Miracle-dz/UniFAR-FTUs huggingface dataset:
The Rational SPDE Approach for Gaussian Random Fields With General Smoothness

Abstract A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form , where is Gaussian white noise, L is a second-order differential operator, and is a parameter that determines the smoothness of u. However, this approach has been limited to the case , which excludes several important models and makes it necessary to keep β fixed during inference. We propose a new method, the rational SPDE approach, which in spatial dimension is applicable for any , and thus remedies the mentioned limitation. The presented scheme combines a finite element discretization with a rational approximation of the function to approximate u. For the resulting approximation, an explicit rate of convergence to u in mean-square sense is derived. Furthermore, we show that our method has the same computational benefits as in the restricted case . Several numerical experiments and a statistical application are used to illustrate the accuracy of the method, and to show that it facilitates likelihood-based inference for all model parameters including β. Supplementary materials for this article are available online.
On Stability of a Class of Filters for Nonlinear Stochastic Systems

This article considers stability properties of a broad class of commonly used filters, including the extended and unscented Kalman filters, for discrete and continuous-time stochastic dynamic systems with non-linear state dynamics and linear measurements. We show that contractivity of the filtering error process and boundedness of the error covariance matrix induce stability of the filter. The results are in the form of time-uniform mean square bounds and exponential concentration inequalities for the filtering error. As is typical of stability analysis of filters for non-linear systems, the assumptions required are stringent. However, in contrast to much of the previous analysis, we provide a number of example of model classes for which these assumptions can be verified a priori. Typical requirements are a contractive drift or sufficient inflation of the error covariance matrix and fully observed state. Numerical experiments using synthetic data are used to validate the derived error bounds.
Improved Chebyshev inequality: new probability bounds with known supremum of PDF

In this paper, we derive new probability bounds for Chebyshev's inequality if the supremum of the probability density function is known.This result holds for one-dimensional or multivariate continuous probability distributions with finite mean and variance (covariance matrix). We also show that the similar result holds for specific discrete probability distributions.
Model Selection via the VC Dimension

We derive an objective function that can be optimized to give an estimator of the Vapnik- Chervonenkis dimension for model selection in regression problems. We verify our estimator is consistent. Then, we verify it performs well compared to seven other model selection techniques. We do this for a variety of types of data sets.
A Parsimonious Tour of Bayesian Model Uncertainty

Modern statistical software and machine learning libraries are enabling semi-automated statistical inference. Within this context, it appears easier and easier to try and fit many models to the data at hand, reversing thereby the Fisherian way of conducting science by collecting data after the scientific hypothesis (and hence the model) has been determined. The renewed goal of the statistician becomes to help the practitioner choose within such large and heterogeneous families of models, a task known as model selection. The Bayesian paradigm offers a systematized way of assessing this problem. This approach, launched by Harold Jeffreys in his 1935 book Theory of Probability, has witnessed a remarkable evolution in the last decades, that has brought about several new theoretical and methodological advances. Some of these recent developments are the focus of this survey, which tries to present a unifying perspective on work carried out by different communities. In particular, we focus on non-asymptotic out-of-sample performance of Bayesian model selection and averaging techniques, and draw connections with penalized maximum likelihood. We also describe recent extensions to wider classes of probabilistic frameworks including high-dimensional, unidentifiable, or likelihood-free models.
Nonparametric Forecasting of Multivariate Probability Density Functions

The study of dependence between random variables is the core of theoretical and applied statistics. Static and dynamic copula models are useful for describing the dependence structure, which is fully encrypted in the copula probability density function. However, these models are not always able to describe the temporal change of the dependence patterns, which is a key characteristic of financial data. We propose a novel nonparametric framework for modelling a time series of copula probability density functions, which allows to forecast the entire function without the need of post-processing procedures to grant positiveness and unit integral. We exploit a suitable isometry that allows to transfer the analysis in a subset of the space of square integrable functions, where we build on nonparametric functional data analysis techniques to perform the analysis. The framework does not assume the densities to belong to any parametric family and it can be successfully applied also to general multivariate probability density functions with bounded or unbounded support. Finally, a noteworthy field of application pertains the study of time varying networks represented through vine copula models. We apply the proposed methodology for estimating and forecasting the time varying dependence structure between the S\&P500 and NASDAQ indices.
Non-Stationary Covariance Estimation using the Stochastic Score Approximation for Large Spatial Data.

