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At least 469 records · Page 26Linked to original sources
arXiv2019

Evaluating the Success of a Data Analysis

A fundamental problem in the practice and teaching of data science is how to evaluate the quality of a given data analysis, which is different than the evaluation of the science or question underlying the data analysis. Previously, we defined a set of principles for describing data analyses that can be used to create a data analysis and to characterize the variation between data analyses. Here, we introduce a metric of quality evaluation that we call the success of a data analysis, which is different than other potential metrics such as completeness, validity, or honesty. We define a successful data analysis as the matching of principles between the analyst and the audience on which the analysis is developed. In this paper, we propose a statistical model and general framework for evaluating the success of a data analysis. We argue that this framework can be used as a guide for practicing data scientists and students in data science courses for how to build a successful data analysis.

stat.OT↗
arXiv2019

Geological modeling using a recursive convolutional neural networks approach

Resource models are constrained by the extent of geological units that often depend on the lithology, alteration and mineralization. A three dimensional model of these geological units must be built from scarce information coming from drillholes and limited understanding about the geological setting in which the ore deposit is places. In this work, we present a new technique for multiple-point geostatistical simulation based on a recursive convolutional neural network approach (RCNN). The method requires conditioning data and a training image that depicts the type of geological structures expected to be found in the deposit. This training image is used to learn the patterns of categories found and these are imposed in the final simulated model conditioned by the categories found during logging at the actual drill-hole samples. A lithological modeling process is carried out in a copper deposit in Chile to demonstrate the method. Comparison with current techniques and spatial metrics are used to clarify concepts and RCNN properties. Also, strengths and weaknesses of the methodology are discussed by briefly reviewing the theoretical perspective and looking into some of its practical aspects.

eess.IV↗
arXiv2019

Methods of Estimation for the Three-Parameter Reflected Weibull Distribution

In this paper, we propose methods for the estimation of parameters for the three-parameter Reflected Weibull distribution. The Moment estimator , Maximum likelihood estimator and Location and Scale Parameters free maximum likelihood estimator. The Location and Scale Parameters free maximum likelihood estimator is based on a data transformation, which avoids the problem of unbounded likelihood estimator. Through Mont Carlo simulations, we further show that the Location and Scale Parameters free maximum likelihood estimator performs better than methods moment and maximum likelihood estimator in terms of bias and root mean squared error. Finally, two examples based on real data sets are presented to illustrate methods.

stat.OT↗
arXiv2019

Which principal components are most sensitive to distributional changes?

PCA is often used in anomaly detection and statistical process control tasks. For bivariate data, we prove that the minor projection (the least varying projection) of the PCA-rotated data is the most sensitive to distributional changes, where sensitivity is defined by the Hellinger distance between distributions before and after a change. In particular, this is almost always the case if only one parameter of the bivariate normal distribution changes, i.e., the change is sparse. Simulations indicate that the minor projections are the most sensitive for a large range of changes and pre-change settings in higher dimensions as well. This motivates using the minor projections for detecting sparse distributional changes in high-dimensional data.

math.ST↗
arXiv2019

Non-Parametric Estimation of Spot Covariance Matrix with High-Frequency Data

Estimating spot covariance is an important issue to study, especially with the increasing availability of high-frequency financial data. We study the estimation of spot covariance using a kernel method for high-frequency data. In particular, we consider first the kernel weighted version of realized covariance estimator for the price process governed by a continuous multivariate semimartingale. Next, we extend it to the threshold kernel estimator of the spot covariances when the underlying price process is a discontinuous multivariate semimartingale with finite activity jumps. We derive the asymptotic distribution of the estimators for both fixed and shrinking bandwidth. The estimator in a setting with jumps has the same rate of convergence as the estimator for diffusion processes without jumps. A simulation study examines the finite sample properties of the estimators. In addition, we study an application of the estimator in the context of covariance forecasting. We discover that the forecasting model with our estimator outperforms a benchmark model in the literature.

