A Tutorial on Bayesian Multi-Model Linear Regression with BAS and JASP
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Anomalous Perception in a Ganzfeld Condition - a Meta-Analysis of More Than 40 Years Investigation [Version 1; Peer Review: Awaiting Peer Review]
F1000Research 2021, 10:234 Last updated: 08 SEP 2021 RESEARCH ARTICLE Stage 2 Registered Report: Anomalous perception in a Ganzfeld condition - A meta-analysis of more than 40 years investigation [version 1; peer review: awaiting peer review] Patrizio E. Tressoldi 1, Lance Storm2 1Studium Patavinum, University of Padua, Padova, Italy 2School of Psychology, University of Adelaide, Adelaide, Australia v1 First published: 24 Mar 2021, 10:234 Open Peer Review https://doi.org/10.12688/f1000research.51746.1 Latest published: 24 Mar 2021, 10:234 https://doi.org/10.12688/f1000research.51746.1 Reviewer Status AWAITING PEER REVIEW Any reports and responses or comments on the Abstract article can be found at the end of the article. This meta-analysis is an investigation into anomalous perception (i.e., conscious identification of information without any conventional sensorial means). The technique used for eliciting an effect is the ganzfeld condition (a form of sensory homogenization that eliminates distracting peripheral noise). The database consists of studies published between January 1974 and December 2020 inclusive. The overall effect size estimated both with a frequentist and a Bayesian random-effect model, were in close agreement yielding an effect size of .088 (.04-.13). This result passed four publication bias tests and seems not contaminated by questionable research practices. Trend analysis carried out with a cumulative meta-analysis and a meta-regression model with Year of publication as covariate, did not indicate sign of decline of this effect size. The moderators analyses show that selected participants outcomes were almost three-times those obtained by non-selected participants and that tasks that simulate telepathic communication show a two- fold effect size with respect to tasks requiring the participants to guess a target. -
Statistical Methods for Data Science, Lecture 5 Interval Estimates; Comparing Systems
Statistical methods for Data Science, Lecture 5 Interval estimates; comparing systems Richard Johansson November 18, 2018 statistical inference: overview I estimate the value of some parameter (last lecture): I what is the error rate of my drug test? I determine some interval that is very likely to contain the true value of the parameter (today): I interval estimate for the error rate I test some hypothesis about the parameter (today): I is the error rate significantly different from 0.03? I are users significantly more satisfied with web page A than with web page B? -20pt “recipes” I in this lecture, we’ll look at a few “recipes” that you’ll use in the assignment I interval estimate for a proportion (“heads probability”) I comparing a proportion to a specified value I comparing two proportions I additionally, we’ll see the standard method to compute an interval estimate for the mean of a normal I I will also post some pointers to additional tests I remember to check that the preconditions are satisfied: what kind of experiment? what assumptions about the data? -20pt overview interval estimates significance testing for the accuracy comparing two classifiers p-value fishing -20pt interval estimates I if we get some estimate by ML, can we say something about how reliable that estimate is? I informally, an interval estimate for the parameter p is an interval I = [plow ; phigh] so that the true value of the parameter is “likely” to be contained in I I for instance: with 95% probability, the error rate of the spam filter is in the interval [0:05; 0:08] -20pt frequentists and Bayesians again. -
How Many Participants Do I Have to Include in Properly Powered
How many participants do we have to include in properly powered experiments? A tutorial of power analysis with some simple guidelines Marc Brysbaert Ghent University Belgium Keywords: power analysis, ANOVA, Bayesian statistics, effect size Address: Marc Brysbaert Department of Experimental Psychology Ghent University H. Dunantlaan 2 9000 Gent, Belgium [email protected] Abstract Given that the average effect size of pairwise comparisons in psychology is d = .4, very few studies are properly powered with less than 50 participants. For most designs and analyses, numbers of 100, 200, and even more are needed. These numbers become feasible with the recent introduction of internet-based studies and experiments, although they also require a change in the way research is evaluated by supervisors, examiners, reviewers, and editors. The present paper describes the numbers needed for the designs most often used by psychologists, including single-variable between-groups and repeated-measures designs with two and three levels, two-factor designs involving two repeated-measures variables or one between-groups variable and one repeated-measures variable (split-plot design). The numbers are given for the traditional, frequentist analysis with p < .05 and Bayesian analysis with BF > 10. These numbers should give a straightforward answer to researchers asking the question: “How many participants do I have to include in my experiment?” We also discuss how researchers can improve the power of their study by including multiple observations per condition per participant. 2 Statistical packages tend to be used as a kind of oracle …. In order to elicit a response from the oracle, one has to click one’s way through cascades of menus. -