We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field is defined as a weighted spatially varying linear combination of a globally stationary process and locally stationary processes. Often in such a model, the difficulty in its practical use is in the definition of the boundaries for the local processes, and therefore we describe one such selection procedure that generally captures complex non-stationary relationships. We generalize the use of stochastic approximation to the score equations for data on a partial grid in this non-stationary case and provide tools for evaluating the approximate score in $O(n\log n)$ operations and $O(n)$ storage. We perform various simulations to explore the effectiveness and speed of the proposed methods and conclude by making inference on the accumulation behavior of arsenic applied to a sand grain.
Conditional Bias Robust Estimation of the Total of Curve Data by Sampling in a Finite Population: An Illustration on Electricity Load Curves

For marketing or power grid management purposes, many studies based on the analysis of total electricity consumption curves of groups of customers are now carried out by electricity companies. Aggregated totals or mean load curves are estimated using individual curves measured at fine time grid and collected according to some sampling design. Due to the skewness of the distribution of electricity consumptions, these samples often contain outlying curves which may have an important impact on the usual estimation procedures. We introduce several robust estimators of the total consumption curve which are not sensitive to such outlying curves. These estimators are based on the conditional bias approach and robust functional methods. We also derive mean square error estimators of these robust estimators, and finally, we evaluate and compare the performance of the suggested estimators on Irish electricity data.
Big data and reliability applications: The complexity dimension

ABSTRACT Big data features not only large volumes of data but also data with complicated structures. Complexity imposes unique challenges on big data analytics. Meeker and Hong (2014; Quality Engineering, pp. 102–16) provided an extensive discussion of the opportunities and challenges on big data and reliability; they also described engineering systems which generate big data that can be used in reliability analysis. Meeker and Hong (2014) focused on large-scale system operating and environment data (i.e., high-frequency multivariate time series data) and provided examples on how to link such data as covariates to traditional reliability responses such as time to failure, time to recurrence of events, and degradation measurements. This article intends to extend that discussion by focusing on how to use data with complicated structures to do reliability analysis. Such data types include high-dimensional sensor data, functional curve data, and image streams. We first provide a review of recent developments in those directions, then we provide a discussion on how analytical methods can be developed to tackle the challenging aspects that arise from the complex features of big data in reliability applications. The use of modern statistical methods such as variable selection, functional data analysis, scalar-on-image regression, spatio-temporal data models, and machine-learning techniques will also be discussed.
A Bayesian semiparametric Jolly–Seber model with individual heterogeneity: An application to migratory mallards at stopover

We propose a Bayesian hierarchical Jolly-Seber model that can account for individual heterogeneity in departure and the dependence of arrival time on covariates. Additionally, our model provides a semiparametric functional form for modeling capture probabilities. The model is flexible and can be used to estimate the stopover duration and stopover population size, which are key to stopover duration analysis. From the modeling perspective, our model allows for individual heterogeneity in departure due to a continuous intrinsic factor that varies with time and individual. A stochastic process is considered to model the change of this intrinsic factor over time. Moreover, our model links extrinsic factors to capture probabilities and arrival time. Consequently, our proposed model enables us to draw inference about the impacts of the intrinsic factor on departure, and extrinsic factors on both capture outcome and arrival time. Through the use of a semiparametric model for capture probabilities, we allow the data to suggest the functional relationship between extrinsic factors and capture probabilities rather than relying on an imposed parametric model. By using data augmentation, we develop a well customized Markov chain Monte Carlo algorithm that is free of tuning. We demonstrate the effectiveness of our model through a motivating example of stopover duration analysis for mallards (Anas platyrhynchos) studied during fall migration in Sweden.
Local average treatment effects estimation via substantive model compatible multiple imputation

Nonadherence to assigned treatment is common in randomized controlled trials (RCTs). Recently, there has been increased interest in estimating causal effects of treatment received, for example, the so‐called local average treatment effect (LATE). Instrumental variables (IV) methods can be used for identification, with estimation proceeding either via fully parametric mixture models or two‐stage least squares (TSLS). TSLS is popular but can be problematic for binary outcomes where the estimand of interest is a causal odds ratio. Mixture models are rarely used in practice, perhaps because of their perceived complexity and need for specialist software. Here, we propose using multiple imputation (MI) to impute the latent compliance class appearing in the mixture models. Since such models include an interaction term between the latent compliance class and randomized treatment, we use “substantive model compatible” MI (SMC MIC), which can additionally handle missing data in outcomes and other variables in the model, before fitting the mixture models via maximum likelihood to the MI data sets and combining results via Rubin's rules. We use simulations to compare the performance of SMC MIC to existing approaches and also illustrate the methods by reanalyzing an RCT in UK primary health. We show that SMC MIC can be more efficient than full Bayesian estimation when auxiliary variables are incorporated, and is superior to two‐stage methods, especially for binary outcomes.
Diffusion approximations and control variates for MCMC