stat.ME↗
arXiv2019

Statistical methods research done as science rather than mathematics

This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this model's restricted likelihood often gives a boundary value for the random effect correlation or variances. We argue that this is a problem; that it is a problem because our discipline has little understanding of how contemporary models and methods map data to inferential summaries; that we lack such understanding, even for models as simple as this, because of a near-exclusive reliance on mathematics as a means of understanding; and that math alone is no longer sufficient. We then argue that as a discipline, we can and should break open our black-box methods by mimicking the five steps that molecular biologists commonly use to break open Nature's black boxes: design a simple model system, formulate hypotheses using that system, test them in experiments on that system, iterate as needed to reformulate and test hypotheses, and finally test the results in an "in vivo" system. We demonstrate this by identifying conditions under which the random-regressions restricted likelihood is likely to be maximized at a boundary value. Resistance to this approach seems to arise from a view that it lacks the certainty or intellectual heft of mathematics, perhaps because simulation experiments in our literature rarely do more than measure a new method's operating characteristics in a small range of situations. We argue that such work can make useful contributions including, as in molecular biology, the findings themselves and sometimes the designs used in the five steps; that these contributions have as much practical value as mathematical results; and that therefore they merit publication as much as the mathematical results our discipline esteems so highly.

stat.OT↗
arXiv2019

Many perspectives on Deborah Mayo's "Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars"

The new book by philosopher Deborah Mayo is relevant to data science for topical reasons, as she takes various controversial positions regarding hypothesis testing and statistical practice, and also as an entry point to thinking about the philosophy of statistics. The present article is a slightly expanded version of a series of informal reviews and comments on Mayo's book. We hope this discussion will introduce people to Mayo's ideas along with other perspectives on the topics she addresses.

stat.OT↗
arXiv2019

Leveraging Uncertainty in Deep Learning for Selective Classification

The wide and rapid adoption of deep learning by practitioners brought unintended consequences in many situations such as in the infamous case of Google Photos' racist image recognition algorithm; thus, necessitated the utilization of the quantified uncertainty for each prediction. There have been recent efforts towards quantifying uncertainty in conventional deep learning methods (e.g., dropout as Bayesian approximation); however, their optimal use in decision making is often overlooked and understudied. In this study, we propose a mixed-integer programming framework for classification with reject option (also known as selective classification), that investigates and combines model uncertainty and predictive mean to identify optimal classification and rejection regions. Our results indicate superior performance of our framework both in non-rejected accuracy and rejection quality on several publicly available datasets. Moreover, we extend our framework to cost-sensitive settings and show that our approach outperforms industry standard methods significantly for online fraud management in real-world settings.

cs.LG↗
arXiv2019

Atlantic Causal Inference Conference (ACIC) Data Analysis Challenge 2017

This brief note documents the data generating processes used in the 2017 Data Analysis Challenge associated with the Atlantic Causal Inference Conference (ACIC). The focus of the challenge was estimation and inference for conditional average treatment effects (CATEs) in the presence of targeted selection, which leads to strong confounding. The associated data files and further plots can be found on the first author's web page.

stat.ME↗
arXiv2019

An illustration of the risk of borrowing information via a shared likelihood

A concrete, stylized example illustrates that inferences may be degraded, rather than improved, by incorporating supplementary data via a joint likelihood. In the example, the likelihood is assumed to be correctly specified, as is the prior over the parameter of interest; all that is necessary for the joint modeling approach to suffer is misspecification of the prior over a nuisance parameter.

stat.OT↗
arXiv2019

A score function for Bayesian cluster analysis

We propose a score function for Bayesian clustering. The function is parameter free and captures the interplay between the within cluster variance and the between cluster entropy of a clustering. It can be used to choose the number of clusters in well-established clustering methods such as hierarchical clustering or $K$-means algorithm.

stat.OT↗
arXiv2020

Estimating Average Treatment Effects Utilizing Fractional Imputation when Confounders are Subject to Missingness

The problem of missingness in observational data is ubiquitous. When the confounders are missing at random, multiple imputation is commonly used; however, the method requires congeniality conditions for valid inferences, which may not be satisfied when estimating average causal treatment effects. Alternatively, fractional imputation, proposed by Kim 2011, has been implemented to handling missing values in regression context. In this article, we develop fractional imputation methods for estimating the average treatment effects with confounders missing at random. We show that the fractional imputation estimator of the average treatment effect is asymptotically normal, which permits a consistent variance estimate. Via simulation study, we compare fractional imputation's accuracy and precision with that of multiple imputation.