DSA 5403 Bayesian Statistics: an Advancing Introduction 16 Units – Each Unit a Week’S Work
DSA 5403 Bayesian Statistics: An Advancing Introduction 16 units – each unit a week’s work. The following are the contents of the course divided into chapters of the book Doing Bayesian Data Analysis . by John Kruschke. The course is structured around the above book but will be embellished with more theoretical content as needed. The book can be obtained from the library : http://www.sciencedirect.com/science/book/9780124058880 Topics: This is divided into three parts From the book: “Part I The basics: models, probability, Bayes' rule and r: Introduction: credibility, models, and parameters; The R programming language; What is this stuff called probability?; Bayes' rule Part II All the fundamentals applied to inferring a binomial probability: Inferring a binomial probability via exact mathematical analysis; Markov chain Monte C arlo; J AG S ; Hierarchical models; Model comparison and hierarchical modeling; Null hypothesis significance testing; Bayesian approaches to testing a point ("Null") hypothesis; G oals, power, and sample size; S tan Part III The generalized linear model: Overview of the generalized linear model; Metric-predicted variable on one or two groups; Metric predicted variable with one metric predictor; Metric predicted variable with multiple metric predictors; Metric predicted variable with one nominal predictor; Metric predicted variable with multiple nominal predictors; Dichotomous predicted variable; Nominal predicted variable; Ordinal predicted variable; C ount predicted variable; Tools in the trunk” Part 1: The Basics: Models, Probability, Bayes’ Rule and R Unit 1 Chapter 1, 2 Credibility, Models, and Parameters, • Derivation of Bayes’ rule • Re-allocation of probability • The steps of Bayesian data analysis • Classical use of Bayes’ rule o Testing – false positives etc o Definitions of prior, likelihood, evidence and posterior Unit 2 Chapter 3 The R language • Get the software • Variables types • Loading data • Functions • Plots Unit 3 Chapter 4 Probability distributions. -
Dentist's Knowledge of Evidence-Based Dentistry and Digital Applications Resources in Saudi Arabia
PTB Reports Research Article Dentist’s Knowledge of Evidence-based Dentistry and Digital Applications Resources in Saudi Arabia Yousef Ahmed Alomi*, BSc. Pharm, MSc. Clin Pharm, BCPS, BCNSP, DiBA, CDE ABSTRACT Critical Care Clinical Pharmacists, TPN Objectives: Drug information resources provide clinicians with safer use of medications and play a Clinical Pharmacist, Freelancer Business vital role in improving drug safety. Evidence-based medicine (EBM) has become essential to medical Planner, Content Editor, and Data Analyst, Riyadh, SAUDI ARABIA. practice; however, EBM is still an emerging dentistry concept. Therefore, in this study, we aimed to Anwar Mouslim Alshammari, B.D.S explore dentists’ knowledge about evidence-based dentistry resources in Saudi Arabia. Methods: College of Destiney, Hail University, SAUDI This is a 4-month cross-sectional study conducted to analyze dentists’ knowledge about evidence- ARABIA. based dentistry resources in Saudi Arabia. We included dentists from interns to consultants and Hanin Sumaydan Saleam Aljohani, those across all dentistry specialties and located in Saudi Arabia. The survey collected demographic Ministry of Health, Riyadh, SAUDI ARABIA. information and knowledge of resources on dental drugs. The knowledge of evidence-based dental care and knowledge of dental drug information applications. The survey was validated through the Correspondence: revision of expert reviewers and pilot testing. Moreover, various reliability tests had been done with Dr. Yousef Ahmed Alomi, BSc. Pharm, the study. The data were collected through the Survey Monkey system and analyzed using Statistical MSc. Clin Pharm, BCPS, BCNSP, DiBA, CDE Critical Care Clinical Pharmacists, TPN Package of Social Sciences (SPSS) and Jeffery’s Amazing Statistics Program (JASP). -
Applications of Computational Statistics with Multiple Regressions
International Journal of Computational and Applied Mathematics. ISSN 1819-4966 Volume 12, Number 3 (2017), pp. 923-934 © Research India Publications http://www.ripublication.com Applications of Computational Statistics with Multiple Regressions S MD Riyaz Ahmed Research Scholar, Department of Mathematics, Rayalaseema University, A.P, India Abstract Applications of Computational Statistics with Multiple Regression through the use of Excel, MATLAB and SPSS. It has been widely used for a long time in various fields, such as operations research and analysis, automatic control, probability statistics, statistics, digital signal processing, dynamic system mutilation, etc. The regress function command in MATLAB toolbox provides a helpful tool for multiple linear regression analysis and model checking. Multiple regression analysis is additionally extremely helpful in experimental scenario wherever the experimenter will management the predictor variables. Keywords - Multiple Linear Regression, Excel, MATLAB, SPSS, least square, Matrix notations 1. INTRODUCTION Multiple linear regressions are one of the foremost wide used of all applied mathematics strategies. Multiple regression analysis is additionally extremely helpful in experimental scenario wherever the experimenter will management the predictor variables [1]. A single variable quantity within the model would have provided an inadequate description since a number of key variables have an effect on the response variable in necessary and distinctive ways that [2]. It makes an attempt to model the link between two or more variables and a response variable by fitting a equation to determined information. Each value of the independent variable x is related to a value of the dependent variable y. The population regression line for p informative variables 924 S MD Riyaz Ahmed x1, x 2 , x 3 ...... -
