Statistical Inference Algorithms Research Articles

Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Leveraging probability and statistical algorithms for enhanced financial risk management

This paper explores the foundations and applications of quantitative analysis in financial risk management. It examines the pivotal role of probability theory, statistical inference, and advanced algorithms in identifying, quantifying, and mitigating financial risks. Key concepts such as the Normal, Poisson, and Binomial distributions are discussed in the context of risk analysis, alongside statistical inference methods like hypothesis testing and confidence intervals. Furthermore, the paper investigates the application of portfolio optimization models, credit risk evaluation techniques, and market risk assessment methodologies in practical risk management scenarios. Additionally, it addresses the challenges posed by model risk, data quality, and regulatory compliance, emphasizing the need for rigorous validation, robust data governance, and ethical considerations in risk management practices. By integrating sophisticated quantitative techniques with real-world applications, financial institutions can enhance their ability to navigate the complexities of modern financial markets and achieve more effective risk management strategies.

Portfolio choice algorithms, including exact stochastic dominance

Assume data on Nj stock (asset) returns are available for p stocks, allowing us to construct approximate density functions f(xj) for (j=1, 2, …, p) from p empirical cumulative distribution functions (ECDFs). Our portfolio choice is designed to rank ECDF-induced, ill-behaved f(xj) densities subject to multiple modes, asymmetric fat tails, dips, turns, and numerous overlaps. Older portfolio theory assumes that parameters like the mean, variance, and percentiles fully describe f(xj). All six of our algorithms avoid (expected) utility theory. The only available algorithm by Anderson for order-k Stochastic Dominance (SDk) needs a trapezoidal approximation. Our new exact algorithm for SDk is based on ECDFs and overcomes pairwise comparisons. We include algorithms for statistical inference using the bootstrap and one for “pandemic proof” out-of-sample portfolio performance comparisons from our R package ‘generalCorr’. We suggest a test for “zero cost profitable arbitrage” and illustrate our algorithms in action by using two sets of recent 169-month stock returns. We do not claim to suggest new optimal portfolios.

Bayesian Inference Algorithm for Estimating Heterogeneity of Regulatory Mechanisms Based on Single-Cell Data

The rapid progress in biological experimental technologies has generated a huge amount of experimental data to investigate complex regulatory mechanisms. Various mathematical models have been proposed to simulate the dynamic properties of molecular processes using the experimental data. However, it is still difficult to estimate unknown parameters in mathematical models for the dynamics in different cells due to the high demand for computing power. In this work, we propose a population statistical inference algorithm to improve the computing efficiency. In the first step, this algorithm clusters single cells into a number of groups based on the distances between each pair of cells. In each cluster, we then infer the parameters of the mathematical model for the first cell. We propose an adaptive approach that uses the inferred parameter values of the first cell to formulate the prior distribution and acceptance criteria of the following cells. Three regulatory network models were used to examine the efficiency and effectiveness of the designed algorithm. The computational results show that the new method reduces the computational time significantly and provides an effective algorithm to infer the parameters of regulatory networks in a large number of cells.

Estimating and forecasting the burden and spread of Colombia’s SARS-CoV2 first wave

Following the rapid dissemination of COVID-19 cases in Colombia in 2020, large-scale non-pharmaceutical interventions (NPIs) were implemented as national emergencies in most of the country’s municipalities, starting with a lockdown on March 20th, 2020. Recently, approaches that combine movement data (measured as the number of commuters between units), metapopulation models to describe disease dynamics subdividing the population into Susceptible-Exposed-Asymptomatic-Infected-Recovered-Diseased and statistical inference algorithms have been pointed as a practical approach to both nowcast and forecast the number of cases and deaths. We used an iterated filtering (IF) framework to estimate the model transmission parameters using the reported data across 281 municipalities from March to late October in locations with more than 50 reported deaths and cases in Colombia. Since the model is high dimensional (6 state variables in every municipality), inference on those parameters is highly non-trivial, so we used an Ensemble-Adjustment-Kalman-Filter (EAKF) to estimate time variable system states and parameters. Our results show the model’s ability to capture the characteristics of the outbreak in the country and provide estimates of the epidemiological parameters in time at the national level. Importantly, these estimates could become the base for planning future interventions as well as evaluating the impact of NPIs on the effective reproduction number (mathscr {R}_{eff}) and the critical epidemiological parameters, such as the contact rate or the reporting rate. However, our forecast presents some inconsistency as it overestimates the deaths for some locations as Medellín. Nevertheless, our approach demonstrates that real-time, publicly available ensemble forecasts can provide short-term predictions of reported COVID-19 deaths in Colombia. Therefore, this model can be used as a forecasting tool to evaluate disease dynamics and aid policymakers in infectious outbreak management and control.

