Miracle-dz/UniFAR-FTUs huggingface dataset:
Bayesian Analysis of Inertial Confinement Fusion Experiments at the National Ignition Facility

We develop a Bayesian inference method that allows the efficient determination of several interesting parameters from complicated high-energy-density experiments performed on the National Ignition Facility (NIF). The model is based on an exploration of phase space using the hydrodynamic code HYDRA. A linear model is used to describe the effect of nuisance parameters on the analysis, allowing an analytic likelihood to be derived that can be determined from a small number of HYDRA runs and then used in existing advanced statistical analysis methods. This approach is applied to a recent experiment in order to determine the carbon opacity and X-ray drive; it is found that the inclusion of prior expert knowledge and fluctuations in capsule dimensions and chemical composition significantly improve the agreement between experiment and theoretical opacity calculations. A parameterisation of HYDRA results is used to test the application of both Markov chain Monte Carlo (MCMC) and genetic algorithm (GA) techniques to explore the posterior. These approaches have distinct advantages and we show that both can allow the efficient analysis of high energy density experiments.
On the performance of FDR control: Constraints and a partial solution

The False Discovery Rate (FDR) paradigm aims to attain certain control on Type I errors with relatively high power for multiple hypothesis testing. The Benjamini–Hochberg (BH) procedure is a wellknown FDR controlling procedure. Under a random effects model, we show that, in general, unlike the FDR, the positive FDR (pFDR) of the BH procedure cannot be controlled at an arbitrarily low level due to the limited evidence provided by the observations to separate false and true nulls. This results in a criticality phenomenon, which is characterized by a transition of the procedure’s power from being positive to asymptotically 0 without any reduction in the pFDR, once the target FDR control level is below a positive critical value. To address the constraints on the power and pFDR control imposed by the criticality phenomenon, we propose a procedure which applies BH-type procedures at multiple locations in the domain of p-values. Both analysis and simulations show that the proposed procedure can attain substantially improved power and pFDR control.
The solution path of the generalized lasso

We present a path algorithm for the generalized lasso problem. This problem penalizes the $\ell_1$ norm of a matrix D times the coefficient vector, and has a wide range of applications, dictated by the choice of D. Our algorithm is based on solving the dual of the generalized lasso, which greatly facilitates computation of the path. For $D=I$ (the usual lasso), we draw a connection between our approach and the well-known LARS algorithm. For an arbitrary D, we derive an unbiased estimate of the degrees of freedom of the generalized lasso fit. This estimate turns out to be quite intuitive in many applications.
Nonparametric Bandits with Covariates

We consider a bandit problem which involves sequential sampling from two populations (arms). Each arm produces a noisy reward realization which depends on an observable random covariate. The goal is to maximize cumulative expected reward. We derive general lower bounds on the performance of any admissible policy, and develop an algorithm whose performance achieves the order of said lower bound up to logarithmic terms. This is done by decomposing the global problem into suitably "localized" bandit problems. Proofs blend ideas from nonparametric statistics and traditional methods used in the bandit literature.
CHARACTERIZING L 2 BOOSTING

We consider L 2 Boosting, a special case of Friedman’s generic boosting algorithm applied to linear regression under L 2 -loss. We study L 2 Boosting for an arbitrary regularization parameter and derive an exact closed form expression for the number of steps taken along a ﬁxed coordinate direction. This relationship is used to describe L 2 Boosting’s solution path, to describe new tools for studying its path, and to characterize some of the algorithm’s unique properties, including active set cycling, a property where the algo-rithm spends lengthy periods of time cycling between the same coordinates when the regularization parameter is arbitrarily small. Our ﬁxed descent analysis also reveals a repressible condition that limits the effectiveness of L 2 Boosting in correlated problems by preventing desirable variables from entering the solution path. As a simple remedy, a data augmentation method similar to that used for the elastic net is used to introduce L 2 -penalization and is shown, in combination with decorrelation, to reverse the repressible condition and circumvents L 2 Boosting’s deﬁciencies in correlated problems. In itself, this presents a new explanation for why the elastic net is successful in correlated problems and why methods like LAR and lasso can perform poorly in such settings.
On the estimation of smooth densities by strict probability densities at optimal rates in sup-norm

