Miracle-dz/UniFAR-FTUs huggingface dataset:
Hidden Multiplicity in Multiway ANOVA: Prevalence and Remedies

Many psychologists do not realize that exploratory use of the popular multiway analysis of variance (ANOVA) harbors a multiple comparison problem. In the case of two factors, three separate null hypotheses are subject to test (i.e., two main effects and one interaction). Consequently, the probability of at least one Type I error (if all null hypotheses are true) is 14% rather than 5% if the three tests are independent. We explain the multiple comparison problem and demonstrate that researchers almost never correct for it. To mitigate the problem, we describe four remedies: the omnibus F test, the control of familywise error rate, the control of false discovery rate, and the preregistration of hypotheses.
Bayesian fractional posteriors

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the contraction property of the fractional posterior in a general misspecified framework. Our contraction results only require a prior mass condition on certain Kullback-Leibler (KL) neighborhood of the true parameter (or the KL divergence minimizer in the misspecified case), and obviate constructions of test functions and sieves commonly used in the literature for analyzing the contraction property of a regular posterior. We show through a counterexample that some condition controlling the complexity of the parameter space is necessary for the regular posterior to contract, rendering additional flexibility on the choice of the prior for the fractional posterior. Second, we derive a novel Bayesian oracle inequality based on a PAC-Bayes inequality in misspecified models. Our derivation reveals several advantages of averaging based Bayesian procedures over optimization based frequentist procedures. As an application of the Bayesian oracle inequality, we derive a sharp oracle inequality in the convex regression problem under an arbitrary dimension. We also illustrate the theory in Gaussian process regression and density estimation problems.
Probabilistic Reduced-Order Modeling for Stochastic Partial Differential Equations

We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve this fine scale variability which unavoidably requires the repeated solution of very large systems of algebraic equations. We establish a physically inspired, data-driven coarse-grained model which learns a low- dimensional set of microstructural features that are predictive of the fine-grained model (FG) response. Once learned, those features provide a sharp distribution over the coarse scale effec- tive coefficients of the PDE that are most suitable for prediction of the fine scale model output. This ultimately allows to replace the computationally expensive FG by a generative proba- bilistic model based on evaluating the much cheaper CG several times. Sparsity enforcing pri- ors further increase predictive efficiency and reveal microstructural features that are important in predicting the FG response. Moreover, the model yields probabilistic rather than single-point predictions, which enables the quantification of the unavoidable epistemic uncertainty that is present due to the information loss that occurs during the coarse-graining process.
Some new ideas in nonparametric estimation

In the framework of an abstract statistical model we discuss how to use the solution of one estimation problem ({\it Problem A}) in order to construct an estimator in another, completely different, {\it Problem B}. As a solution of {\it Problem A} we understand a data-driven selection from a given family of estimators $\mathbf{A}(\mH)=\big\{\widehat{A}_\mh, \mh\in\mH\big\}$ and establishing for the selected estimator so-called oracle inequality. %parameterized by some se t$\mH$. If $\hat{\mh}\in\mH$ is the selected parameter and $\mathbf{B}(\mH)=\big\{\widehat{B}_\mh, \mh\in\mH\big\}$ is an estimator's collection built in {\it Problem B} we suggest to use the estimator $\widehat{B}_{\hat{\mh}}$. We present very general selection rule led to selector $\hat{\mh}$ and find conditions under which the estimator $\widehat{B}_{\hat{\mh}}$ is reasonable. Our approach is illustrated by several examples related to adaptive estimation.
Anytime Monte Carlo

Abstract Monte Carlo algorithms simulates some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the number of samples simulated being random. To complicate matters, the real time taken for each simulation may depend on the sample produced, so that the samples themselves are not independent of their number, and a length bias with respect to compute time is apparent. This is especially problematic when a Markov chain Monte Carlo (MCMC) algorithm is used and the final state of the Markov chain—rather than an average over all states—is required, which is the case in parallel tempering implementations of MCMC. The length bias does not diminish with the compute budget in this case. It also occurs in sequential Monte Carlo (SMC) algorithms, which is the focus of this paper. We propose an anytime framework to address the concern, using a continuous-time Markov jump process to study the progress of the computation in real time. We first show that for any MCMC algorithm, the length bias of the final state’s distribution due to the imposed real-time computing budget can be eliminated by using a multiple chain construction. The utility of this construction is then demonstrated on a large-scale SMC$ {}^2 $ implementation, using four billion particles distributed across a cluster of 128 graphics processing units on the Amazon EC2 service. The anytime framework imposes a real-time budget on the MCMC move steps within the SMC$ {}^2 $ algorithm, ensuring that all processors are simultaneously ready for the resampling step, demonstrably reducing idleness to due waiting times and providing substantial control over the total compute budget.
Incremental Nonlinear System Identification and Adaptive Particle Filtering Using Gaussian Process

