An introduction to mathematical statistics, and the theory of distributions. […] This book is an introduction to the theory of statistical probability and distributions. This book can be read without relying on any specific statistical software, though sometimes R code (R Core Team 2024) is included to demonstrate ideas, and to discuss simulation. The callouts used in this book have meanings; for example: These chunks introduce the objectives for the chapters of the book. These chunks highlight common mistakes or warnings, about a particular concept or about using a formula. These chunks … Read more →

Surrogates: a new graduate level textbook on topics lying at the interface between machine learning, spatial statistics, computer simulation, meta-modeling (i.e., emulation), and design of experiments. Gaussian process emphasis facilitates flexible nonparametric and nonlinear modeling, with applications to uncertainty quantification, sensitivity analysis, calibration of computer models to field data, sequential design and (blackbox) optimization under uncertainty. Presentation targets numerically competent scientists in the engineering, physical, and biological sciences. Treatment includes historical perspective and canonical examples, but primarily concentrates on modern statistical methods, computation and implementation in R at modern scale. Rmarkdown facilitates a fully reproducible tour complete with motivation from, application to, and illustration with, compelling real-data examples. Read more →

This is a free, activity-based introductory statistics class, suitable for high-school and college students. The course is designed around active learning, statistical modeling, and simulation-based inference. Students use Monte Carlo Simulation to model variability, and they make conclusions based on the outcomes of their models. This book is part of the free Statistical Reasoning: A Modeling and Simulation Approach curriculum. More resources are available at https://www.fapeck.com/statistical-reasoning/ This work is licensed under a Creative Commons Attribution 4.0 International License. … Read more →

Statistical Thinking: A Simulation Approach to Modeling Uncertainty (UM Spring 2023 edition) […] This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to share, remix, and make commercial use of the work under the condition that you provide proper attribution. To reference this work, use: Peck, F.A., Zieffler, A., & Catalysts for Change. (2023). Statistical Thinking: A simulation approach to uncertainty (University of Montana, Spring 2023 ed.). https://bookdown.org/frederick_peck/statistical_thinking_um_spring_2023_ed/ The work to create the … Read more →

This book covers the ins and outs of developing and analyzing matrix projection models and integral projection models in R using the CRAN-based package lefko3. It covers all aspects of building and analyzing these models, from life history model development all the way to the development of replicated, stochastic, density dependent projection simulations. [...] All content copyright 2022 Richard P. Shefferson This book is dedicated to the people of Ukraine, who are teaching the world every day that all people have the inherent human right to self-determination. Richard P. Shefferson ... Read more →

Notes for STA 440/441 at Murray State University for students in Dr. Christopher Mecklin’s class. […] Let’s start with an informal notion of probability, where we try to assign a numerical percentage or proportion or fraction to something happening. For example, you might be interested in the chance that it will rain tomorrow. How would you go about assigning a numerical value to this event? This would be an example of the subjective approach to probability, based on an event that cannot be repeated, although a weather forecaster might run many simulations of a weather model (which would be … Read more →

This tutorial shows how to create very simple simulation or agent-based models of cultural evolution in R [...] This tutorial shows how to create very simple simulation or agent-based models of cultural evolution in R (R Core Team 2021). Currently these are: Each model is contained in a separate RMarkdown (Rmd) file. You can either (i) download each of these Rmd files from https://github.com/amesoudi/cultural_evolution_ABM_tutorial then open them in RStudio or another IDE, executing the code as you read the explanatory text, or (ii) read the online version of the tutorial at ... Read more →

Research has suggested that conceptual processing depends on both language-based and sensorimotor information. In this thesis, I investigate the nature of these systems and their interplay at three levels of the experimental structure—namely, individuals, words and tasks. In Study 1, I contributed to a multi-lab replication of the object orientation effect, which has been used to test sensorimotor simulation. The effect did not appear in any of the 18 languages examined, and it was not influenced by individual differences in mental rotation. Next, in Study 2, we drew on three existing data sets that implemented semantic priming, semantic decision and lexical decision. We extended these data sets with measures of language-based and vision-based information, and analysed their interactions with participants’ vocabulary size and gender, and with presentation speed. The analysis had a conservative structure of fixed and random effects. First, we found that language-based information was more important than vision-based information. Second, in the semantic priming study—whose task required distinguishing between words and nonwords—, both language-based and vision-based information were more influential when words were presented faster. Third, a ‘task-relevance advantage’ was identified in higher-vocabulary participants. Specifically, in lexical decision, higher-vocabulary participants were more sensitive to language-based information than lower-vocabulary participants, whereas in semantic decision, higher-vocabulary participants were more sensitive to word concreteness. Fourth, we demonstrated the influence of the analytical method on the results. Last, we estimated the sample size required to investigate various effects. We found that 300 participants were sufficient to examine the effect of language-based information in words, whereas more than 1,000 participants were necessary to examine the effect of vision-based information and the interactions of both former variables with vocabulary size, gender and presentation speed. This power analysis suggests that larger sample sizes are necessary to investigate perceptual simulation and individual differences in conceptual processing. Read more →