It is shown that the variable bandwidth density estimator proposed by McKay (1993a and b) following earlier findings by Abramson (1982) approximates density functions in $C^4(\mathbb R^d)$ at the minimax rate in the supremum norm over bounded sets where the preliminary density estimates on which they are based are bounded away from zero. A somewhat more complicated estimator proposed by Jones McKay and Hu (1994) to approximate densities in $C^6(\mathbb R)$ is also shown to attain minimax rates in sup norm over the same kind of sets. These estimators are strict probability densities.
New concentration inequalities for suprema of empirical processes

While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive concentration inequalities assuming only low moments for an envelope of the empirical process. These concentration inequalities are beneficial even when the envelope is much larger than the single functions under consideration.
Dose Finding with Escalation with Overdose Control (EWOC) in Cancer Clinical Trials

Traditionally, the major objective in phase I trials is to iden- tify a working-dose for subsequent studies, whereas the major endpoint in phase II and III trials is treatment efficacy. The dose sought is typ- ically referred to as the maximum tolerated dose (MTD). Several sta- tistical methodologies have been proposed to select the MTD in cancer phase I trials. In this manuscript, we focus on a Bayesian adaptive design, known as escalation with overdose control (EWOC). Several aspects of this design are discussed, including large sample properties of the sequence of doses selected in the trial, choice of prior distri- butions, and use of covariates. The methodology is exemplified with real-life examples of cancer phase I trials. In particular, we show in the recently completed ABR-217620 (naptumomab estafenatox) trial that omitting an important predictor of toxicity when dose assignments to cancer patients are determined results in a high percent of patients experiencing severe side effects and a significant proportion treated at sub-optimal doses.
Asymptotics of the discrete log‐concave maximum likelihood estimator and related applications

The assumption of log‐concavity is a flexible and appealing non‐parametric shape constraint in distribution modelling. In this work, we study the log‐concave maximum likelihood estimator of a probability mass function. We show that the maximum likelihood estimator is strongly consistent and we derive its pointwise asymptotic theory under both the well‐specified and misspecified settings. Our asymptotic results are used to calculate confidence intervals for the true log‐concave probability mass function. Both the maximum likelihood estimator and the associated confidence intervals may be easily computed by using the R package logcondiscr. We illustrate our theoretical results by using recent data from the H1N1 pandemic in Ontario, Canada.
Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality

We address the problem of density estimation with L s-loss by selection of kernel estimators. We develop a selection procedure and derive corresponding L s-risk oracle inequalities. It is shown that the proposed selection rule leads to the estimator being minimax adaptive over a scale of the anisotropic Nikol'skii classes. The main technical tools used in our derivations are uniform bounds on the L s-norms of empirical processes developed recently by Goldenshluger and Lepski [Ann. Probab. (2011), to appear].
Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations

The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partial noncentering can be used to accelerate convergence in MCMC and EM algorithms but are still not well studied for variational Bayes (VB) methods. As a fast deterministic approach to posterior approximation, VB is attracting increasing interest due to its suitability for large high-dimensional data. Use of different parametrizations for VB has not only computational but also statistical implications, as different parametrizations are associated with different factorized posterior approximations. We examine the use of partially noncentered parametrizations in VB for generalized linear mixed models (GLMMs). Our paper makes four contributions. First, we show how to implement an algorithm called nonconjugate variational message passing for GLMMs. Second, we show that the partially noncentered parametrization can adapt to the quantity of information in the data and determine a parametrization close to optimal. Third, we show that partial noncentering can accelerate convergence and produce more accurate posterior approximations than centering or noncentering. Finally, we demonstrate how the variational lower bound, produced as part of the computation, can be useful for model selection.
Generalized density clustering

We study generalized density-based clustering in which sharply defined clusters such as clusters on lower-dimensional manifolds are allowed. We show that accurate clustering is possible even in high dimensions. We propose two data-based methods for choosing the bandwidth and we study the stability properties of density clusters. We show that a simple graph-based algorithm successfully approximates the high density clusters.
Efficient hierarchical clustering for continuous data