An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model inside a particle filter framework. Model updating is done at measurement sample rate using stochastic gradient descent based optimization implemented in the state estimation filtering loop. The performance of the proposed method is compared with state-of-the-art Gaussian process based batch learning methods. Finally, it is shown that the state estimation performance significantly improves due to the online learning of state dynamics.
Estimating Nonlinear Dynamics with the ConvNet Smoother

Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on assumptions of linearity and Gaussianity that are rarely met in practice. In this paper, we introduced a new dynamical smoothing method that exploits the remarkable capabilities of convolutional neural networks to approximate complex non-linear functions. The main idea is to generate a training set composed of both latent states and observations from an ensemble of simulators and to train the deep network to recover the former from the latter. Importantly, this method only requires the availability of the simulators and can therefore be applied in situations in which either the latent dynamical model or the observation model cannot be easily expressed in closed form. In our simulation studies, we show that the resulting ConvNet smoother has almost optimal performance in the Gaussian case even when the parameters are unknown. Furthermore, the method can be successfully applied to extremely non-linear and non-Gaussian systems. Finally, we empirically validate our approach via the analysis of measured brain signals.
On variance estimation for generalizing from a trial to a target population

Randomized controlled trials (RCTs) provide strong internal validity compared with observational studies. However, selection bias threatens the external validity of randomized trials. Thus, RCT results may not apply to either broad public policy populations or narrow populations, such as specific insurance pools. Some researchers use propensity scores (PSs) to generalize results from an RCT to a target population. In this scenario, a PS is defined as the probability of participating in the trial conditioning on observed covariates. We study a model-free inverse probability weighted estimator (IPWE) of the average treatment effect in a target population with data from a randomized trial. We present variance estimators and compare the performance of our method with that of model-based approaches. We examine the robustness of the model-free estimators to heterogeneous treatment effects.
Generalizing rate heterogeneity across sites in statistical phylogenetics

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterized by an instantaneous rate matrix. Early models assumed the same rate matrix governed substitutions at all sites of the alignment, ignoring variation in evolutionary pressures. Substantial improvements in phylogenetic inference and model fit were achieved by augmenting these models with multiplicative random effects that describe the result of variation in selective constraints and allow sites to evolve at different rates which linearly scale a baseline rate matrix. Motivated by this pioneering work, we consider an extension using a quadratic, rather than linear, transformation. The resulting models allow for variation in the selective coefficients of different types of point mutation at a site in addition to variation in selective constraints. We derive properties of the extended models. For certain non-stationary processes, the extension gives a model that allows variation in sequence composition, both across sites and taxa. We adopt a Bayesian approach, describe an MCMC algorithm for posterior inference and provide software. Our quadratic models are applied to alignments spanning the tree of life and compared with site-homogeneous and linear models.
DCA: Dynamic Correlation Analysis

In high-throughput data, dynamic correlation between genes, i.e. changing correlation patterns under different biological conditions, can reveal important regulatory mechanisms. Given the complex nature of dynamic correlation, and the underlying conditions for dynamic correlation may not manifest into clinical observations, it is difficult to recover such signal from the data. Current methods seek underlying conditions for dynamic correlation by using certain observed genes as surrogates, which may not faithfully represent true latent conditions. In this study we develop a new method that directly identifies strong latent signals that regulate the dynamic correlation of many pairs of genes, named DCA: Dynamic Correlation Analysis. At the center of the method is a new metric for the identification of gene pairs that are highly likely to be dynamically correlated, without knowing the underlying conditions of the dynamic correlation. We validate the performance of the method with extensive simulations. In real data analysis, the method reveals novel latent factors with clear biological meaning, bringing new insights into the data.
Stability revisited: new generalisation bounds for the Leave-one-Out

