Miracle-dz/UniFAR-FTUs huggingface dataset:
The Horseshoe+ Estimator of Ultra-Sparse Signals

We propose a new prior for ultra-sparse signal detection that we term the "horseshoe+ prior. " The horseshoe+ prior is a natural extension of the horseshoe prior that has achieved success in the estimation and detection of sparse signals and has been shown to possess a number of desirable theoretical properties while enjoying computational feasibility in high dimensions. The horseshoe+ prior builds upon these advantages. Our work proves that the horseshoe+ posterior concentrates at a rate faster than that of the horseshoe in the Kullback-Leibler (K-L) sense. We also establish theoretically that the proposed estimator has lower posterior mean squared error in estimating signals compared to the horseshoe and achieves the optimal Bayes risk in testing up to a constant. For global-local scale mixture priors, we develop a new technique for analyzing the marginal sparse prior densities using the class of Meijer-G functions. In simulations, the horseshoe+ estimator demonstrates superior performance in a standard design setting against competing methods, including the horseshoe and Dirichlet-Laplace estimators. We conclude with an illustration on a prostate cancer data set and by pointing out some directions for future research.
A Location-Mixture Autoregressive Model for Online Forecasting of Lung Tumor Motion

Lung tumor tracking for radiotherapy requires real-time, multiple-step ahead forecasting of a quasi-periodic time series recording instantaneous tumor locations. We introduce a location-mixture autoregressive (LMAR) process that admits multimodal conditional distributions, fast approximate inference using the EM algorithm and accurate multiple-step ahead predictive distributions. LMAR outperforms several commonly used methods in terms of out-of-sample prediction accuracy using clinical data from lung tumor patients. With its superior predictive performance and real-time computation, the LMAR model could be effectively implemented for use in current tumor tracking systems.
Regression modeling on stratified data with the lasso

We consider the estimation of regression models on strata defined using a categorical covariate, in order to identify interactions between this categorical covariate and the other predictors. A basic approach requires the choice of a reference stratum. We show that the performance of a penalized version of this approach depends on this arbitrary choice. We propose a refined approach that bypasses this arbitrary choice, at almost no additional computational cost. Regarding model selection consistency, our proposal mimics the strategy based on an optimal and covariate-specific choice for the reference stratum. Results from an empirical study confirm that our proposal generally outperforms the basic approach in the identification and description of the interactions. An illustration on gene expression data is provided.
Distribution System Load and Forecast Model

Abstract—This short document provides experimental evidencefor the set of assumptions on the mean load and forecast errorsmade in [6] and [7]. We show that the mean load at any givennode is distributed normally, where we compute the mean andvariance. We then present an aggregation-error curve for a singleday ahead forecaster. Residual analysis shows that beyond 500customers, gaussian residuals is a reasonable model. We then showthe forecaster has uncorrelated errors. I. S TATISTICAL M ODELING OF P ROTECTIVE L OADS The model for the distribution system used in [6] and [7]is of a tree Twhere vertices in the network are loads whileedges of the network are protective relays which can disconnectloads from the network. To determine a statistical model of theloads for use in simulation we rely on the Paciﬁc NorthwestNational Laboratories Taxonomy Feeders [2]. For each oneof the feeders, the individual loads were aggregated aroundthe respective protective device. For this analysis, fuses andswitches are considered. We analyze all 23 feeders and performaggregate analysis based on the combined load information.An empirical histogram of the load values is given in Figure1(a). We propose that the loads at each node in the networkfollow a generalized Pareto distribution which is of the form.f(x;;˙;) =1˙1+x ˙
The Population Posterior and Bayesian Inference on Streams

Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop population variational Bayes, a new approach for using Bayesian modeling to analyze streams of data. It approximates a new type of distribution, the population posterior, which combines the notion of a population distribution of the data with Bayesian inference in a probabilistic model. We study our method with latent Dirichlet allocation and Dirichlet process mixtures on several large-scale data sets.
On the optimal estimation of probability measures in weak and strong topologies