This is a demo of our simulation. […] This is a detailed demo of a simulation to test the sensitivity of PLIS procedure and conventional p-value procedure using logistics regression. While PLIS procedure incorporates the correlation among SNPs to adjust for Linkage Disequilibrium (LD), conducting multiple logistics regressions assumes that SNPs are independent from one another. The main idea here: We don’t have info for all SNPs along our chromosomes for research. Thus, when missing the data for true causal SNPs, we want to detect the SNPs that are physically close to the causal SNPs so … Read more →

Statistical Thinking: A Simulation Approach to Modeling Uncertainty (UM STAT 216 edition) […] This book is a modified version of the work below: Zieffler, A., & Catalysts for Change. (2019). Statistical Thinking: A simulation approach to uncertainty (4.2th ed.). Minneapolis, MN: Catalyst Press. http://zief0002.github.io/statistical-thinking/ This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to share, remix, and make commercial use of the work under the condition that you provide proper attribution. To reference this work, use: The work to … Read more →

This textbook presents a simulation-based approach to probability, using the Symbulate package. […] Why study probability? Why use simulation to study probability? The examples in this book are used to both motivate new topics and to help you practice your understanding of the material. You should attempt the examples on your own before reading the solutions. To encourage you to do so, the solutions have been hidden. You can reveal the solution by clicking on the Show/hide solution button. Here is where a solution would be, but be sure to think about the problem on your own first! (Careful: … Read more →

Mixed BART Models: maths and discussion […] This documents works as a summary of our work towards building a “Mixed model” style BART. All the maths in detail will be written here, as well as our simulation … Read more →

Franchise Hockey Manager 6 Saves in R […] This tutorial hopes to teach you how to use R to parse and aggregate multiple saves from Franchise Hockey Manager 6, for instance when running multiple tests on the same season of Simulation Hockey League. It has been updated to show the teams and Casino Lines for S61. Two things are needed from FHM for this tutorial to work. A tldr is found in chapter 4. This chapter only contains all the code that you need to … Read more →

This course provides an overview of skills needed for reproducible research and open science using the statistical programming language R. Students will learn about data visualisation, data tidying and wrangling, archiving, iteration and functions, probability and data simulations, general linear models, and reproducible workflows. Learning is reinforced through weekly assignments that involve working with different types of data. Read more →

Statistical Thinking: A Simulation Approach to Modeling Uncertainty (UM STAT 216 edition) […] This book is a slightly modified version of the work below: Zieffler, A., & Catalysts for Change. (2019). Statistical Thinking: A simulation approach to uncertainty (4.2th ed.). Minneapolis, MN: Catalyst Press. http://zief0002.github.io/statistical-thinking/ This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to share, remix, and make commercial use of the work under the condition that you provide proper attribution. To reference this work, use: The … Read more →

These are lecture notes for the module Simulation and Modelling to Understand Change given in the School of Human Sciences and Technology at IE University, Madrid, Spain. The module is given in the 2nd semester of the 1st year of the bachelor in Data and Business Analytics. Knowledge of basic elements of R programming as well as probability and statistics is assumed. […] These are lecture notes for the module Simulation and Modelling to Understand Change given in the School of Human Sciences and Technology at IE University, Madrid, Spain. The module is given in the 2nd semester of the 1st … Read more →

Building Pension Models and Actuarial Tools Using R and R Shiny […] This interactive report has been created to demonstrate the functionality of R Markdown and Bookdown, as an additional tool that actuaries and others can avail of. Each page of the application (with the exception of the combined SORP Calculator and Drawdown Simulation) has been rebuilt using miniUI [1], an R library used to create Shiny Widgets. However, these “mini-apps” do not fully replicate the main application. Similarly, this interactive report does not intend to replace the original - it merely serves to compliment … Read more →

P2 - Simulering af Data […] The aim of the project was to identify alternatives to classical inference methods if the assumptions of these were not met and evaluate their performance. To examine this question, a classical inference method, the t-test, and how it can be used for hypothesis testing, is described. Furthermore, it is shown how the programming language R can be utilized to perform these simulations quickly and simply. Then, by means of simulations, it is examined whether the results are credible if the samples are not normally distributed when working with an unpaired t-test. … Read more →

Stochastic Simulation and Statistics in Tidyverse. […] This is the website hosting all the theories and and practices regarding stochastic simulation and statistics. It has the following … Read more →

Let’s Explore Statistics […] Many researchers learn statistics as a series of flowcharts and heuristics without ever diving into the deep mathematical concepts that underlie the choices they have been taught to make. I think everyone wishes they understood statistics better but it is easy to become overwhelmed with equations and proofs. Most of my knowledge in both math and statistics is self-taught through experience and exploration. This book is an organized assortment of simulations and examples that have personally helped me think through these difficult topics. Inspiration for this … Read more →

Simple Simulation and the James-Stein Estimator […] This is the website for “Simulation And The James-Stein Estimator In R”. This technical document is short, covering some common ways to generate data and exploring the James-Stein Estimator. This will teach you how to do run simulations to observe the properties of the James-Stein Estimator in R — specifically using the tidyverse: You’ll learn how to generate data to prove theoretical results. In the computer age of statistics the data scientist has the power of machines to run simulations for testing a methods before putting a method into … Read more →