Miracle-dz/UniFAR-FTUs huggingface dataset:
Utilizing Distance Metrics on Lineups to Examine What People Read From Data Plots

Graphics play a crucial role in statistical analysis and data mining. This paper describes metrics developed to assist the use of lineups for making inferential statements. Lineups embed the plot of the data among a set of null plots, and engage a human observer to select the plot that is most different from the rest. If the data plot is selected it corresponds to the rejection of a null hypothesis. Metrics are calculated in association with lineups, to measure the quality of the lineup, and help to understand what people see in the data plots. The null plots represent a finite sample from a null distribution, and the selected sample potentially affects the ease or difficulty of a lineup. Distance metrics are designed to describe how close the true data plot is to the null plots, and how close the null plots are to each other. The distribution of the distance metrics is studied to learn how well this matches to what people detect in the plots, the effect of null generating mechanism and plot choices for particular tasks. The analysis was conducted on data that has already been collected from Amazon Turk studies conducted with lineups for studying an array of data analysis tasks.
Regression version of the Matsumoto-Yor type characterization of the gamma and Kummer distributions

In this paper we study a Matsumoto-Yor type property for the gamma and Kummer inde- pendent variables discovered in Koudou and Vallois (2012). We prove that constancy of regressions of U = (1 + 1/(X + Y ))=(1 + 1/X) given V = X + Y and of 1/U given V , where X and Y are indepen- dent and positive random variables, characterizes the gamma and Kummer distributions. This result completes characterizations by independence of U and V obtained, under smoothness assumptions for densities, in Koudou and Vallois (2011, 2012). Since we work with differential equations for the Laplace transforms, no density assumptions are needed.
A theory of nonparametric regression in the presence of complex nuisance components

In this paper, we consider the nonparametric random regression model $Y=f_1(X_1)+f_2(X_2)+\epsilon$ and address the problem of estimating the function $f_1$. The term $f_2(X_2)$ is regarded as a nuisance term which can be considerably more complex than $f_1(X_1)$. Under minimal assumptions, we prove several nonasymptotic $L^2(\mathbb{P}^X)$-risk bounds for our estimators of $f_1$. Our approach is geometric and based on considerations in Hilbert spaces. It shows that the performance of our estimators is closely related to geometric quantities, such as minimal angles and Hilbert-Schmidt norms. Our results establish new conditions under which the estimators of $f_1$ have up to first order the same sharp upper bound as the corresponding estimators of $f_1$ in the model $Y=f_1(X_1)+\epsilon$. As an example we apply the results to an additive model in which the number of components is very large or in which the nuisance components are considerably less smooth than $f_1$. In particular, the results apply to an asymptotic scenario in which the number of components is allowed to increase with the sample size.
A Generalized Savage-Dickey Ratio

In this brief research note I present a generalized version of the Savage-Dickey Density Ratio for representation of the Bayes factor (or marginal likelihood ratio) of nested statistical models; the new version takes the form of a Radon-Nikodym derivative and is thus applicable to a wider family of probability spaces than the original (restricted to those admitting an ordinary Lebesgue density). A derivation is given following the measure-theoretic construction of Marin & Robert (2010), and the equivalent estimator is demonstrated in application to a distributional modeling problem.
An RKHS Approach to Estimation with Sparsity Constraints

The investigation of the effects of sparsity or sparsity constraints in signal processing problems has received considerable attention recently. Sparsity constraints refer to the a priori information that the object or signal of interest can be represented by using only few elements of a predefined dictionary. Within this thesis, sparsity refers to the fact that a vector to be estimated has only few nonzero entries. One specific field concerned with sparsity constraints has become popular under the name Compressed Sensing (CS). Within CS, the sparsity is exploited in order to perform (nearly) lossless compression. Moreover, this compression is carried out jointly or simultaneously with the process of sensing a physical quantity. In contrast to CS, one can alternatively use sparsity to enhance signal processing methods. Obviously, sparsity constraints can only improve the obtainable estimation performance since the constraints can be interpreted as an additional prior information about the unknown parameter vector which is to be estimated. Our main focus will be on this aspect of sparsity, i.e., we analyze how much we can gain in estimation performance due to the sparsity constraints.
Nelson-Aalen tail product-limit process and extreme value index estimation under random censorship