Given random samples drawn i.i. d. from a probability measure $\mathbb{P}$ (defined on say, $\mathbb{R}^d$), it is well-known that the empirical estimator is an optimal estimator of $\mathbb{P}$ in weak topology but not even a consistent estimator of its density (if it exists) in the strong topology (induced by the total variation distance). On the other hand, various popular density estimators such as kernel and wavelet density estimators are optimal in the strong topology in the sense of achieving the minimax rate over all estimators for a Sobolev ball of densities. Recently, it has been shown in a series of papers by Gin\'{e} and Nickl that these density estimators on $\mathbb{R}$ that are optimal in strong topology are also optimal in $\|\cdot\|_{\mathcal{F}}$ for certain choices of $\mathcal{F}$ such that $\|\cdot\|_{\mathcal{F}}$ metrizes the weak topology, where $\|\mathbb{P}\|_{\mathcal{F}}:=\sup\{\int f\,\mathrm{d}\mathbb{P}: f\in\mathcal{F}\}$. In this paper, we investigate this problem of optimal estimation in weak and strong topologies by choosing $\mathcal{F}$ to be a unit ball in a reproducing kernel Hilbert space (say $\mathcal{F}_H$ defined over $\mathbb{R}^d$), where this choice is both of theoretical and computational interest. Under some mild conditions on the reproducing kernel, we show that $\|\cdot\|_{\mathcal{F}_H}$ metrizes the weak topology and the kernel density estimator (with $L^1$ optimal bandwidth) estimates $\mathbb{P}$ at dimension independent optimal rate of $n^{-1/2}$ in $\|\cdot\|_{\mathcal{F}_H}$ along with providing a uniform central limit theorem for the kernel density estimator.
Hierarchical reverberation mapping

Reverberation mapping (RM) is an important technique in studies of active galactic nuclei (AGN). The key idea of RM is to measure the time lag $\tau$ between variations in the continuum emission from the accretion disc and subsequent response of the broad line region (BLR). The measurement of $\tau$ is typically used to estimate the physical size of the BLR and is combined with other measurements to estimate the black hole mass $M_{\rm BH}$. A major difficulty with RM campaigns is the large amount of data needed to measure $\tau$. Recently, Fine et al (2012) introduced a new approach to RM where the BLR light curve is sparsely sampled, but this is counteracted by observing a large sample of AGN, rather than a single system. The results are combined to infer properties of the sample of AGN. In this letter we implement this method using a hierarchical Bayesian model and contrast this with the results from the previous stacked cross-correlation technique. We find that our inferences are more precise and allow for more straightforward interpretation than the stacked cross-correlation results.
Fractionally integrated COGARCH processes

We construct fractionally integrated continuous-time GARCH models, which capture the observed long range dependence of squared volatility in high-frequency data. Since the usual Molchan-Golosov and Mandelbrot-van-Ness fractional kernels lead to problems in the definition of the model, we resort to moderately long memory processes by choosing a fractional parameter $d\in(-0.5,0)$ and remove the singularities of the kernel to obtain non-pathological sample paths. The volatility of the new fractional COGARCH process has positive features like stationarity, and its covariance function shows an algebraic decay, which make it applicable to econometric high-frequency data. In an empirical application the model is fitted to exchange rate data using a simulation-based version of the generalised method of moments.
Exact post-selection inference, with application to the lasso

We develop a general approach to valid inference after model selection. At the core of our framework is a result that characterizes the distribution of a post-selection estimator conditioned on the selection event. We specialize the approach to model selection by the lasso to form valid confidence intervals for the selected coefficients and test whether all relevant variables have been included in the model.
Capacity Value of Additional Generation: Probability Theory and Sampling Uncertainty

The concept of capacity value is widely used to quantify the contribution of additional generation (most notably renewables) within generation adequacy assessments. This paper surveys the existing probability theory of assessment of the capacity value of additional generation, and discusses the available statistical estimation methods for risk measures which depend on the joint distribution of demand and available additional capacity (with particular reference to wind). Preliminary results are presented on assessment of sampling uncertainty in hindcast LOLE and capacity value calculations, using bootstrap resampling. These results indicate strongly that, if the hindcast calculation is dominated by extremes of demand minus wind, there is very large sampling uncertainty in the results due to very limited historic experience of high demands coincident with poor wind resource. For meaningful calculations, some form of statistical smoothing will therefore be required in distribution estimation.
Measuring the vulnerability of the Uruguayan population to vector-borne diseases via spatially hierarchical factor models

We propose a model-based vulnerability index of the population from Uruguay to vector-borne diseases. We have available measurements of a set of variables in the census tract level of the 19 Departmental capitals of Uruguay. In particular, we propose an index that combines different sources of information via a set of micro-environmental indicators and geographical location in the country. Our index is based on a new class of spatially hierarchical factor models that explicitly account for the different levels of hierarchy in the country, such as census tracts within the city level, and cities in the country level. We compare our approach with that obtained when data are aggregated in the city level. We show that our proposal outperforms current and standard approaches, which fail to properly account for discrepancies in the region sizes, for example, number of census tracts. We also show that data aggregation can seriously affect the estimation of the cities vulnerability rankings under benchmark models.
The McDonald Modified Weibull Distribution: Properties and Applications