AMaLa: Analysis of Directed Evolution Experiments via Annealed Mutational Approximated Landscape.

We present Annealed Mutational approximated Landscape (AMaLa), a new method to infer fitness landscapes from Directed Evolution experiments sequencing data. Such experiments typically start from a single wild-type sequence, which undergoes Darwinian in vitro evolution via multiple rounds of mutation and selection for a target phenotype. In the last years, Directed Evolution is emerging as a powerful instrument to probe fitness landscapes under controlled experimental conditions and as a relevant testing ground to develop accurate statistical models and inference algorithms (thanks to high-throughput screening and sequencing). Fitness landscape modeling either uses the enrichment of variants abundances as input, thus requiring the observation of the same variants at different rounds or assuming the last sequenced round as being sampled from an equilibrium distribution. AMaLa aims at effectively leveraging the information encoded in the whole time evolution. To do so, while assuming statistical sampling independence between sequenced rounds, the possible trajectories in sequence space are gauged with a time-dependent statistical weight consisting of two contributions: (i) an energy term accounting for the selection process and (ii) a generalized Jukes–Cantor model for the purely mutational step. This simple scheme enables accurately describing the Directed Evolution dynamics and inferring a fitness landscape that correctly reproduces the measures of the phenotype under selection (e.g., antibiotic drug resistance), notably outperforming widely used inference strategies. In addition, we assess the reliability of AMaLa by showing how the inferred statistical model could be used to predict relevant structural properties of the wild-type sequence.

Differential privacy in health research: A scoping review.

Differential privacy is a relatively new method for data privacy that has seen growing use due its strong protections that rely on added noise. This study assesses the extent of its awareness, development, and usage in health research. A scoping review was conducted by searching for ["differential privacy" AND "health"] in major health science databases, with additional articles obtained via expert consultation. Relevant articles were classified according to subject area and focus. A total of 54 articles met the inclusion criteria. Nine articles provided descriptive overviews, 31 focused on algorithm development, 9 presented novel data sharing systems, and 8 discussed appraisals of the privacy-utility tradeoff. The most common areas of health research where differential privacy has been discussed are genomics, neuroimaging studies, and health surveillance with personal devices. Algorithms were most commonly developed for the purposes of data release and predictive modeling. Studies on privacy-utility appraisals have considered economic cost-benefit analysis, low-utility situations, personal attitudes toward sharing health data, and mathematical interpretations of privacy risk. Differential privacy remains at an early stage of development for applications in health research, and accounts of real-world implementations are scant. There are few algorithms for explanatory modeling and statistical inference, particularly with correlated data. Furthermore, diminished accuracy in small datasets is problematic. Some encouraging work has been done on decision making with regard to epsilon. The dissemination of future case studies can inform successful appraisals of privacy and utility. More development, case studies, and evaluations are needed before differential privacy can see widespread use in health research.

Evolutionary Determined Epistasis Advances Conformational Sampling, Molecular Design and Evolutionary Models

The use of coevolutionary information, i.e. the knowledge of amino acid or nucleotide interactions maintained through evolution in a given protein/RNA family, has provided a framework to study structural biology in a predictive manner. Amino acid couplings, obtained from statistical inference algorithms like Direct Coupling Analysis, have been fundamental to predict non-local interactions in protein three-dimensional structure, being now the core of state-of-the-art protein structure prediction algorithms. Coevolutionary information has had an impact in understanding conformational plasticity, complex prediction in molecular interactions and specificity in signal transduction. Here, we describe how integration of the statistical mechanics of sequences with experimental data helps us advance applications in engineering allosteric transcriptional repressors and synthetic biology and the exploration of the conformational dynamics of biomolecules. We also show how is it possible to develop more comprehensive models of sequence evolution that unify several features of independent models by integrating epistatic contributions in the formulation of evolutionary landscapes. These studies showcase the spectrum of novel applications in the field of molecular coevolution and its potential to study mutational landscapes of biomolecules.