On the basis of Nelson-Aalen nonparametric estimator of the cumulative distribution function, we provide a weak approximation to tail product-limit process for randomly right-censored heavy-tailed data. In this context, a new consistent reduced-bias estimator of the extreme value index is introduced and its asymptotic normality is established only by assuming the second-order regular variation of the underlying distribution function. A simulation study shows that the newly proposed estimator performs better than the existing ones.
Event Conditional Correlation: Or How Non-Linear Linear Dependence Can Be

Entries of datasets are often collected only if an event occurred: taking a survey, enrolling in an experiment and so forth. However, such partial samples bias classical correlation estimators. Here we show how to correct for such sampling effects through two complementary estimators of event conditional correlation: the correlation of two random variables conditional on a given event. First, we provide under minimal assumptions proof of consistency and asymptotic normality for the proposed estimators. Then, through synthetic examples, we show that these estimators behave well in small-sample and yield powerful methodologies for non-linear regression as well as dependence testing. Finally, by using the two estimators in tandem, we explore counterfactual dependence regimes in a financial dataset. By so doing we show that the contagion which took place during the 2007--2011 financial crisis cannot be explained solely by increased financial risk.
Consistent Estimation of Low-Dimensional Latent Structure in High-Dimensional Data

We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space that spans the conditional means, it is possible to consistently recover the structure using only information up to the second moments of these random variables. This finding, specialized to one-parameter exponential families whose variance function is quadratic in their means, allows for the derivation of an explicit estimator of such latent structure. This approach serves as a latent variable model estimator and as a tool for dimension reduction for a high-dimensional matrix of data composed of many related variables. Our theoretical results are verified by simulation studies and an application to genomic data.
Sequential Monte Carlo with Highly Informative Observations

We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is simulating bridges between given initial and final values. The basic idea is to introduce a schedule of intermediate weighting and resampling times between observation times, which guide particles towards the final state. This can always be done for continuous-time models, and may be done for discrete-time models under sparse observation regimes; our main focus is on continuous-time diffusion processes. The methods are broadly applicable in that they support multivariate models with partial observation, do not require simulation of the backward transition (which is often unavailable), and, where possible, avoid pointwise evaluation of the forward transition. When simulating bridges, the last characteristic cannot be avoided entirely without concessions, and we suggest an $\.
Markov Random Fields and Mass Spectra Discrimination

For mass spectra acquired from cancer patients by MALDI or SELDI techniques, automated discrimination between cancer types or stages has often been implemented by machine learnings. These techniques typically generate "black-box" classifiers, which are difficult to interpret biologically. We develop new and efficient signature discovery algorithms leading to interpretable signatures combining the discriminating power of explicitly selected small groups of biomarkers, identified by their m/z ratios. Our approach is based on rigorous stochastic modeling of "homogeneous" datasets of mass spectra by a versatile class of parameterized Markov Random Fields. We present detailed algorithms validated by precise theoretical results. We also outline the successful tests of our approach to generate efficient explicit signatures for six benchmark discrimination tasks, based on mass spectra acquired from colorectal cancer patients, as well as from ovarian cancer patients.
Reduced-rank Regression in Sparse Multivariate Varying-Coefficient Models with High-dimensional Covariates

In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction methods in sparse multivariate regression models. Previous studies on joint variable and rank selection have focused on parametric models while here we consider the more challenging varying-coefficient models which make the investigation on nonlinear interactions of variables possible. Spline approximation, rank constraints and concave group penalties are utilized for model estimation. Asymptotic oracle properties of the estimators are presented. We also propose reduced-rank independent screening to deal with the situation when the dimension is so high that penalized estimation cannot be efficiently applied. In simulations, we show the advantages of simultaneously performing variable and rank selection. A real data set is analyzed to illustrate the good prediction performance when incorporating interactions between genetic variables and an index variable.
Model Comparison and Assessment for Single Particle Tracking in Biological Fluids

ABSTRACT State-of-the-art techniques in passive particle-tracking microscopy provide high-resolution path trajectories of diverse foreign particles in biological fluids. For particles on the order of 1 μm diameter, these paths are generally inconsistent with simple Brownian motion. Yet, despite an abundance of data confirming these findings and their wide-ranging scientific implications, stochastic modeling of the complex particle motion has received comparatively little attention. Even among posited models, there is virtually no literature on likelihood-based inference, model comparisons, and other quantitative assessments. In this article, we develop a rigorous and computationally efficient Bayesian methodology to address this gap. We analyze two of the most prevalent candidate models for 30-sec paths of 1 μm diameter tracer particles in human lung mucus: fractional Brownian motion (fBM) and a Generalized Langevin Equation (GLE) consistent with viscoelastic theory. Our model comparisons distinctly favor GLE over fBM, with the former describing the data remarkably well up to the timescales for which we have reliable information. Supplementary materials for this article are available online.
Bayesian benchmark dose analysis

