtain sufficient neutron statistics from a rock specimen. It was confirmed experimentally that the measured strain values are correlated with the applied confining pressure and stress. The lattice strains of quartz minerals measured by neutron diffraction showed linear deformation behavior, indicating that elastic strain accumulated in the minerals. This apparatus will enable the finding of new insights into the deformation mechanisms of rocks.

Conditional Goodness-of-Fit Tests for Discrete Distributions

In this paper, we address the problem of testing goodness-of-fit for discrete distributions, where we focus on the geometric distribution. We define new likelihood-based goodness-of-fit tests using the beta-geometric distribution and the type I discrete Weibull distribution as alternative distributions. The tests are compared in a simulation study, where also the classical goodness-of-fit tests are considered for comparison. Throughout the paper we consider conditional testing given a minimal sufficient statistic under the null hypothesis, which enables the calculation of exact p values. For this purpose, a new method is developed for drawing conditional samples from the geometric distribution and the negative binomial distribution. We also explain briefly how the conditional approach can be modified for the binomial, negative binomial and Poisson distributions. It is finally noted that the simulation method may be extended to other discrete distributions having the same sufficient statistic, by using the Metropolis–Hastings algorithm.

Macro‐Finance Decoupling: Robust Evaluations of Macro Asset Pricing Models

This paper shows that robust inference under weak identification is important to the evaluation of many influential macro asset pricing models, including (time‐varying) rare‐disaster risk models and long‐run risk models. Building on recent developments in the conditional inference literature, we provide a novel conditional specification test by simulating the critical value conditional on a sufficient statistic. This sufficient statistic can be intuitively interpreted as a measure capturing the macroeconomic information decoupled from the underlying content of asset pricing theories. Macro‐finance decoupling is an effective way to improve the power of the specification test when asset pricing theories are difficult to refute because of a severe imbalance in the information content about the key model parameters between macroeconomic moment restrictions and asset pricing cross‐equation restrictions. We apply the proposed conditional specification test to the evaluation of a time‐varying rare‐disaster risk model and the construction of robust model uncertainty sets.

On the Optimality of Sufficient Statistics-Based Quantizers.

Let X be a random variable taking values in a set X, and let {Pθ; θ ∈ Θ} be a family of distributions indexed by the parameter vector θ taking values in a set Θ. A quantized random variable γ(X) is obtained by employing a quantizer γ: X→ {1,…,K}. It is shown that any extreme point of the set of all possible probability distributions of γ(X) can be achieved by a deterministic quantizer that decides based only on the sufficient statistics. Using this fact, optimality properties of deterministic sufficient statistics-based quantizers are established for the problem of parameter estimation. It is proven that there always exists an optimal partitioning of sufficient statistics into K convex polytopes which maximizes the trace of the Fisher information matrix when {Pθ; θ ∈ Θ} belongs to the exponential family. Furthermore, the optimality of likelihood ratio statistic for simple hypothesis testing follows as a consequence of this result, thereby demonstrating a link between parameter estimation and hypothesis testing.