Arxiv:1803.00360V2 [Stat.CO] 2 Mar 2018 Prone to Misinterpretation [2, 3]
Computing Bayes factors to measure evidence from experiments: An extension of the BIC approximation Thomas J. Faulkenberry∗ Tarleton State University Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of the hesitance to adopt this approach may stem from an unfamiliarity with the computational tools necessary for computing Bayes factors. Previous work has shown that closed form approximations of Bayes factors are relatively easy to obtain for between-groups methods, such as an analysis of variance or t-test. In this paper, I extend this approximation to develop a formula for the Bayes factor that directly uses infor- mation that is typically reported for ANOVAs (e.g., the F ratio and degrees of freedom). After giving two examples of its use, I report the results of simulations which show that even with minimal input, this approximate Bayes factor produces similar results to existing software solutions. Note: to appear in Biometrical Letters. I. INTRODUCTION A. The Bayes factor Bayesian inference is a method of measurement that is Hypothesis testing is the primary tool for statistical based on the computation of P (H j D), which is called inference across much of the biological and behavioral the posterior probability of a hypothesis H, given data D. sciences. As such, most scientists are trained in classical Bayes' theorem casts this probability as null hypothesis significance testing (NHST). The scenario for testing a hypothesis is likely familiar to most readers of this journal. -
Simple Linear Regression with Least Square Estimation: an Overview
Aditya N More et al, / (IJCSIT) International Journal of Computer Science and Information Technologies, Vol. 7 (6) , 2016, 2394-2396 Simple Linear Regression with Least Square Estimation: An Overview Aditya N More#1, Puneet S Kohli*2, Kshitija H Kulkarni#3 #1-2Information Technology Department,#3 Electronics and Communication Department College of Engineering Pune Shivajinagar, Pune – 411005, Maharashtra, India Abstract— Linear Regression involves modelling a relationship amongst dependent and independent variables in the form of a (2.1) linear equation. Least Square Estimation is a method to determine the constants in a Linear model in the most accurate way without much complexity of solving. Metrics where such as Coefficient of Determination and Mean Square Error is the ith value of the sample data point determine how good the estimation is. Statistical Packages is the ith value of y on the predicted regression such as R and Microsoft Excel have built in tools to perform Least Square Estimation over a given data set. line The above equation can be geometrically depicted by Keywords— Linear Regression, Machine Learning, Least Squares Estimation, R programming figure 2.1. If we draw a square at each point whose length is equal to the absolute difference between the sample data point and the predicted value as shown, each of the square would then represent the residual error in placing the I. INTRODUCTION regression line. The aim of the least square method would Linear Regression involves establishing linear be to place the regression line so as to minimize the sum of relationships between dependent and independent variables. -
The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models
Technical Report 101 The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models Chandra R. Bhat Center for Transportation Research September 2014 Data-Supported Transportation Operations & Planning Center (D-STOP) A Tier 1 USDOT University Transportation Center at The University of Texas at Austin D-STOP is a collaborative initiative by researchers at the Center for Transportation Research and the Wireless Networking and Communications Group at The University of Texas at Austin. DISCLAIMER The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the U.S. Department of Transportation’s University Transportation Centers Program, in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof. Technical Report Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. D-STOP/2016/101 4. Title and Subtitle 5. Report Date The Composite Marginal Likelihood (CML) Inference Approach September 2014 with Applications to Discrete and Mixed Dependent Variable 6. Performing Organization Code Models 7. Author(s) 8. Performing Organization Report No. Chandra R. Bhat Report 101 9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) Data-Supported Transportation Operations & Planning Center (D- STOP) 11. Contract or Grant No. The University of Texas at Austin DTRT13-G-UTC58 1616 Guadalupe Street, Suite 4.202 Austin, Texas 78701 12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered Data-Supported Transportation Operations & Planning Center (D- STOP) The University of Texas at Austin 14. -