The present paper provides a new generic strategy leading to non-asymptotic theoretical guarantees on the Leave-one-Out procedure applied to a broad class of learning algorithms. This strategy relies on two main ingredients: the new notion of $L^q$ stability, and the strong use of moment inequalities. $L^q$ stability extends the ongoing notion of hypothesis stability while remaining weaker than the uniform stability. It leads to new PAC exponential generalisation bounds for Leave-one-Out under mild assumptions. In the literature, such bounds are available only for uniform stable algorithms under boundedness for instance. Our generic strategy is applied to the Ridge regression algorithm as a first step.
Guarantees in Wasserstein Distance for the Langevin Monte Carlo Algorithm

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the continuous diffusion process associated with the algorithm converges exponentially fast to the target distribution along with some technical assumptions. While such an exponential convergence holds for example in the log-concave measure case, it also holds for the more general case of asymptoticaly log-concave measures. Our results thus extends the known rates of convergence in total variation and Wasserstein distances which have only been obtained in the log-concave case. Moreover, using a sharper approximation bound of the continuous process, we obtain better asymptotic rates than traditional results. We also look into variations of the Langevin Monte Carlo algorithm using other discretization schemes. In a first time, we look into the use of the Ozaki's discretization but are unable to obtain any significative improvement in terms of convergence rates compared to the Euler's scheme. We then provide a (sub-optimal) way to study more general schemes, however our approach only holds for the log-concave case.
A regional compound Poisson process for hurricane and tropical storm damage

In light of intense hurricane activity along the US Atlantic coast, attention has turned to understanding both the economic effect and the behaviour of these storms. The compound Poisson–log‐normal process has been proposed as a model for aggregate storm damage but does not shed light on regional analysis since storm path data are not used. We propose a fully Bayesian regional prediction model which uses conditional auto‐regressive models to account for both storm paths and spatial patterns for storm damage. When fitted to historical data, the analysis from our model both confirms previous findings and reveals new insights on regional storm tendencies. Posterior predictive samples can also be used for pricing regional insurance premiums, which we illustrate by using three different risk measures.
Quantifying Heteroskedasticity via Bhattacharyya Distance

Heteroskedasticity is a statistical anomaly that describes differing variances of error terms in a time series dataset. The presence of heteroskedasticity in data imposes serious challenges for forecasting models and many statistical tests are not valid in the presence of heteroskedasticity. Heteroskedasticity of the data affects the relation between the predictor variable and the outcome, which leads to false positive and false negative decisions in the hypothesis testing. Available approaches to study heteroskedasticity thus far adopt the strategy of accommodating heteroskedasticity in the time series and consider it an inevitable source of noise. In these existing approaches, two forecasting models are prepared for normal and heteroskedastic scenarios and a statistical test is to determine whether or not the data is heteroskedastic. This work-in-progress research introduces a quantifying measurement for heteroskedasticity. The idea behind the proposed metric is the fact that a heteroskedastic time series features a uniformly distributed local variances. The proposed measurement is obtained by calculating the local variances using linear time invariant filters. A probability density function of the calculated local variances is then derived and compared to a uniform distribution of theoretical ultimate heteroskedasticity using statistical divergence measurements. The results demonstrated on synthetic datasets shows a strong correlation between the proposed metric and number of variances locally estimated in a heteroskedastic time series.
A Stream-Suitable Kolmogorov-Smirnov-Type Test for Big Data Analysis

Big Data has become an ever more commonplace setting that is encountered by data analysts. In the Big Data setting, analysts are faced with very large numbers of observations as well as data that arrive as a stream, both of which are phenomena that many traditional statistical techniques are unable to contend with. Unfortunately, many of these traditional techniques are useful and cannot be discarded. One such technique is the Kolmogorov-Smirnov (KS) test for goodness-of-fit (GoF). A Big Data and stream-appropriate KS-type test is derived via the chunked-and-averaged (CA) estimator paradigm. The new test is termed the CAKS GoF test. The CAKS test statistic is proved to be asymptotically normal, allowing for the large sample testing of GoF. Furthermore, theoretical results demonstrate that the CAKS test is consistent against both fixed alternatives, where the null and the true data generating distribution are a fixed distance apart, and alternatives that approach the null at a slow enough rate. Numerical results demonstrate that the CAKS test is effective in identifying deviation in the distribution with respect to changes in mean, variance, and shape. Furthermore, it is found that the CAKS test is faster than the KS test, for large numbers of observation, and can be applied to sample sizes of 10^{9} and beyond.
Bayesian Community Detection