A new methodology is presented for the construction of control variates to reduce the variance of additive functionals of Markov Chain Monte Carlo (MCMC) samplers. Our control variates are defined as linear combinations of functions whose coefficients are obtained by minimizing a proxy for the asymptotic variance. The construction is theoretically justified by two new results. We first show that the asymptotic variances of some well-known MCMC algorithms, including the Random Walk Metropolis and the (Metropolis) Unadjusted/Adjusted Langevin Algorithm, are close to the asymptotic variance of the Langevin diffusion. Second, we provide an explicit representation of the optimal coefficients minimizing the asymptotic variance of the Langevin diffusion. Several examples of Bayesian inference problems demonstrate that the corresponding reduction in the variance is significant, and that in some cases it can be dramatic.
New formulation of the Logistic-Normal process to analyze trajectory tracking data

Improved communication systems, shrinking battery sizes and the price drop of tracking devices have led to an increasing availability of trajectory tracking data. These data are often analyzed to understand animals behavior using mixture-type model. Due to their straightforward implementation and efficiency, hidden Markov mod- els are generally used but they are based on assumptions that are rarely verified on real data. In this work we propose a new model based on the Logistic-Normal process. Due to a new formalization and the way we specify the coregionalization matrix of the associated multivariate Gaussian process, we show that our model, differently from other proposals, is invariant with respect to the choice of the reference element and the ordering of the probability vectors components. We estimate the model under a Bayesian framework, using an approximation of the Gaussian process needed to avoid impractical computational time. After a simulation study, where we show the ability of the model to retrieve the parameters used to simulate the data, the model is applied to the real data example, that motivated this work, where a wolf is observed before and after the procreation. Results are easy interpretable showing differences in the two time windows.
The Holdout Randomization Test: Principled and Easy Black Box Feature Selection

We consider the problem of feature selection using black box predictive models. For example, high-throughput devices in science are routinely used to gather thousands of features for each sample in an experiment. The scientist must then sift through the many candidate features to find explanatory signals in the data, such as which genes are associated with sensitivity to a prospective therapy. Often, predictive models are used for this task: the model is fit, error on held out data is measured, and strong performing models are assumed to have discovered some fundamental properties of the system. A model-specific heuristic is then used to inspect the model parameters and rank important features, with top features reported as "discoveries. " However, such heuristics provide no statistical guarantees and can produce unreliable results. We propose the holdout randomization test (HRT) as a principled approach to feature selection using black box predictive models. The HRT is model agnostic and produces a valid p-value for each feature, enabling control over the false discovery rate (or Type I error) for any predictive model. Further, the HRT is computationally efficient and, in simulations, has greater power than a competing knockoffs-based approach. Code is available at this https URL.
Multiple Imputation: A Review of Practical and Theoretical Findings

Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for generating and using multiple imputations. A review of strategies for generating imputations follows, including recent developments in flexible joint modeling and sequential regression/chained equations/fully conditional specification approaches. Finally, we compare and contrast different methods for generating imputations on a range of criteria before identifying promising avenues for future research.
Geostatistical Modeling to Capture Seismic‐Shaking Patterns From Earthquake‐Induced Landslides