A Smart Landing Platform With Data-Driven Analytic Procedures for UAV Preflight Safety Diagnosis

Due to the limitation imposed by hardware and form factor considerations, multirotor unmanned aircraft (drones) are unable to conduct preflight physical checks on their own capacity. Critical safety checks involve detecting various anomalies such as imbalanced payload, damaged propellers, mulfunctioning motors and poorly calibrated compass, etc. Human efforts are currently required for performing such tasks, which impedes large-scale deployments of drones and increases the operational costs. In this work, we propose a weight-measuring landing platform along with a set of statistical inference algorithms aimed at performing safety checks for any multicopter aircraft that lands on the platform. We develop a nonconvex nonlinear least squares model for estimating the center of gravity and orientation of the aircraft, and derive a recursive formula for calculating the optimal solution. In numeric experiments, our analytical solution method has been able to find the global solution orders-of-magnitude faster than a global optimization solver. We have conducted real-system tests on a quadcopter drone deliberately configured to carry misplaced payload, and to use damaged propellers. Experiment results show that the platform is able to detect and profile these common safety issues with high accuracy.

Statistical Physics for Medical Diagnostics: Learning, Inference, and Optimization Algorithms.

It is widely believed that cooperation between clinicians and machines may address many of the decisional fragilities intrinsic to current medical practice. However, the realization of this potential will require more precise definitions of disease states as well as their dynamics and interactions. A careful probabilistic examination of symptoms and signs, including the molecular profiles of the relevant biochemical networks, will often be required for building an unbiased and efficient diagnostic approach. Analogous problems have been studied for years by physicists extracting macroscopic states of various physical systems by examining microscopic elements and their interactions. These valuable experiences are now being extended to the medical field. From this perspective, we discuss how recent developments in statistical physics, machine learning and inference algorithms are coming together to improve current medical diagnostic approaches.

Asymptotically Exact Data Augmentation: Models, Properties, and Algorithms

Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain Monte Carlo ones. Nonetheless, introducing appropriate auxiliary variables while preserving the initial target probability distribution and offering a computationally efficient inference cannot be conducted in a systematic way. To deal with such issues, this article studies a unified framework, coined asymptotically exact data augmentation (AXDA), which encompasses both well-established and more recent approximate augmented models. In a broader perspective, this article shows that AXDA models can benefit from interesting statistical properties and yield efficient inference algorithms. In non-asymptotic settings, the quality of the proposed approximation is assessed with several theoretical results. The latter are illustrated on standard statistical problems. Supplementary materials including computer code for this article are available online.

Advancing Fusion with Machine Learning Research Needs Workshop Report

Machine learning and artificial intelligence (ML/AI) methods have been used successfully in recent years to solve problems in many areas, including image recognition, unsupervised and supervised classification, game-playing, system identification and prediction, and autonomous vehicle control. Data-driven machine learning methods have also been applied to fusion energy research for over 2 decades, including significant advances in the areas of disruption prediction, surrogate model generation, and experimental planning. The advent of powerful and dedicated computers specialized for large-scale parallel computation, as well as advances in statistical inference algorithms, have greatly enhanced the capabilities of these computational approaches to extract scientific knowledge and bridge gaps between theoretical models and practical implementations. Large-scale commercial success of various ML/AI applications in recent years, including robotics, industrial processes, online image recognition, financial system prediction, and autonomous vehicles, have further demonstrated the potential for data-driven methods to produce dramatic transformations in many fields. These advances, along with the urgency of need to bridge key gaps in knowledge for design and operation of reactors such as ITER, have driven planned expansion of efforts in ML/AI within the US government and around the world. The Department of Energy (DOE) Office of Science programs in Fusion Energy Sciences (FES) and Advanced Scientific Computing Research (ASCR) have organized several activities to identify best strategies and approaches for applying ML/AI methods to fusion energy research. This paper describes the results of a joint FES/ASCR DOE-sponsored Research Needs Workshop on Advancing Fusion with Machine Learning, held April 30–May 2, 2019, in Gaithersburg, MD (full report available at https://science.osti.gov/-/media/fes/pdf/workshop-reports/FES_ASCR_Machine_Learning_Report.pdf). The workshop drew on broad representation from both FES and ASCR scientific communities, and identified seven Priority Research Opportunities (PRO’s) with high potential for advancing fusion energy. In addition to the PRO topics themselves, the workshop identified research guidelines to maximize the effectiveness of ML/AI methods in fusion energy science, which include focusing on uncertainty quantification, methods for quantifying regions of validity of models and algorithms, and applying highly integrated teams of ML/AI mathematicians, computer scientists, and fusion energy scientists with domain expertise in the relevant areas.

