Miracle-dz/UniFAR-FTUs huggingface dataset:
A Unified View of False Discovery Rate Control: Reconciliation of Bayesian and Frequentist Approaches

This paper explores the intrinsic connections between the Bayesian false discovery rate (FDR) control procedures and their counterpart of frequentist procedures. We attempt to offer a unified view of FDR control within and beyond the setting of testing exchangeable hypotheses. Under the standard two-groups model and the Oracle condition, we show that the Bayesian and the frequentist methods can achieve asymptotically equivalent FDR control at arbitrary levels. Built on this result, we further illustrate that rigorous post-fitting model diagnosis is necessary and effective to ensure robust FDR controls for parametric Bayesian approaches. Additionally, we show that the Bayesian FDR control approaches are coherent and naturally extended to the setting beyond testing exchangeable hypotheses. Particularly, we illustrate that $p$-values are no longer the natural statistical instruments for optimal frequentist FDR control in testing non-exchangeable hypotheses. Finally, we illustrate that simple numerical recipes motivated by our theoretical results can be effective in examining some key model assumptions commonly assumed in both Bayesian and frequentist procedures (e.g., zero assumption).
A framework for adaptive MCMC targeting multimodal distributions

We propose a new Monte Carlo method for sampling from multimodal distributions. The idea of this technique is based on splitting the task into two: finding the modes of a target distribution $\pi$ and sampling, given the knowledge of the locations of the modes. The sampling algorithm relies on steps of two types: local ones, preserving the mode; and jumps to regions associated with different modes. Besides, the method learns the optimal parameters of the algorithm while it runs, without requiring user intervention. Our technique should be considered as a flexible framework, in which the design of moves can follow various strategies known from the broad MCMC literature. In order to design an adaptive scheme that facilitates both local and jump moves, we introduce an auxiliary variable representing each mode and we define a new target distribution $\tilde{\pi}$ on an augmented state space $\mathcal{X}~\times~\mathcal{I}$, where $\mathcal{X}$ is the original state space of $\pi$ and $\mathcal{I}$ is the set of the modes. As the algorithm runs and updates its parameters, the target distribution $\tilde{\pi}$ also keeps being modified. This motivates a new class of algorithms, Auxiliary Variable Adaptive MCMC. We prove general ergodic results for the whole class before specialising to the case of our algorithm.
Seeking evidence of absence: Reconsidering tests of model assumptions

Statistical tests can only reject the null hypothesis, never prove it. However, when researchers test modeling assumptions, they often interpret the failure to reject a null of "no violation" as evidence that the assumption holds. We discuss the statistical and conceptual problems with this approach. We show that equivalence/non-inferiority tests, while giving correct Type I error, have low power to rule out many violations that are practically significant. We suggest sensitivity analyses that may be more appropriate than hypothesis testing.
High-dimensional covariance matrices in elliptical distributions with application to spherical test

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among their coordinates, which have great impact on the asymptotic behaviors of linear spectral statistics. Taking such kind of dependency into consideration, we establish a new central limit theorem for the linear spectral statistics in this paper for a class of elliptical populations. This general theoretical result has wide applications and, as an example, it is then applied to test the sphericity of elliptical populations.
corr2D: Implementation of Two-Dimensional Correlation Analysis in R

In the package corr2D two-dimensional correlation analysis is implemented in R. This paper describes how two-dimensional correlation analysis is done in the package and how the mathematical equations are translated into R code. The paper features a simple tutorial with executable code for beginners, insight into at the calculations done before the correlation analysis, a detailed look at the parallelization of the fast Fourier transformation based correlation analysis and a speed test of the calculation. The package corr2D offers the possibility to preprocess, correlate and postprocess spectroscopic data using exclusively the R language. Thus, corr2D is a welcome addition to the toolbox of spectroscopists and makes two-dimensional correlation analysis more accessible and transparent.
Structural-Factor Modeling of High-Dimensional Time Series: Another Look at Approximate Factor Models with Diverging Eigenvalues

This article proposes a new approach to modeling high-dimensional time series data by providing a simple and natural way to understand the mechanism of factor models. We treat a p-dimensional time series as a nonsingular linear transformation of certain common factors and structured idiosyncratic components. Unlike the approximate factor models, we allow the largest eigenvalues of the covariance matrix of the idiosyncratic components to diverge as the dimension p increases, which is reasonable in the high-dimensional setting. A white noise testing procedure for high-dimensional random vectors is proposed to determine the number of common factors under the assumption that the idiosyncratic term is a vector white noise. We also introduce a projected Principal Component Analysis (PCA) to eliminate the diverging effect of the noises. Asymptotic properties of the proposed method are established for both fixed p and diverging p as the sample size n tends to infinity. Both simulated and real examples are used to assess the performance of the proposed method. We also compare our method with two commonly used methods in the literature and find that the proposed approach not only provides interpretable results, but also performs well in out-of-sample forecasting.
Convergence and perturbation theory for an infinite-dimensional Metropolis-Hastings algorithm with self-decomposable priors