We investigate earthquake‐induced landslides using a geostatistical model featuring a latent spatial effect (LSE). The LSE represents the spatially structured residuals in the data, which remain after adjusting for covariate effects. To determine whether the LSE captures the residual signal from a given trigger, we test the LSE in reproducing the pattern of seismic shaking from the distribution of seismically induced landslides, without prior knowledge of the earthquake being included in the model. We assessed the landslide intensity, that is, the expected number of landslides per mapping unit, for the area in which landslides triggered by the Wenchuan and Lushan earthquakes overlap. We examined this area to test our method on landslide inventories located in near and far fields of the earthquake. We generated three models for both earthquakes: (i) seismic parameters only (proxy for the trigger); (ii) the LSE only; and (iii) both seismic parameters and the LSE. The three configurations share the same morphometric covariates. This allowed us to study the LSE pattern and assess whether it approximated the seismic effects. Our results show that the LSE reproduced the shaking patterns for both earthquakes. In addition, the models including the LSE perform better than conventional models featuring seismic parameters only. Due to computational limitations we carried out a detailed analysis for a relatively small area (2,112 km2), using a data set with higher spatial resolution. Results were consistent with those of a subsequent analysis for a larger area (14,648 km2) using coarser‐resolution data.
K-sample omnibus non-proportional hazards tests based on right-censored data

This work presents novel and powerful tests for comparing non-proportional hazard functions, based on sample–space partitions. Right censoring introduces two major difficulties, which make the existing sample–space partition tests for uncensored data non-applicable: (i) the actual event times of censored observations are unknown and (ii) the standard permutation procedure is invalid in case the censoring distributions of the groups are unequal. We overcome these two obstacles, introduce invariant tests, and prove their consistency. Extensive simulations reveal that under non-proportional alternatives, the proposed tests are often of higher power compared with existing popular tests for non-proportional hazards. Efficient implementation of our tests is available in the R package KONPsurv, which can be freely downloaded from CRAN.
The Language of Betting as a Strategy for Statistical and Scientific Communication

The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of statistical tests, tending to misstate their meaning and exaggerate their certainty. We can communicate the meaning and limitations of statistical evidence more clearly using the language of betting. This paper calls attention to a simple betting interpretation of likelihood ratios. This interpretation leads to methods that lend themselves to meta-analysis and accounting for multiple testing. It is closely related to the interpretation of probability as frequency, but it does not encourage the fallacy that probabilistic models imply the existence of unseen alternative worlds. For more on the betting interpretation of probability, see \cite{Shafer/Vovk:2019} and the other working papers at www.probabilityandfinance. com.
In Search of Meaning: Lessons, Resources and Next Steps for Computational Analysis of Financial Discourse

We critically assess mainstream accounting and finance research applying methods from computational linguistics (CL) to study financial discourse. We also review common themes and innovations in the literature and assess the incremental contributions of work applying CL methods over manual content analysis. Key conclusions emerging from our analysis are: (a) accounting and finance research is behind the curve in terms of CL methods generally and word sense disambiguation in particular; (b) implementation issues mean the proposed benefits of CL are often less pronounced than proponents suggest; (c) structural issues limit practical relevance; and (d) CL methods and high quality manual analysis represent complementary approaches to analyzing financial discourse. We describe four CL tools that have yet to gain traction in mainstream AF research but which we believe offer promising ways to enhance the study of meaning in financial discourse. The four approaches are named entity recognition, summarization, semantics and corpus linguistics.
Bayesian Inference Using Synthetic Likelihood: Asymptotics and Adjustments

ABSTRACT Implementing Bayesian inference is often computationally challenging in complex models, especially when calculating the likelihood is difficult. Synthetic likelihood is one approach for carrying out inference when the likelihood is intractable, but it is straightforward to simulate from the model. The method constructs an approximate likelihood by taking a vector summary statistic as being multivariate normal, with the unknown mean and covariance estimated by simulation. Previous research demonstrates that the Bayesian implementation of synthetic likelihood can be more computationally efficient than approximate Bayesian computation, a popular likelihood-free method, in the presence of a high-dimensional summary statistic. Our article makes three contributions. The first shows that if the summary statistics are well-behaved, then the synthetic likelihood posterior is asymptotically normal and yields credible sets with the correct level of coverage. The second contribution compares the computational efficiency of Bayesian synthetic likelihood and approximate Bayesian computation. We show that Bayesian synthetic likelihood is computationally more efficient than approximate Bayesian computation. Based on the asymptotic results, the third contribution proposes using adjusted inference methods when a possibly misspecified form is assumed for the covariance matrix of the synthetic likelihood, such as diagonal or a factor model, to speed up computation. Supplementary materials for this article are available online.
On causal discovery with an equal-variance assumption

Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variance. We show that this fact is implied by an ordering among conditional variances. We demonstrate that ordering estimates of these variances yields a simple yet state-of-the-art method for causal structure learning that is readily extendable to high-dimensional problems.