We present an new sequential Monte Carlo sampler for coalescent based Bayesian hierarchical clustering. Our model is appropriate for modeling non-i.i. d. data and offers a substantial reduction of computational cost when compared to the original sampler without resorting to approximations. We also propose a quadratic complexity approximation that in practice shows almost no loss in performance compared to its counterpart. We show that as a byproduct of our formulation, we obtain a greedy algorithm that exhibits performance improvement over other greedy algorithms, particularly in small data sets. In order to exploit the correlation structure of the data, we describe how to incorporate Gaussian process priors in the model as a flexible way to model non-i.i. d. data. Results on artificial and real data show significant improvements over closely related approaches.
Statistical Analysis of Air Traffic in Latvian Region

The goal of the research is statistical analyzes of air traffic in airport 'Riga' zone. Special statistical methods oriented to the concrete object area - airspace of Latvia are developed. Some experiments are made to discover season's and during twenty-four hours unstationarity of this process. Air traffic intensity for some stationary period for some airways is estimated.
Flexible Low-Rank Statistical Modeling with Side Information

We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly incorporates row and column features, smoothing kernels, and other sources of side information by penalizing deviations from the row and column models. Moreover, a large class of these models can be estimated scalably using convex optimization. The computational bottleneck in each case is one singular value decomposition per iteration of a large but easy-to-apply matrix. Our framework generalizes traditional convex matrix completion and multi-task learning methods as well as maximum a posteriori estimation under a large class of popular hierarchical Bayesian models.
The ranking lasso and its application to sport tournaments

Ranking a vector of alternatives on the basis of a series of paired comparisons is a relevant topic in many instances. A popular example is ranking contestants in sport tournaments. To this purpose, paired comparison models such as the Bradley-Terry model are often used. This paper suggests fitting paired comparison models with a lasso-type procedure that forces contestants with similar abilities to be classified into the same group. Benefits of the proposed method are easier interpretation of rankings and a significant improvement of the quality of predictions with respect to the standard maximum likelihood fitting. Numerical aspects of the proposed method are discussed in detail. The methodology is illustrated through ranking of the teams of the National Football League 2010-2011 and the American College Hockey Men's Division I 2009-2010.
Structural Intervention Distance (SID) for Evaluating Causal Graphs

Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well-suited for evaluating graphs that are used for computing interventions. Instead of DAGs it is also possible to compare CPDAGs, completed partially directed acyclic graphs that represent Markov equivalence classes. Since it differs significantly from the popular Structural Hamming Distance (SHD), the SID constitutes a valuable additional measure. We discuss properties of this distance and provide an efficient implementation with software code available on the first author's homepage (an R package is under construction).
Generalizing the No-U-Turn Sampler to Riemannian Manifolds

Hamiltonian Monte Carlo provides efficient Markov transitions at the expense of introducing two free parameters: a step size and total integration time. Because the step size controls discretization error it can be readily tuned to achieve certain accuracy criteria, but the total integration time is left unconstrained. Recently Hoffman and Gelman proposed a criterion for tuning the integration time in certain systems with their No U-Turn Sampler, or NUTS. In this paper I investigate the dynamical basis for the success of NUTS and generalize it to Riemannian Manifold Hamiltonian Monte Carlo.
A generalization of a Gaussian semiparametric estimator on multivariate long-range dependent processes

In this paper, we propose and study a general class of Gaussian semiparametric estimators (GSE) of the fractional differencing parameter in the context of long-range dependent multivariate time series. We establish large sample properties of the estimator without assuming Gaussianity. The class of models considered here satisfies simple conditions on the spectral density function, restricted to a small neighbourhood of the zero frequency and includes important class of vector autoregressive fractionally integrated moving average processes. We also present a simulation study to assess the finite sample properties of the proposed estimator based on a smoothed version of the GSE which supports its competitiveness.
Maximum Fidelity