We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a generalized Bernoulli prior on the class labels, and a beta prior on the edge probabilities. We show that this estimator is strongly consistent when the expected degree is at least of order $\log^2{n}$, where $n$ is the number of nodes in the network.
Modeling Group Dynamics Using Probabilistic Tensor Decompositions

We propose a probabilistic modeling framework for learning the dynamic patterns in the collective behaviors of social agents and developing profiles for different behavioral groups, using data collected from multiple information sources. The proposed model is based on a hierarchical Bayesian process, in which each observation is a finite mixture of an set of latent groups and the mixture proportions (i.e., group probabilities) are drawn randomly. Each group is associated with some distributions over a finite set of outcomes. Moreover, as time evolves, the structure of these groups also changes; we model the change in the group structure by a hidden Markov model (HMM) with a fixed transition probability. We present an efficient inference method based on tensor decompositions and the expectation-maximization (EM) algorithm for parameter estimation.
Adaptive Clustering Using Kernel Density Estimators

We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive finite sample guarantees, consistency, rates of convergence, and an adaptive data-driven strategy for choosing the kernel bandwidth. For these results we do not need continuity assumptions on the density such as H\"{o}lder continuity, but only require intuitive geometric assumptions of non-parametric nature.
ON STOCHASTIC COMPARISONS FOR LOAD-SHARING SERIES AND PARALLEL SYSTEMS

We study the allocation strategies for redundant components in the load-sharing series/parallel systems. We show that under the specified assumptions, the allocation of a redundant component to the stochastically weakest (strongest) component of a series (parallel) system is the best strategy to achieve its maximal reliability. The results have been studied under cumulative exposure model and for a general scenario as well. They have a clear intuitive meaning; however, the corresponding additional assumptions are not obvious, which can be seen from the proofs of our theorems.
Effect Heterogeneity and Variable Selection for Standardizing Experimental Findings

Randomized trials are rarely representative of the general population. To account for this, results may be standardized to a target population which may be different from the one in which the trial was conducted. In this paper, we discuss three different approaches for reasoning about which covariates must be standardized over. This includes the traditional approach based on standard effect measures such as the risk difference or the risk ratio, Bareinboim and Pearl's graphical approach based on selection diagrams, and a new approach based on Counterfactual Outcome State Transition parameters. We compare and contrast these approaches, and argue that the choice must be informed by expert beliefs about which assumptions are most likely to be approximately true in the specific scientific context.
The Graphical Horseshoe Estimator for Inverse Covariance Matrices

Abstract We develop a new estimator of the inverse covariance matrix for high-dimensional multivariate normal data using the horseshoe prior. The proposed graphical horseshoe estimator has attractive properties compared to other popular estimators, such as the graphical lasso and the graphical smoothly clipped absolute deviation. The most prominent benefit is that when the true inverse covariance matrix is sparse, the graphical horseshoe provides estimates with small information divergence from the sampling model. The posterior mean under the graphical horseshoe prior can also be almost unbiased under certain conditions. In addition to these theoretical results, we also provide a full Gibbs sampler for implementing our estimator. MATLAB code is available for download from github at http://github.com/liyf1988/GHS. The graphical horseshoe estimator compares favorably to existing techniques in simulations and in a human gene network data analysis. Supplementary materials for this article are available online.
Extreme Value Theory for Time Series using Peak-Over-Threshold method

This brief paper summarize the chances offered by the Peak-Over-Threshold method, related with analysis of extremes. Identification of appropriate Value at Risk can be solved by fitting data with a Generalized Pareto Distribution. Also an estimation of value for the Expected Shortfall can be useful, and the application of these few concepts are valid for the most wide range of risk analysis, from the financial application to the operational risk assessment, through the analysis for climate time series; resolving the problem of borderline data.