Statistical inference of multivariable modal stability margins of time-delay perturbed power systems

This paper proposes a modal statistical inference algorithm to define multivariable operational stability limits of time-delay perturbed dynamic systems by employing remote sensor signals. Our proposal overcomes the drawbacks of linear independence and inter-area geometry of time-delays to analyze multiple-input, multiple-output dynamic systems. The manuscript contributes with: (a) the study of stability margins under distributed uncertainty and time-delays for large power systems, (b) the determination of stability conditions of inter-area oscillations through a new probabilistic modeling approach under the influence of intermissions, and (c) the usage of the proposed methodology to derive controlled stability limits and assess the modal resilience of perturbed power systems. Studies on the multi-scale signals sensitivity and multivariable polynomial intersection from empirical perspectives in modal stability analysis are also explored. Results on an IEEE 16-generator 68-bus system are presented to illustrate the effectiveness of the proposed algorithm. The estimation of multivariable operational stability limits and time-delays of inter-area oscillation modes are verified with the vector fitting procedure and first-order Padé approximation.

Alveolar Osteitis Following Tooth Extraction: Systematic Review and Google Trends Analysis Instigated by the First Upper Premolar Case Reported from Iraq

Introduction： Alveolar osteitis is a painful condition that may occur following permanent teeth extraction due to the failure of formation of a blood clot or its dislodgement before the complete healing of the wound. We aim to provide a systematic review and trends analytic on the epidemiology and the digital epidemiology as well as the management of alveolar osteitis and to seek any available data in connection with alveolar osteitis following upper premolar tooth extraction. Methods： This study represents a combinatory of literature review, analytics of Google Trends, and the first documented case from Iraq of alveolar osteitis following extraction of the maxillary first premolar. Three literature databases were explored, using Boolean operators, including NCBI-PubMed, Elsevier, and the Cochrane Library. Google Trends database was examined to assess the digital epidemiology. Results：The total number of hits was 54417. There was an overall deficit of literature concerning the condition in connection with the extraction of maxillary premolars. The digital epidemiology was limited to twenty-two countries including three countries from the Middle East accounting for 13.63% of the total geographic mapping while Iraq was absent. Conclusion：Our exceptional case report instigated a systematic analytic of a trends database and the literature. The analysis confirmed the inadequacy of studies from the Middle East. Future studies should deploy the use of machine learning algorithms for a rigour statistical inference based on data from online and offline big data repositories of public health records.
  

Inference From Randomized Transmissions by Many Backscatter Sensors

Attaining the vision of Smart Cities requires the deployment of an enormous number of sensors for monitoring various conditions of the environment. Backscatter-sensors have emerged to be a promising solution due to the uninterruptible energy supply and relative simple hardwares. On the other hand, backscatter-sensors with limited signal-processing capabilities are unable to support conventional algorithms for multiple-access and channel-training. Thus, the key challenge in designing backscatter-sensor networks is to enable readers to accurately detect sensing-values given simple ALOHA random access, primitive transmission schemes, and no knowledge of channel-states. We tackle this challenge by proposing the novel framework of backscatter sensing featuring random-encoding at sensors and statistical-inference at readers. Specifically, assuming the on/off keying for backscatter transmissions, the practical random-encoding scheme causes the on/off transmission of a sensor to follow a distribution parameterized by the sensing values. Facilitated by the scheme, statistical-inference algorithms are designed to enable a reader to infer sensing-values from randomized transmissions by multiple sensors. The specific design procedure involves the construction of Bayesian networks, namely deriving conditional distributions for relating unknown parameters and variables to signals observed by the reader. Then based on the Bayesian networks and the well-known expectation-maximization principle, inference algorithms are derived to recover sensing-values.