An important objective in environmental risk assessment is the estimation of minimum exposure levels called benchmark doses (BMDs), which induce a pre‐specified benchmark response in a target population. Established inferential approaches for BMD analysis typically involve one‐sided, frequentist confidence limits, leading in practice to what are called benchmark dose lower Limits (BMDLs). Appeal to Bayesian modeling and credible limits for building BMDLs is far less developed, however. Indeed, for the few existing forms of Bayesian BMDs, informative prior information is seldom incorporated. We develop reparameterized quantal‐response models that explicitly describe the BMD as a target parameter. Our goal is to obtain an improved estimation and calculation archetype for the BMD and for the BMDL by quantifying prior beliefs representing parameter uncertainty in the statistical model. Implementation is facilitated via a Monte Carlo‐based adaptive Metropolis algorithm to approximate the posterior distribution. An example from environmental carcinogenicity testing illustrates the methodology. Copyright © 2015 John Wiley & Sons, Ltd.
BAYESIAN LINEAR REGRESSION WITH SPARSE PRIORS

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse vector, and to give optimal prediction of the response vector. It is also shown to select the correct sparse model, or at least the coefficients that are significantly different from zero. The asymptotic shape of the posterior distribution is characterized and employed to the construction and study of credible sets for uncertainty quantification.
Projective Stochastic Equations and Nonlinear Long Memory

A projective moving average {X t , t ∈ ℤ} is a Bernoulli shift written as a backward martingale transform of the innovation sequence. We introduce a new class of nonlinear stochastic equations for projective moving averages, termed projective equations, involving a (nonlinear) kernel Q and a linear combination of projections of X t on ‘intermediate’ lagged innovation subspaces with given coefficients α i and β i,j . The class of such equations includes usual moving average processes and the Volterra series of the LARCH model. Solvability of projective equations is obtained using a recursive equality for projections of the solution X t . We show that, under certain conditions on Q, α i , and β i,j , this solution exhibits covariance and distributional long memory, with fractional Brownian motion as the limit of the corresponding partial sums process.
Forecasting high-dimensional realized volatility matrices using a factor model

Modelling and forecasting covariance matrices of asset returns play a crucial role in many financial fields, such as portfolio allocation and asset pricing. The availability of high-frequency intraday data enables the modelling of the realized covariance matrix directly. However, most models in the literature suffer from the curse of dimensionality, i.e. the number of parameters needed increases at the rate of the square of the number of assets. To solve the problem, we propose a factor model with a diagonal Conditional Autoregressive Wishart model for the factor realized covariance matrices. Consequently, the positive definiteness of the estimated covariance matrix is ensured with the proposed model. Asymptotic theory is derived for the estimated parameters. In the extensive empirical analysis, we find that the number of parameters can be reduced significantly; to only about one-tenth of the benchmark model. Furthermore, the proposed model maintains a comparable performance with a benchmark vector autoregressive model for different forecast horizons.
A remark on the rates of convergence for integrated volatility estimation in the presence of jumps

The optimal rate of convergence of estimators of the integrated volatility, for a discontinuous It\^{o} semimartingale sampled at regularly spaced times and over a fixed time interval, has been a long-standing problem, at least when the jumps are not summable. In this paper, we study this optimal rate, in the minimax sense and for appropriate "bounded" nonparametric classes of semimartingales. We show that, if the $r$th powers of the jumps are summable for some $r\in[0,2)$, the minimax rate is equal to $\min(\sqrt{n},(n\log n)^{(2-r)/2})$, where $n$ is the number of observations.
Variations of Q–Q Plots: The Power of Our Eyes!