We study a Metropolis-Hastings algorithm for target measures that are absolutely continuous with respect to a large class of prior measures on Banach spaces. The algorithm is shown to have a spectral gap in a Wasserstein-like semimetric weighted by a Lyapunov function. A number of error bounds are given for computationally tractable approximations of the algorithm including bounds on the closeness of Cesaro averages and other pathwise quantities. Several applications illustrate the breadth of problems to which the results apply such as discretization by Galerkin-type projections and approximate simulation of the proposal via perturbation theory.
Large-Scale Model Selection with Misspecification

Model selection is crucial to high-dimensional learning and inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work assumes implicitly that the models are correctly specified or have fixed dimensionality. Yet both features of model misspecification and high dimensionality are prevalent in practice. In this paper, we exploit the framework of model selection principles in misspecified models originated in Lv and Liu (2014) and investigate the asymptotic expansion of Bayesian principle of model selection in the setting of high-dimensional misspecified models. With a natural choice of prior probabilities that encourages interpretability and incorporates Kullback-Leibler divergence, we suggest the high-dimensional generalized Bayesian information criterion with prior probability (HGBIC_p) for large-scale model selection with misspecification. Our new information criterion characterizes the impacts of both model misspecification and high dimensionality on model selection. We further establish the consistency of covariance contrast matrix estimation and the model selection consistency of HGBIC_p in ultra-high dimensions under some mild regularity conditions. The advantages of our new method are supported by numerical studies.
Estimating Causal Effects Under Interference Using Bayesian Generalized Propensity Scores

In most real-world systems units are interconnected and can be represented as networks consisting of nodes and edges. For instance, in social systems individuals can have social ties, family or financial relationships. In settings where some units are exposed to a treatment and its effect spills over connected units, estimating both the direct effect of the treatment and spillover effects presents several challenges. First, assumptions on the way and the extent to which spillover effects occur along the observed network are required. Second, in observational studies, where the treatment assignment is not under the control of the investigator, confounding and homophily are potential threats to the identification and estimation of causal effects on networks. Here, we make two structural assumptions: i) neighborhood interference, which assumes interference operates only through a function of the immediate neighbors' treatments ii) unconfoundedness of the individual and neighborhood treatment, which rules out the presence of unmeasured confounding variables, including those driving homophily. Under these assumptions we develop a new covariate-adjustment estimator for treatment and spillover effects in observational studies on networks. Estimation is based on a generalized propensity score that balances individual and neighborhood covariates across units under different levels of individual treatment and of exposure to neighbors' treatment. Adjustment for propensity score is performed using a penalized spline regression. Inference capitalizes on a three-step Bayesian procedure which allows to take into account the uncertainty in the propensity score estimation and avoiding model feedback. Finally, correlation of interacting units is taken into account using a community detection algorithm and incorporating random effects in the outcome model.
THE EFFECTS OF DEPOSITION CONDITIONS ON RF SPUTTERED GALLIUM TIN ZINC OXIDE THIN FILM TRANSISTORS

Bradley, Tanina. THE EFFECTS OF DEPOSITION CONDITIONS ON RF SPUTTERED GALLIUM TIN ZINC OXIDE THIN FILM TRANSISTORS. (Major Professor: Dr. Shanthi Iyer), North Carolina Agricultural and Technical State University. Thin film transistors (TFTs) were fabricated with a transparent amorphous gallium tin zinc oxide (GSZO) channel layer. GSZO is a promising, low cost replacement for the commonly used indium gallium zinc oxide (IGZO). The transistors were fabricated on Si substrates to optimize performance prior to transferring device production to flexible substrates. This dissertation will address the effects of deposition and post-deposition parameters on the film properties and interface traps. It will also address the parameters’ resultant effects on device performance and stability with the use of various characterization techniques. Film properties were studied using x-ray diffraction (XRD) and transmission measurements to assess the structural and optical properties of the deposited films. X-ray photoelectron spectroscopy (XPS) analysis was performed to determine the surface composition of the channel layer, and correlate the surface properties to the resulting device performance. Enhancement and depletion mode devices were fabricated. TFT performance was evaluated through the current-voltage (I-V) characteristics of the devices under normal, electrically stressed and photo-excited conditions operating conditions. Depletion mode TFTs were produced with drain current (ID)= 10 -6 A, threshold voltage (VT)= -3 V, subthreshold swing (SS)= 1.3 V/decade, and on/off current ratio (Ion/off)= 10 6 when operated in the dark without gate stress. TFTs with 10 sccm oxygen incorporation during deposited and post-deposition annealing at 250 °C exhibits the best performance amongst enhancement mode devices with ID of 10 -7 A, VT of 3 V SS of 1.33 V / decade, and Ion/off of 10 6 . In addition, a stable RT deposited TFT has been achieved with 2 sccm oxygen incorporation, and 250 °C post deposition annealing temperature, that exhibits a ΔVT as low as ~0.5 V for a 3hour stress period under a gate bias of 1.2 and 12 V.
Concentration of scalar ergodic diffusions and some statistical implications

