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At least 505 records · Page 28Linked to original sources
arXiv2020

A Pólya-Gamma Sampler for a Generalized Logistic Regression

In this paper we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalised logistic regression model. We propose a Pólya-Gamma sampler algorithm that allows us to sample from the exact posterior distribution, rather than relying on approximations. A simulation study illustrates the flexibility and accuracy of the proposed approach to capture heavy and light tails in binary response data of different dimensions. The methodology is applied to two different real datasets, where we demonstrate that the Pólya-Gamma sampler provides more precise estimates than the empirical likelihood method, outperforming approximate approaches.

stat.ME↗
arXiv2019

Distributionally Robust Optimization with Correlated Data from Vector Autoregressive Processes

We present a distributionally robust formulation of a stochastic optimization problem for non-i.i.d vector autoregressive data. We use the Wasserstein distance to define robustness in the space of distributions and we show, using duality theory, that the problem is equivalent to a finite convex-concave saddle point problem. The performance of the method is demonstrated on both synthetic and real data.

math.OC↗
arXiv2021

Inference In High-dimensional Single-Index Models Under Symmetric Designs

The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression parameter is identifiable. We construct estimates of the regression coefficients of interest that are similar to the debiased lasso estimates in the standard linear model and exhibit similar properties: root-n-consistency and asymptotic normality. The procedure completely bypasses the estimation of the unknown link function, which can be extremely challenging depending on the underlying structure of the problem. Furthermore, under Gaussianity, we propose more efficient estimates of the coefficients by expanding the link function in the Hermite polynomial basis. Finally, we illustrate our approach via carefully designed simulation experiments.

math.ST↗
arXiv2021

A new approach of chain sampling inspection plan

To develop decision rules regarding acceptance or rejection of production lots based on sample data is the purpose of acceptance sampling inspection plan. Dependent sampling procedures cumulate results from several preceding production lots when testing is expensive or destructive. This chaining of past lots reduce the sizes of the required samples, essential for acceptance or rejection of production lots. In this article, a new approach for chaining the past lot(s) results proposed, named as modified chain group acceptance sampling inspection plan, requires a smaller sample size than the commonly used sampling inspection plan, such as group acceptance sampling inspection plan and single acceptance sampling inspection plan. A comparison study has been done between the proposed and group acceptance sampling inspection plan as well as single acceptance sampling inspection plan. A example has been given to illustrate the proposed plan in a good manner.

stat.OT↗
arXiv2020

INTEREST: INteractive Tool for Exploring REsults from Simulation sTudies

Simulation studies allow us to explore the properties of statistical methods. They provide a powerful tool with a multiplicity of aims; among others: evaluating and comparing new or existing statistical methods, assessing violations of modelling assumptions, helping with the understanding of statistical concepts, and supporting the design of clinical trials. The increased availability of powerful computational tools and usable software has contributed to the rise of simulation studies in the current literature. However, simulation studies involve increasingly complex designs, making it difficult to provide all relevant results clearly. Dissemination of results plays a focal role in simulation studies: it can drive applied analysts to use methods that have been shown to perform well in their settings, guide researchers to develop new methods in a promising direction, and provide insights into less established methods. It is crucial that we can digest relevant results of simulation studies. Therefore, we developed INTEREST: an INteractive Tool for Exploring REsults from Simulation sTudies. The tool has been developed using the Shiny framework in R and is available as a web app or as a standalone package. It requires uploading a tidy format dataset with the results of a simulation study in R, Stata, SAS, SPSS, or comma-separated format. A variety of performance measures are estimated automatically along with Monte Carlo standard errors; results and performance summaries are displayed both in tabular and graphical fashion, with a wide variety of available plots. Consequently, the reader can focus on simulation parameters and estimands of most interest. In conclusion, INTEREST can facilitate the investigation of results from simulation studies and supplement the reporting of results, allowing researchers to share detailed results from their simulations and readers to explore them freely.

stat.AP↗
arXiv2019

Investigating the completeness and omission roads of OpenStreetMap data in Hubei, China by comparing with Street Map and Street View

OpenStreetMap (OSM) is a free map of the world which can be edited by global volunteers. Existing studies have showed that completeness of OSM road data in some developing countries (e.g. China) is much lower, resulting in concern in utilizing the data in various applications. But very few have focused on investigating what types of road are still poorly mapped. This study aims not only to investigate the completeness of OSM road datasets in China but also to investigate what types of road (called omission roads) have not been mapped, which is achieved by referring to both Street Map and Street View. 16 prefecture-level divisions in the urban areas of Hubei (China) were used as study areas. Results showed that: (1) the completeness for most prefecture-level divisions was at a low-to-medium level; most roads (in the Street Map), however, with traffic conditions had already been mapped well. (2) Most of the omission OSM roads were either private roads, or public roads not having yet been named and with only one single lane, indicating their lack of importance in the urban road network. We argue that although the OSM road datasets in China are incomplete, they may still be used for several applications.