Abstract In statistical modeling, we strive to specify models that resemble data collected in studies or observed from processes. Consequently, distributional specification and parameter estimation are central to parametric models. Graphical procedures, such as the quantile–quantile (Q–Q) plot, are arguably the most widely used method of distributional assessment, though critics find their interpretation to be overly subjective. Formal goodness of fit tests are available and are quite powerful, but only indicate whether there is a lack of fit, not why there is lack of fit. In this article, we explore the use of the lineup protocol to inject rigor into graphical distributional assessment and compare its power to that of formal distributional tests. We find that lineup tests are considerably more powerful than traditional tests of normality. A further investigation into the design of Q–Q plots shows that de-trended Q–Q plots are more powerful than the standard approach as long as the plot preserves distances in x and y to be the same. While we focus on diagnosing nonnormality, our approach is general and can be directly extended to the assessment of other distributions.
Penalised inference for autoregressive moving average models with time-dependent predictors

Linear models that contain a time-dependent response and explanatory variables have attracted much interest in recent years. The most general form of the existing approaches is of a linear regression model with autoregressive moving average residuals. The addition of the moving average component results in a complex model with a very challenging implementation. In this paper, we propose to account for the time dependency in the data by explicitly adding autoregressive terms of the response variable in the linear model. In addition, we consider an autoregressive process for the errors in order to capture complex dynamic relationships parsimoniously. To broaden the application of the model, we present an $l_1$ penalized likelihood approach for the estimation of the parameters and show how the adaptive lasso penalties lead to an estimator which enjoys the oracle property. Furthermore, we prove the consistency of the estimators with respect to the mean squared prediction error in high-dimensional settings, an aspect that has not been considered by the existing time-dependent regression models. A simulation study and real data analysis show the successful applications of the model on financial data on stock indexes.
Supervised Classification Using Sparse Fisher's LDA

It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications where classification is needed in the high-dimensional setting. Naive implementation of Fisher's rule in this case fails to provide good results because the sample covariance matrix is singular. Moreover, by constructing a classifier that relies on all features the interpretation of the results is challenging. Our goal is to provide robust classification that relies only on a small subset of important features and accounts for the underlying correlation structure. We apply a lasso-type penalty to the discriminant vector to ensure sparsity of the solution and use a shrinkage type estimator for the covariance matrix. The resulting optimization problem is solved using an iterative coordinate ascent algorithm. Furthermore, we analyze the effect of nonconvexity on the sparsity level of the solution and highlight the difference between the penalized and the constrained versions of the problem. The simulation results show that the proposed method performs favorably in comparison to alternatives. The method is used to classify leukemia patients based on DNA methylation features.
Modeling US housing prices by spatial dynamic structural equation models

This article proposes a spatial dynamic structural equation model for the analysis of housing prices at the State level in the USA. The study contributes to the existing literature by extending the use of dynamic factor models to the econometric analysis of multivariate lattice data. One of the main advantages of our model formulation is that by modeling the spatial variation via spatially structured factor loadings, we entertain the possibility of identifying similarity "regions" that share common time series components. The factor loadings are modeled as conditionally independent multivariate Gaussian Markov Random Fields, while the common components are modeled by latent dynamic factors. The general model is proposed in a state-space formulation where both stationary and nonstationary autoregressive distributed-lag processes for the latent factors are considered. For the latent factors which exhibit a common trend, and hence are cointegrated, an error correction specification of the (vector) autoregressive distributed-lag process is proposed. Full probabilistic inference for the model parameters is facilitated by adapting standard Markov chain Monte Carlo (MCMC) algorithms for dynamic linear models to our model formulation. The fit of the model is discussed for a data set of 48 States for which we model the relationship between housing prices and the macroeconomy, using State level unemployment and per capita personal income.
A Bayesian semiparametric approach to learning about gene–gene interactions in case-control studies

ABSTRACT Gene–gene interactions are often regarded as playing significant roles in influencing variabilities of complex traits. Although much research has been devoted to this area, to date a comprehensive statistical model that addresses the various sources of uncertainties, seem to be lacking. In this paper, we propose and develop a novel Bayesian semiparametric approach composed of finite mixtures based on Dirichlet processes and a hierarchical matrix-normal distribution that can comprehensively account for the unknown number of sub-populations and gene–gene interactions. Then, by formulating novel and suitable Bayesian tests of hypotheses we attempt to single out the roles of the genes, individually, and in interaction with other genes, in case-control studies. We also attempt to identify the significant loci associated with the disease. Our model facilitates a highly efficient parallel computing methodology, combining Gibbs sampling and Transformation-based MCMC (TMCMC). Application of our ideas to biologically realistic data sets revealed quite encouraging performance. We also applied our ideas to a real, myocardial infarction dataset, and obtained interesting results that partly agree with, and also complement, the existing works in this area, to reveal the importance of sophisticated and realistic modeling of gene–gene interactions.