Decoding communities in networks.

According to a recent information-theoretical proposal, the problem of defining and identifying communities in networks can be interpreted as a classical communication task over a noisy channel: memberships of nodes are information bits erased by the channel, edges and nonedges in the network are parity bits introduced by the encoder but degraded through the channel, and a community identification algorithm is a decoder. The interpretation is perfectly equivalent to the one at the basis of well-known statistical inference algorithms for community detection. The only difference in the interpretation is that a noisy channel replaces a stochastic network model. However, the different perspective gives the opportunity to take advantage of the rich set of tools of coding theory to generate novel insights on the problem of community detection. In this paper, we illustrate two main applications of standard coding-theoretical methods to community detection. First, we leverage a state-of-the-art decoding technique to generate a family of quasioptimal community detection algorithms. Second and more important, we show that the Shannon's noisy-channel coding theorem can be invoked to establish a lower bound, here named as decodability bound, for the maximum amount of noise tolerable by an ideal decoder to achieve perfect detection of communities. When computed for well-established synthetic benchmarks, the decodability bound explains accurately the performance achieved by the best community detection algorithms existing on the market, telling us that only little room for their improvement is still potentially left.

Effective Online Bayesian Phylogenetics via Sequential Monte Carlo with Guided Proposals.

Modern infectious disease outbreak surveillance produces continuous streams of sequence data which require phylogenetic analysis as data arrives. Current software packages for Bayesian phylogenetic inference are unable to quickly incorporate new sequences as they become available, making them less useful for dynamically unfolding evolutionary stories. This limitation can be addressed by applying a class of Bayesian statistical inference algorithms called sequential Monte Carlo (SMC) to conduct online inference, wherein new data can be continuously incorporated to update the estimate of the posterior probability distribution. In this article, we describe and evaluate several different online phylogenetic sequential Monte Carlo (OPSMC) algorithms. We show that proposing new phylogenies with a density similar to the Bayesian prior suffers from poor performance, and we develop “guided” proposals that better match the proposal density to the posterior. Furthermore, we show that the simplest guided proposals can exhibit pathological behavior in some situations, leading to poor results, and that the situation can be resolved by heating the proposal density. The results demonstrate that relative to the widely used MCMC-based algorithm implemented in MrBayes, the total time required to compute a series of phylogenetic posteriors as sequences arrive can be significantly reduced by the use of OPSMC, without incurring a significant loss in accuracy.

Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.

In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA) overcomes the main limitations of the standard Linear Noise Approximation (LNA) to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.

Statistical Inference of Transit Passenger Boarding Strategies from Farecard Data

This research considers how one might deduce the set of attractive routes for public transit passengers, as part of a boarding strategy, from passengers’ daily choices of which path to take. From the set of attractive routes (attractive set), a public transit passenger may be assumed to board the first service that arrives at the origin stop. To determine the attractive set, a statistical inference algorithm was developed and tested using a public transit farecard data set. The proposed algorithm was developed from an exact method that investigates the distribution of repeated boarding transactions in a farecard data set and infers the so-called steady-state strategies over the observation period. The advantage of the proposed method is in identifying and eliminating occasional and tried-but-rejected path alternatives recorded during the study period. The method was tested in a case study using 6 months of farecard transactions of regular passengers for multiple major origin–destination pairs in the transit network of Brisbane, Australia. Some behavioral aspects of passengers’ attractive routes are also reported and discussed.

ArchimedesOne

Knowledge bases are becoming increasingly important in structuring and representing information from the web. Meanwhile, web-scale information poses significant scalability and quality challenges to knowledge base systems. To address these challenges, we develop a probabilistic knowledge base system, A rchimedes O ne , by scaling up the knowledge expansion and statistical inference algorithms. We design a web interface for users to query and update large knowledge bases. In this paper, we demonstrate the A rchimedes O ne system to showcase its efficient query and inference engines. The demonstration serves two purposes: 1) to provide an interface for users to interact with A rchimedes O ne through load, search, and update queries; and 2) to validate our approaches of knowledge expansion by applying inference rules in batches using relational operations and query-driven inference by focusing computation on the query facts. We compare A rchimedes O ne with state-of-the-art approaches using two knowledge bases: NELL-sports with 4.5 million facts and Reverb-Sherlock with 15 million facts.