A six parameter distribution so-called the McDonald modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the beta modified Weibull, Kumaraswamy modified Weibull, McDonald Weibull and modified Weibull distribution,among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments.We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.
Change point analysis of second order characteristics in non-stationary time series

A restrictive assumption in the work on testing for structural breaks in time series consists in the fact that the model is formulated such that the stochastic process under the null hypothesis of “no change-point” is stationary. This assumption is crucial to derive (asymptotic) critical values for the corresponding testing procedures using an elegant and powerful mathematical theory, but it might be not very realistic from a practical point of view. For example, if change point analysis for a particular parameter of the process (such as the variance) is performed, it is not necessary clear why other parameters (such as the mean or higher order moments) have to stay constant under the hypothesis that there is no change point in the parameter of interest. This paper develops change point analysis under less restrictive assumptions and deals with
Identification Problem for The Analysis of Binary Data with Non-ignorable Missing

When a missing-data mechanism is NMAR or non-ignorable, missingness is itself vital information and it must be taken into the likelihood, which, however, needs to introduce additional parameters to be estimated. The incompleteness of the data and introduction of more parameters can cause the identification problem. When a response variable is binary, it becomes a more serious problem because of less information of bi- nary data, however, there are no methods to briefly verify whether a mode is identified or not. Therefore, we provide a new necessary and sufficient condition to easily check model identifiability when analyzing binary data with non-ignorable missing by condi- tional models. This condition can give us what condition is needed for a model to have identifiability as well as make easily check the identifiability of a model.
Robust Estimation under Heavy Contamination using Enlarged Models

In data analysis, contamination caused by outliers is inevitable, and robust statistical methods are strongly demanded. In this paper, our concern is to develop a new approach for robust data analysis based on scoring rules. The scoring rule is a discrepancy measure to assess the quality of probabilistic forecasts. We propose a simple way of estimating not only the parameter in the statistical model but also the contamination ratio of outliers. Estimating the contamination ratio is important, since one can detect outliers out of the training samples based on the estimated contamination ratio. For this purpose, we use scoring rules with an extended statistical models, that is called the enlarged models. Also, the regression problems are considered. We study a complex heterogeneous contamination, in which the contamination ratio of outliers in the dependent variable may depend on the independent variable. We propose a simple method to obtain a robust regression estimator under heterogeneous contamination. In addition, we show that our method provides also an estimator of the expected contamination ratio that is available to detect the outliers out of training samples. Numerical experiments demonstrate the effectiveness of our methods compared to the conventional estimators.
A note on a Bayesian nonparametric estimator of the discovery probability

Favaro, Lijoi, and Pruenster (2012, Biometrics, 68, 1188--1196) derive a novel Bayesian nonparametric estimator of the probability of detecting at the $(n+m+1)$th observation a species already observed with any given frequency in an enlarged sample of size $n+m$, conditionally on a basic sample of size $n$. Unfortunately the general result under Gibbs priors (Theorem 2), and consequently the explicit result under $(\alpha, \theta)$ Poisson-Dirichlet priors (Proposition 3), appear to be wrong. Here we provide the correct formulas for both the results, obtained by means of a new technique devised in Cerquetti (2013). We verify the correctness of our derivation by an explicit counterproof for the two-parameter Poisson-Dirichlet case.
Estimating parameters of a multipartite loglinear graph model via the EM algorithm

We will amalgamate the Rash model (for rectangular binary tables) and the newly introduced $\alpha$-$\beta$ models (for random undirected graphs) in the framework of a semiparametric probabilistic graph model. Our purpose is to give a partition of the vertices of an observed graph so that the generated subgraphs and bipartite graphs obey these models, where their strongly connected parameters give multiscale evaluation of the vertices at the same time. In this way, a heterogeneous version of the stochastic block model is built via mixtures of loglinear models and the parameters are estimated with a special EM iteration. In the context of social networks, the clusters can be identified with social groups and the parameters with attitudes of people of one group towards people of the other, which attitudes depend on the cluster memberships. The algorithm is applied to randomly generated and real-word data.
Criteria for posterior consistency

Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria for posterior consistency with i.i. d. data. We formulate a versatile posterior consistency theorem that applies both to well- and mis-specified models and which we use to re-derive Schwartz's theorem, consider Kullback-Leibler consistency and formulate consistency theorems in which priors charge metric balls. It is generalized to sieved models with Barron's negligible prior mass condition and to separable models with variations on Walker's consistency theorem. Results also apply to marginal semi-parametric consistency: support boundary estimation is considered explicitly and consistency is proved in a model for which Kullback-Leibler priors do not exist. Other examples include consistent density estimation in mixture models with Dirichlet or Gibbs-type priors of full weak support. Regarding posterior convergence at a rate, it is shown that under a mild integrability condition, the second-order Ghosal-Ghosh-van der Vaart prior mass condition can be relaxed to a lower bound to the prior mass in Schwartz's Kullback-Leibler neighbourhoods. The posterior rate of convergence is derived in a simple, parametric model for heavy-tailed distributions in which the Ghosal-Ghosh-van der Vaart condition cannot be satisfied by any prior.
Comparing Seventeen Interval Estimates for a Bivariate Normal Correlation Coefficient

In this paper, we consider the problem of constructing confid ence interval for the correlation coefficient in a bivariate normal distribution. For this problem, we found fifteen appr oaches in literatures. Also, we have proposed a generalized confidence interval and a parametric bootstrap confidence interval. Th e coverage probabilities and expected lengths of these seventeen approaches are evaluated and compared via simulation study. In addition, robustness of the methods is considered in the comparisons by the non-normal distributions. Two real examples are given to illustrate the approaches.
Do debit cards decrease cash demand? Evidence from a causal analysis using Principal Stratification

It has been argued that innovation in transaction technology may modify the cash holding behaviour of agents, as debit card holders may either withdraw cash from ATMs or purchase items using POS devices at retailers. In this paper, within the Rubin Causal Model, we investigate the causal effects of the use of debit cards on the cash inventories held by households using data from the Italy Survey of Household Income and Wealth (SHIW). We adopt the principal stratification approach to incorporate the share of debit card holders who do not use this payment instrument. We use a regression model with the propensity score as the single predictor to adjust for the imbalance in observed covariates. We further develop a sensitivity analysis approach to assess the sensitivity of the proposed model to violation to the key unconfoundedness assumption. Our empirical results suggest statistically significant negative effects of debit cards on the household cash level in Italy.
Wmixnet: Software for Clustering the Nodes of Binary and Valued Graphs using the Stochastic Block Model

Clustering the nodes of a graph allows the analysis of the topology of a network. The stochastic block model is a clustering method based on a probabilistic model. Initially developed for binary networks it has recently been extended to valued networks possibly with covariates on the edges. We present an implementation of a variational EM algorithm. It is written using C++, parallelized, available under a GNU General Public License (version 3), and can select the optimal number of clusters using the ICL criteria. It allows us to analyze networks with ten thousand nodes in a reasonable amount of time.
Efficient variational inference for generalized linear mixed models with large datasets

The article develops a hybrid Variational Bayes algorithm that combines the mean-field and fixed-form Variational Bayes methods. The new estimation algorithm can be used to approximate any posterior without relying on conjugate priors. We propose a divide and recombine strategy for the analysis of large datasets, which partitions a large dataset into smaller pieces and then combines the variational distributions that have been learnt in parallel on each separate piece using the hybrid Variational Bayes algorithm. The proposed method is applied to fitting generalized linear mixed models. The computational efficiency of the parallel and hybrid Variational Bayes algorithm is demonstrated on several simulated and real datasets.
Contributors of carbon dioxide in the atmosphere in Europe

Carbon dioxide, along with atmospheric temperature are interacting to cause what we have defined as global warming. In the present study we develop a statistical model using real data to identify the attributable variables (risk factors) that cause the CO2 emissions in the atmosphere in Europe. Some scientists believe that there are more than nineteen attributable variables that cause the CO2 in our atmosphere. However, our study has identified only three individual risk factors and five interactions among the attributable variables that cause almost all the CO2 emissions in the atmosphere in Europe. We rank the risk factors and interactions according to the amount of CO2 they generate. In addition, we compare the present findings of the European data with a similar study for the Continental United States [1, 2]. For example, in the US, liquid fuels ranks number one, while in Europe is gas fuels. In fact, liquid fuels in Europe is the least contributable variable of CO2 in the atmosphere, and gas fuels ranks seventh.
Targeting Customers for Demand Response Based on Big Data

Selecting customers for demand response programs is challenging and existing methodologies are hard to scale and poor in performance. The existing methods were limited by lack of temporal consumption information at the individual customer level. We propose a scalable methodology for demand response targeting utilizing novel data available from smart meters. The approach relies on formulating the problem as a stochastic integer program involving predicted customer responses. A novel approximation is developed algorithm so it can scale to problems involving millions of customers. The methodology is tested experimentally using real utility data.