cs.CY↗
arXiv2019

Data Science in Biomedicine

We highlight the role of Data Science in Biomedicine. Our manuscript goes from the general to the particular, presenting a global definition of Data Science and showing the trend for this discipline together with the terms of cloud computing and big data. In addition, since Data Science is mostly related to areas like economy or business, we describe its importance in biomedicine. Biomedical Data Science (BDS) presents the challenge of dealing with data coming from a range of biological and medical research, focusing on methodologies to advance the biomedical science discoveries, in an interdisciplinary context.

stat.OT↗
arXiv2019

Justifying the Norms of Inductive Inference

Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential favoring, even when that is inappropriate. The purpose of this paper is to study inductive inference in a very general setting where finding the truth is not necessarily the goal and where the measure of evidential favoring is not necessarily the likelihood. I use an accuracy argument to argue for probabilism and I develop a new kind of argument to argue for two general updating rules, both of which are reasonable in different contexts. One of the updating rules has standard Bayesian updating, Bissiri et al's (2016) general Bayesian updating, Douven's (2016) IBE-based updating, and Vassend's (2019a) quasi-Bayesian updating as special cases. The other updating rule is novel.

stat.OT↗
arXiv2019

Uncovering Sociological Effect Heterogeneity using Machine Learning

Individuals do not respond uniformly to treatments, events, or interventions. Sociologists routinely partition samples into subgroups to explore how the effects of treatments vary by covariates like race, gender, and socioeconomic status. In so doing, analysts determine the key subpopulations based on theoretical priors. Data-driven discoveries are also routine, yet the analyses by which sociologists typically go about them are problematic and seldom move us beyond our expectations, and biases, to explore new meaningful subgroups. Emerging machine learning methods allow researchers to explore sources of variation that they may not have previously considered, or envisaged. In this paper, we use causal trees to recursively partition the sample and uncover sources of treatment effect heterogeneity. We use honest estimation, splitting the sample into a training sample to grow the tree and an estimation sample to estimate leaf-specific effects. Assessing a central topic in the social inequality literature, college effects on wages, we compare what we learn from conventional approaches for exploring variation in effects to causal trees. Given our use of observational data, we use leaf-specific matching and sensitivity analyses to address confounding and offer interpretations of effects based on observed and unobserved heterogeneity. We encourage researchers to follow similar practices in their work on variation in sociological effects.

stat.OT↗
arXiv2020

An introduction to Bent Jorgensen's ideas

We briefly expose some key aspects of the theory and use of dispersion models, for which Bent Jorgensen played a crucial role as a driving force and an inspiration source. Starting with the general notion of dispersion models, built using minimalistic mathematical assumptions, we specialize in two classes of families of distributions with different statistical flavors: exponential dispersion and proper dispersion models. The construction of dispersion models involves the solution of integral equations that are, in general, untractable. These difficulties disappear when a more mathematical structure is assumed: it reduces to the calculation of a moment generating function or of a Riemann-Stieltjes integral for the exponential dispersion and the proper dispersion models, respectively. A new technique for constructing dispersion models based on characteristic functions is introduced turning the integral equations above into a tractable convolution equation and yielding examples of dispersion models that are neither proper dispersion nor exponential dispersion models. A corollary is that the cardinality of regular and non-regular dispersion models are both large. Some selected applications are discussed including exponential families non-linear models (for which generalized linear models are particular cases) and several models for clustered and dependent data based on a latent Levy process.

stat.OT↗
arXiv2020

A Conceptual Introduction to Markov Chain Monte Carlo Methods

Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random samples. This article provides a basic introduction to MCMC methods by establishing a strong conceptual understanding of what problems MCMC methods are trying to solve, why we want to use them, and how they work in theory and in practice. To develop these concepts, I outline the foundations of Bayesian inference, discuss how posterior distributions are used in practice, explore basic approaches to estimate posterior-based quantities, and derive their link to Monte Carlo sampling and MCMC. Using a simple toy problem, I then demonstrate how these concepts can be used to understand the benefits and drawbacks of various MCMC approaches. Exercises designed to highlight various concepts are also included throughout the article.

stat.OT↗
arXiv2020

Causal screening for dynamical systems

Many classical algorithms output graphical representations of causal structures by testing conditional independence among a set of random variables. In dynamical systems, local independence can be used analogously as a testable implication of the underlying data-generating process. We suggest some inexpensive methods for causal screening which provide output with a sound causal interpretation under the assumption of ancestral faithfulness. The popular model class of linear Hawkes processes is used to provide an example of a dynamical causal model. We argue that for sparse causal graphs the output will often be close to complete. We give examples of this framework and apply it to a challenging biological system.