We derive uniform concentration inequalities for continuous-time analogues of empirical processes and related stochastic integrals of scalar ergodic diffusion processes. Thereby, we lay the foundation typically required for the study of sup-norm properties of estimation procedures for a large class of diffusion processes. In the classical i.i. d. context, a key device for the statistical sup-norm analysis is provided by Talagrand-type concentration inequalities. Aiming for a parallel substitute in the diffusion framework, we present a systematic, self-contained approach to such uniform concentration inequalities via martingale approximation and moment bounds obtained by the generic chaining method. The developed machinery is of independent probabilistic interest and can serve as a starting point for investigations of other processes such as more general Markov processes, in particular multivariate or discretely observed diffusions. As a first concrete statistical application, we analyse the sup-norm error of estimating the invariant density of an ergodic diffusion via the natural local time estimator and the classical nonparametric kernel density estimator, respectively.
Statistical post‐processing of dual‐resolution ensemble forecasts

The computational cost as well as the probabilistic skill of ensemble forecasts depends on the spatial resolution of the numerical weather prediction model and the ensemble size. Periodically, e.g. when more computational resources become available, it is appropriate to reassess the balance between resolution and ensemble size. Recently, it has been proposed to investigate this balance in the context of dual‐resolution ensembles, which use members with two different resolutions to make probabilistic forecasts. This study investigates whether statistical post‐processing of such dual‐resolution ensemble forecasts changes the conclusions regarding the optimal dual‐resolution configuration.
Simultaneous penalized M-estimation of covariance matrices using geodesically convex optimization

A common assumption when sampling $p$-dimensional observations from $K$ distinct group is the equality of the covariance matrices. In this paper, we propose two penalized $M$-estimation approaches for the estimation of the covariance or scatter matrices under the broader assumption that they may simply be close to each other, and hence roughly deviate from some positive definite "center". The first approach begins by generating a pooled $M$-estimator of scatter based on all the data, followed by a penalised $M$-estimator of scatter for each group, with the penalty term chosen so that the individual scatter matrices are shrunk towards the pooled scatter matrix. In the second approach, we minimize the sum of the individual group $M$-estimation cost functions together with an additive joint penalty term which enforces some similarity between the individual scatter estimators, i.e. shrinkage towards a mutual center. In both approaches, we utilize the concept of geodesic convexity to prove the existence and uniqueness of the penalized solution under general conditions. We consider three specific penalty functions based on the Euclidean, the Riemannian, and the Kullback-Leibler distances. In the second approach, the distance based penalties are shown to lead to estimators of the mutual center that are related to the arithmetic, the Riemannian and the harmonic means of positive definite matrices, respectively. A penalty based on an ellipticity measure is also considered which is particularly useful for shape matrix estimators. Fixed point equations are derived for each penalty function and the benefits of the estimators are illustrated in regularized discriminant analysis problem.
On the Log Partition Function of Ising Model on Stochastic Block Model

A sparse stochastic block model (SBM) with two communities is defined by the community probability $\pi_0,\pi_1$, and the connection probability between communities $a,b\in\{0,1\}$, namely $q_{ab} = \frac{\alpha_{ab}}{n}$. When $q_{ab}$ is constant in $a,b$, the random graph is simply the Erd\H{o}s-R\'{e}ny random graph. We evaluate the log partition function of the Ising model on sparse SBM with two communities. As an application, we give consistent parameter estimation of the sparse SBM with two communities in a special case. More specifically, let $d_0,d_1$ be the average degree of the two communities, i.e., $d_0\overset{def}{=}\pi_0\alpha_{00}+\pi_1\alpha_{01},d_1\overset{def}{=}\pi_0\alpha_{10}+\pi_1\alpha_{11}$. We focus on the regime $d_0=d_1$ (the regime $d_0\ne d_1$ is trivial). In this regime, there exists $d,\lambda$ and $r\geq 0$ with $\pi_0=\frac{1}{1+r}, \pi_1=\frac{r}{1+r}$, $\alpha_{00}=d(1+r\lambda), \alpha_{01}=\alpha_{10} = d(1-\lambda), \alpha_{11} = d(1+\frac{\lambda}{r})$. We give a consistent estimator of $r$ when $\lambda<0$. The estimator of $\lambda$ given by \citep{mossel2015reconstruction} is valid in the general situation. We also provide a random clustering algorithm which does not require knowledge of parameters and which is positively correlated with the true community label when $\lambda<0$.
How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms

In this paper we consider two topological transforms that are popular in applied topology: the Persistent Homology Transform and the Euler Characteristic Transform. Both of these transforms are of interest for their mathematical properties as well as their applications to science and engineering, because they provide a way of summarizing shapes in a topological, yet quantitative, way. Both transforms take a shape, viewed as a tame subset M M of R d \mathbb { R}^d , and associates to each direction v ∈ S d − 1 v\in S^{d-1} a shape summary obtained by scanning M M in the direction v v . These shape summaries are either persistence diagrams or piecewise constant integer-valued functions called Euler curves. By using an inversion theorem of Schapira, we show that both transforms are injective on the space of shapes, i.e. each shape has a unique transform. Moreover, we prove that these transforms determine continuous maps from the sphere to the space of persistence diagrams, equipped with any Wasserstein p p -distance, or the space of Euler curves, equipped with certain L p L^p norms. By making use of a stratified space structure on the sphere, induced by hyperplane divisions, we prove additional uniqueness results in terms of distributions on the space of Euler curves. Finally, our main result proves that any shape in a certain uncountable space of PL embedded shapes with plausible geometric bounds can be uniquely determined using only finitely many directions.
A note on "MLE in logistic regression with a diverging dimension"

This short note is to point the reader to notice that the proof of high dimensional asymptotic normality of MLE estimator for logistic regression under the regime $p_n=o(n)$ given in paper: "Maximum likelihood estimation in logistic regression models with a diverging number of covariates. Electronic Journal of Statistics, 6, 1838-1846. " is wrong.
Resampling-Based Analysis of Multivariate Data and Repeated Measures Designs with the R Package MANOVA.RM

The numerical availability of statistical inference methods for a modern and robust analysis of longitudinal- and multivariate data in factorial experiments is an essential element in research and education. While existing approaches that rely on specific distributional assumptions of the data (multivariate normality and/or characteristic covariance matrices) are implemented in statistical software packages, there is a need for user-friendly software that can be used for the analysis of data that do not fulfill the aforementioned assumptions and provide accurate p-value and confidence interval estimates. Therefore, newly developed statistical methods for the analysis of repeated measures designs and multivariate data that neither assume multivariate normality nor specific covariance matrices have been implemented in the freely available R-package MANOVA.RM. The package is equipped with a graphical user interface for plausible applications in academia and other educational purpose. Several motivating examples illustrate the application of the methods.
Nonparametric Bayesian posterior contraction rates for scalar diffusions with high-frequency data

We consider inference in the scalar diffusion model $dX_t=b(X_t)dt+\sigma(X_t)dW_t$ with discrete data $(X_{j\Delta_n})_{0\leq j \leq n}$, $n\to \infty,~\Delta_n\to 0$ and periodic coefficients. For $\sigma$ given, we prove a general theorem detailing conditions under which Bayesian posteriors will contract in $L^2$-distance around the true drift function $b_0$ at the frequentist minimax rate (up to logarithmic factors) over Besov smoothness classes. We exhibit natural nonparametric priors which satisfy our conditions. Our results show that the Bayesian method adapts both to an unknown sampling regime and to unknown smoothness.
A Scan Procedure for Multiple Testing

In a multiple testing framework, we propose a method that identifies the interval with the highest estimated false discovery rate of P-values and rejects the corresponding null hypotheses. Unlike the Benjamini-Hochberg method, which does the same but over intervals with an endpoint at the origin, the new procedure `scans' all intervals. In parallel with \citep*{storey2004strong}, we show that this scan procedure provides strong control of asymptotic false discovery rate. In addition, we investigate its asymptotic false non-discovery rate, deriving conditions under which it outperforms the Benjamini-Hochberg procedure. For example, the scan procedure is superior in power-law location models.
Augmented minimax linear estimation

Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized treatments. In this paper, we discuss a general approach to estimating such quantities: we begin with a simple plug-in estimator based on an estimate of the conditional expectation function, and then correct the plug-in estimator by subtracting a minimax linear estimate of its error. We show that our method is semiparametrically efficient under weak conditions and observe promising performance on both real and simulated data.