The Bayesian Approach to Statistics
THE BAYESIAN APPROACH TO STATISTICS ANTHONY O’HAGAN INTRODUCTION the true nature of scientific reasoning. The fi- nal section addresses various features of modern By far the most widely taught and used statisti- Bayesian methods that provide some explanation for the rapid increase in their adoption since the cal methods in practice are those of the frequen- 1980s. tist school. The ideas of frequentist inference, as set out in Chapter 5 of this book, rest on the frequency definition of probability (Chapter 2), BAYESIAN INFERENCE and were developed in the first half of the 20th century. This chapter concerns a radically differ- We first present the basic procedures of Bayesian ent approach to statistics, the Bayesian approach, inference. which depends instead on the subjective defini- tion of probability (Chapter 3). In some respects, Bayesian methods are older than frequentist ones, Bayes’s Theorem and the Nature of Learning having been the basis of very early statistical rea- Bayesian inference is a process of learning soning as far back as the 18th century. Bayesian from data. To give substance to this statement, statistics as it is now understood, however, dates we need to identify who is doing the learning and back to the 1950s, with subsequent development what they are learning about. in the second half of the 20th century. Over that time, the Bayesian approach has steadily gained Terms and Notation ground, and is now recognized as a legitimate al- ternative to the frequentist approach. The person doing the learning is an individual This chapter is organized into three sections. -
Scalable and Robust Bayesian Inference Via the Median Posterior
Scalable and Robust Bayesian Inference via the Median Posterior CS 584: Big Data Analytics Material adapted from David Dunson’s talk (http://bayesian.org/sites/default/files/Dunson.pdf) & Lizhen Lin’s ICML talk (http://techtalks.tv/talks/scalable-and-robust-bayesian-inference-via-the-median-posterior/61140/) Big Data Analytics • Large (big N) and complex (big P with interactions) data are collected routinely • Both speed & generality of data analysis methods are important • Bayesian approaches offer an attractive general approach for modeling the complexity of big data • Computational intractability of posterior sampling is a major impediment to application of flexible Bayesian methods CS 584 [Spring 2016] - Ho Existing Frequentist Approaches: The Positives • Optimization-based approaches, such as ADMM or glmnet, are currently most popular for analyzing big data • General and computationally efficient • Used orders of magnitude more than Bayes methods • Can exploit distributed & cloud computing platforms • Can borrow some advantages of Bayes methods through penalties and regularization CS 584 [Spring 2016] - Ho Existing Frequentist Approaches: The Drawbacks • Such optimization-based methods do not provide measure of uncertainty • Uncertainty quantification is crucial for most applications • Scalable penalization methods focus primarily on convex optimization — greatly limits scope and puts ceiling on performance • For non-convex problems and data with complex structure, existing optimization algorithms can fail badly CS 584 [Spring 2016] - -
Isye 6416: Computational Statistics Lecture 1: Introduction
ISyE 6416: Computational Statistics Lecture 1: Introduction Prof. Yao Xie H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology What this course is about I Interface between statistics and computer science I Closely related to data mining, machine learning and data analytics I Aim at the design of algorithm for implementing statistical methods on computers I computationally intensive statistical methods including resampling methods, Markov chain Monte Carlo methods, local regression, kernel density estimation, artificial neural networks and generalized additive models. Statistics data: images, video, audio, text, etc. sensor networks, social networks, internet, genome. statistics provide tools to I model data e.g. distributions, Gaussian mixture models, hidden Markov models I formulate problems or ask questions e.g. maximum likelihood, Bayesian methods, point estimators, hypothesis tests, how to design experiments Computing I how do we solve these problems? I computing: find efficient algorithms to solve them e.g. maximum likelihood requires finding maximum of a cost function I \Before there were computers, there were algorithms. But now that there are computers, there are even more algorithms, and algorithms lie at the heart of computing. " I an algorithm: a tool for solving a well-specified computational problem I examples: I The Internet enables people all around the world to quickly access and retrieve large amounts of information. With the aid of clever algorithms, sites on the Internet are able to manage and manipulate this large volume of data. I The Human Genome Project has made great progress toward the goals of identifying all the 100,000 genes in human DNA, determining the sequences of the 3 billion chemical base pairs that make up human DNA, storing this information in databases, and developing tools for data analysis.