stat.OT↗
arXiv2019

Spatial methods and their applications to environmental and climate data

Environmental and climate processes are often distributed over large space-time domains. Their complexity and the amount of available data make modelling and analysis a challenging task. Statistical modelling of environment and climate data can have several different motivations including interpretation or characterisation of the data. Results from statistical analysis are often used as a integral part of larger environmental studies. Spatial statistics is an active and modern statistical field, concerned with the quantitative analysis of spatial data; their dependencies and uncertainties. Spatio-temporal statistics extends spatial statistics through the addition of time to the, two or three, spatial dimensions. The focus of this introductory paper is to provide an overview of spatial methods and their application to environmental and climate data. This paper also gives an overview of several important topics including large data sets and non-stationary covariance structures. Further, it is discussed how Bayesian hierarchical models can provide a flexible way of constructing models. Hierarchical models may seem to be a good solution, but they have challenges of their own such as, parameter estimation. Finally, the application of spatio-temporal models to the LANDCLIM data (LAND cover - CLIMate interactions in NW Europe during the Holocene) will be discussed.

stat.ME↗
arXiv2019

A reckless guide to P-values: local evidence, global errors

This chapter demystifies P-values, hypothesis tests and significance tests, and introduces the concepts of local evidence and global error rates. The local evidence is embodied in \textit{this} data and concerns the hypotheses of interest for \textit{this} experiment, whereas the global error rate is a property of the statistical analysis and sampling procedure. It is shown using simple examples that local evidence and global error rates can be, and should be, considered together when making inferences. Power analysis for experimental design for hypothesis testing are explained, along with the more locally focussed expected P-values. Issues relating to multiple testing, HARKing, and P-hacking are explained, and it is shown that, in many situation, their effects on local evidence and global error rates are in conflict, a conflict that can always be overcome by a fresh dataset from replication of key experiments. Statistics is complicated, and so is science. There is no singular right way to do either, and universally acceptable compromises may not exist. Statistics offers a wide array of tools for assisting with scientific inference by calibrating uncertainty, but statistical inference is not a substitute for scientific inference. P-values are useful indices of evidence and deserve their place in the statistical toolbox of basic pharmacologists.

stat.OT↗
arXiv2019

Scalings for Tokamak Energy Confinement

On the basis of an analysis of the ITER L-mode energy confinement database, two new scaling expressions for tokamak L-mode energy confinement are proposed, namely a power law scaling and an offset-linear scaling. The analysis indicates that the present multiplicity of scaling expressions for the energy confinement time TE in tokamaks (Goldston, Kaye, Odajima-Shimomura, Rebut-Lallia, etc.) is due both to the lack of variation of a key parameter combination in the database, fs = 0.32 R a^.75 k^ 5 ~ A a^.25 k^.5, and to variations in the dependence of rE on the physical parameters among the different tokamaks in the database. By combining multiples of fs and another factor, fq = 1.56 a^2 kB/R Ip = qeng/3.2, which partially reflects the tokamak to tokamak variation of the dependence of TE on q and therefore implicitly the dependence of TE on Ip and n,., the two proposed confinement scaling expressions can be transformed to forms very close to most of the common scaling expressions. To reduce the multiplicity of the scalings for energy confinement, the database must be improved by adding new data with significant variations in fs, and the physical reasons for the tokamak to tokamak variation of some of the dependences of the energy confinement time on tokamak parameters must be clarified

physics.plasm-ph↗
arXiv2019

Computing the Expected Value of Sample Information Efficiently: Expertise and Skills Required for Four Model-Based Methods

Objectives: Value of information (VOI) analyses can help policy-makers make informed decisions about whether to conduct and how to design future studies. Historically, a computationally expensive method to compute the Expected Value of Sample Information (EVSI) restricted the use of VOI to simple decision models and study designs. Recently, four EVSI approximation methods have made such analyses more feasible and accessible. We provide practical recommendations for analysts computing EVSI by evaluating these novel methods. Methods: Members of the Collaborative Network for Value of Information (ConVOI) compared the inputs, analyst's expertise and skills, and software required for four recently developed approximation methods. Information was also collected on the strengths and limitations of each approximation method. Results: All four EVSI methods require a decision-analytic model's probabilistic sensitivity analysis (PSA) output. One of the methods also requires the model to be re-run to obtain new PSA outputs for each EVSI estimation. To compute EVSI, analysts must be familiar with at least one of the following skills: advanced regression modeling, likelihood specification, and Bayesian modeling. All methods have different strengths and limitations, e.g., some methods handle evaluation of study designs with more outcomes more efficiently while others quantify uncertainty in EVSI estimates. All methods are programmed in the statistical language R and two of the methods provide online applications. Conclusion: Our paper helps to inform the choice between four efficient EVSI estimation methods, enabling analysts to assess the methods' strengths and limitations and select the most appropriate EVSI method given their situation and skills.

stat.OT↗
arXiv2019

A Step by Step Mathematical Derivation and Tutorial on Kalman Filters

We present a step by step mathematical derivation of the Kalman filter using two different approaches. First, we consider the orthogonal projection method by means of vector-space optimization. Second, we derive the Kalman filter using Bayesian optimal filtering. We provide detailed proofs for both methods and each equation is expanded in detail.

stat.OT↗