The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation: Which candidate distribution provides the best fit to the observed data? , (2) Goodness-of-fit : How concordant is this distribution with the observed data? , and (3) Uncertainty : How concordant are other candidate distributions with the observed data? A simple unified approach for univariate data that addresses these traditionally distinct statistical notions is presented called “maximum fidelity”. Maximum fidelity is a frequentist approach (in the strict manner of Peirce and Wilson) that is fundamentally based on model concordance with the observed data. The fidelity statistic is a general information measure based on the coordinate-independent cumulative distribution and critical yet previously neglected symmetry considerations. A highly accurate gamma-function approximation for the distribution of the fidelity under the null hypothesis (valid for any number of data points) allows direct conversion of fidelity to absolute model concordance (p value), permitting immediate computation of the concordance landscape over the entire model parameter space. Maximization of the fidelity allows identification of the most concordant model distribution, generating a method for parameter estimation. Neighboring, less concordant distributions provide the “uncertainty” in this estimate. Detailed comparisons with other well-established statistical approaches reveal that maximum fidelity provides an optimal approach for parameter estimation (superior to maximum likelihood) and a generally optimal approach for goodness-of-fit assessment of arbitrary models applied to any number of univariate data points distributed on the circle or the line. Extensions of this approach to binary data, binned data, and multidimensional data are described, along with improved versions of classical parametric and nonparametric statistical tests. Maximum fidelity provides a philosophically consistent, robust, and seemingly optimal foundation for statistical inference. All findings in this manuscript are presented in an elementary way in order to be immediately accessible to researchers in the sciences, social sciences, and all other fields utilizing statistical analysis (medicine, engineering, finance, etc.). 1 ar X iv :1 30 1. 51 86 v1 [ m at h. ST ] 2 2 Ja n 20 13
Estimating the Size and Distribution of Networked Populations with Snowball Sampling

A new strategy is introduced for estimating population size and networked population characteristics. Sample selection is based on a multi-wave snowball sampling design. A generalized stochastic block model is posited for the population’s network graph. Inference is based on a Bayesian data augmentation procedure. Applications are provided to simulated populations and an empirical population. The results demonstrate that statistically efficient estimates of the size and distribution of the population can be achieved.
Dimension-Independent MCMC Sampling for Inverse Problems with Non-Gaussian Priors

The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem. A challenge of particular importance arises in Bayesian inverse problems where the target distribution may be supported on an infinite dimensional space. In practice this involves the approximation of measures defined on sequences of spaces of increasing dimension. Motivated by an elliptic inverse problem with non-Gaussian prior, we study the design of proposal chains for the Metropolis-Hastings algorithm with dimension independent performance. Dimension-independent bounds on the Monte-Carlo error of MCMC sampling for Gaussian prior measures have already been established. In this paper we provide a simple recipe to obtain these bounds for non-Gaussian prior measures. To illustrate the theory we consider an elliptic inverse problem arising in groundwater flow. We explicitly construct an efficient Metropolis-Hastings proposal based on local proposals, and we provide numerical evidence which supports the theory.
A hierarchical latent class model for predicting disability small area counts from survey data

We consider the estimation of the number of severely disabled people by using data from the Italian survey on ‘Health conditions and appeal to Medicare’. In this survey, disability is indirectly measured by using a set of categorical items, which consider a set of functions concerning the ability of a person to accomplish everyday tasks. Latent class models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey is designed to provide reliable estimates at the level of administrative regions (‘Nomenclature des unités territoriales statistiques’, level 2), whereas local authorities are interested in quantifying the number of people who belong to each latent class at a subregional level. Therefore, small area estimation techniques should be used. The challenge is that the variable of interest is not observed. Adopting a full Bayesian approach, we base small area estimation on a latent class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data by using penalized splines. Demmler–Reinsch bases are shown to improve speed and mixing of Markov chain Monte Carlo chains used to simulate posteriors.
On asymptotics of ICA estimators and their performance indices

Independent component analysis (ICA) has become a popular multivariate analysis and signal processing technique with diverse applications. This paper is targeted at discussing theoretical large sample properties of ICA unmixing matrix functionals. We provide a formal definition of unmixing matrix functional and consider two popular estimators in detail: the family based on two scatter matrices with the independence property (e.g., FOBI estimator) and the family of deflation-based fastICA estimators. The limiting behavior of the corresponding estimates is discussed and the asymptotic normality of the deflation-based fastICA estimate is proven under general assumptions. Furthermore, properties of several performance indices commonly used for comparison of different unmixing matrix estimates are discussed and a new performance index is proposed. The proposed index fullfills three desirable features which promote its use in practice and distinguish it from others. Namely, the index possesses an easy interpretation, is fast to compute and its asymptotic properties can be inferred from asymptotics of the unmixing matrix estimate. We illustrate the derived asymptotical results and the use of the proposed index with a small simulation study.