stat.ME↗
arXiv2020

Semi-Supervised Learning, Causality and the Conditional Cluster Assumption

While the success of semi-supervised learning (SSL) is still not fully understood, Schölkopf et al. (2012) have established a link to the principle of independent causal mechanisms. They conclude that SSL should be impossible when predicting a target variable from its causes, but possible when predicting it from its effects. Since both these cases are somewhat restrictive, we extend their work by considering classification using cause and effect features at the same time, such as predicting disease from both risk factors and symptoms. While standard SSL exploits information contained in the marginal distribution of all inputs (to improve the estimate of the conditional distribution of the target given inputs), we argue that in our more general setting we should use information in the conditional distribution of effect features given causal features. We explore how this insight generalises the previous understanding, and how it relates to and can be exploited algorithmically for SSL.

stat.ML↗
arXiv2019

Incorporating Open Data into Introductory Courses in Statistics

The 2016 Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report emphasized six recommendations to teach introductory courses in statistics. Among them: use of real data with context and purpose. Many educators have created databases consisting of multiple data sets for use in class; sometimes making hundreds of data sets available. Yet `the context and purpose' component of the data may remain elusive if just a generic database is made available. We describe the use of open data in introductory courses. Countries and cities continue to share data through open data portals. Hence, educators can find regional data that engages their students more effectively. We present excerpts from case studies that show the application of statistical methods to data on: crime, housing, rainfall, tourist travel, and others. Data wrangling and discussion of results are recognized as important case study components. Thus the open data based case studies attend most GAISE College Report recommendations. Reproducible \textsf{R} code is made available for each case study. Example uses of open data in more advanced courses in statistics are also described.

stat.AP↗
arXiv2019

Frequentist Inference without Repeated Sampling

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation is applied to statistical inference using urn models. Both classical and limiting relative frequency interpretations can be used to communicate statistical inference, and the effectiveness of each is discussed. Recent descriptions of p-values, confidence intervals, and power are viewed through the lens of classical probability based on a single random sample from the population.

stat.OT↗
arXiv2019

On the probability of a causal inference is robust for internal validity

The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a causal inference is robust for internal validity, i.e., the PIV, as a robustness index of causal inference. Formally, the PIV is the probability of rejecting the null hypothesis again based on both the observed sample and the counterfactuals, provided the same null hypothesis has already been rejected based on the observed sample. Under either frequentist or Bayesian framework, one can bound the PIV of an inference based on his bounded belief about the counterfactuals, which is often needed when the unconfoundedness assumption is dubious. The PIV is equivalent to statistical power when the NHST is thought to be based on both the observed sample and the counterfactuals. We summarize the process of evaluating internal validity with the PIV into an eight-step procedure and illustrate it with an empirical example (i.e., Hong and Raudenbush (2005)).

stat.AP↗
arXiv2019

A Role for Symmetry in the Bayesian Solution of Differential Equations

The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also be performed in this context. Competing statistical paradigms can be considered and Bayesian probabilistic numerical methods (PNMs) are obtained when Bayesian statistical principles are deployed. Bayesian PNM have the appealing property of being closed under composition, such that uncertainty due to different sources of discretisation in a numerical method can be jointly modelled and rigorously propagated. Despite recent attention, no exact Bayesian PNM for the numerical solution of ordinary differential equations (ODEs) has been proposed. This raises the fundamental question of whether exact Bayesian methods for (in general nonlinear) ODEs even exist. The purpose of this paper is to provide a positive answer for a limited class of ODE. To this end, we work at a foundational level, where a novel Bayesian PNM is proposed as a proof-of-concept. Our proposal is a synthesis of classical Lie group methods, to exploit underlying symmetries in the gradient field, and non-parametric regression in a transformed solution space for the ODE. The procedure is presented in detail for first and second order ODEs and relies on a certain strong technical condition -- existence of a solvable Lie algebra -- being satisfied. Numerical illustrations are provided.

stat.OT↗