# Kurse und Workshops

Der Leibniz-WissenschaftsCampus bietet für seine Mitglieder Kurse und Workshops an, die der methodischen oder fachübergreifenden Weiterbildung dienen. Das Angebot richtet sich in erster Linie an Doktorandinnen und Doktoranden sowie PostDocs zu Beginn ihrer wissenschaftlichen Laufbahn. Die Kurse werden in Rücksprache mit den Mitgliedern organisiert.

# Kursprogramm 2017

# Creating efficient designs with Bayesian Sequential Testing: an R tutorial

**What is this workshop about? **Current debates on the reproducibility of scientific findings have identified underpowered studies as a core problem, resulting in the demand for larger sample sizes. This can pose a major challenge for resource-intensive fields such as group research because extreme sample sizes are often not an option. One solution to this problem is Bayesian Sequential Testing (BST).

Compared to regular null hypothesis significance testing (NSHT), BST requires, amongst other

advantages, smaller sample sizes without sacrificing information.

In this course, I will introduce the logic of Bayesian hypothesis testing and BST by taking the example of the independent samples t-test. Using this example, I will compare BST to NSHT in terms of required sample size as well as type I and II errors. I will further demonstrate how the specification of the Bayesian t-test influences both required sample size and error rates. Finally, I will outline the potential for and benefits of cumulative science that emerge when combining BST with open science (particularly open materials and data).

In this course, participants will learn to design a study plan and data collection rule using BST as well as analyzing data with Bayesian hypothesis test (again, we will use the independent samples t-test an example). The course will also cover some hands-on tips how to deal with real-life obstacles such as resource limitations and inconclusive results.

**When? **June 27th, 9-12

**Where? **German Primate Center (DPZ), Old lecture hall

**What is the target group? **everyone interested

**When can I register? **until June 13th, 2017

**How** **can I register? **Please send an email to: cschloegl(at)dpz.eu

**What is the maximum number of participants? **30

**Topics of the workshop include:**

- The conceptual underpinnings of Bayesian Statistics and sequential testing
- Specification of a Bayesian t-test and selection of the appropriate prior probability
- Interpreting the output of the Bayesian t-test

**Requirements:**

- Prior experience with R is helpful but not required
- Basic understanding of elementary statistics (especially the independent samples t-test)
- Please ensure that you have a recent version of R installed on your computer (https://cran.rproject.org/) and, optionally, RStudio (https://www.rstudio.com/) for a nicer user interface
- The course will require the R package “BayesFactor”, so you should either install it beforehand or make sure, you can download and install it during the workshop

# Bayesian Statistics

**What is this workshop about? **

As Andrew Gelman writes in his handy statistical lexicon (http://andrewgelman.com/2008/10/03/bayes_bayesians/):

*Every* *statistician uses Bayesian inference when it is appropriate (that* *is, when there is a clear probability model for the sampling of parameters).* *A Bayesian statistician is someone who will use Bayesian inference for all* *problems, even when it is inappropriate. I am a Bayesian statistician myself* *(for the usual reason that, even when inappropriate, Bayesian methods seem to work well).*

Bayesian statistics is a powerful school for statistical inference, because it provides very natural solutions to problems that are very difficult to resolve in the classical framework of frequentist statistics (see the explanations in the description to the *Hierarchical* *Regression Models *workshop). Moreover, with the revolution that came with Markov chain Monte Carlo (MCMC) techniques, post-estimation calculations are practically much more easily feasible, which makes Bayesian inference very appealing in many applied scenarios where the classical framework is actually equally appropriate.

**When? **September 4 – 8, 2017, with an additional practice/question day on September 12, 2017. 9.00h – 13.00h each day.

**Where? **German Primate Center (DPZ), seminar room E0.14.

**What is the target group? **PhD students, post-docs.

**When can I register? **July 24 – August 20, 2017.

**How** **can I register? **Please send an email to: hsennhenn-reulen(at)dpz.eu

**What is the maximum number of participants? **15 (minimum number: 5).

**What are the contents I can expect?**

• **What is Statistical Inference? **Statistical inference and models; Four general

tasks in statistical inference; Two general approaches: Frequentist (exclusively

likelihood-based), and Bayesian inference.

• **Bayesian and Frequentist Perspectives on Statistical Inference**

• **Ba****yesian** **Inference **Posterior distribution; Bayesian point estimates; Credible regions; Bayesian tests; Choice of the prior distribution; Numerical methods for Bayesian inference.

• **Ba****yesian** **Inference using MCMC Sampling **Metropolis-Hastings-algorithm and Gibbs-sampler.

• **Bay****esian ****Regressi****on** Linear regression; Logit regression.

• **Bayesian Model Choice**

# Hierarchical Regression Models

**What is this workshop about? **

Hierarchical regression models are particularly suitable for research designs in which data are organized in more than one observation level (which is the case in many research designs within the ScienceCampus): The primary observation units are usually individuals who are nested within higher order units, such as groups, or when repeated measurements of individuals are examined.

**When? **November 6 – 10, 2017, with an additional practice/question day on November 14, 2017. 9.00h – 13.00h each day.

**Where? **German Primate Center (DPZ), seminar room E0.14.

**What is the target group? **PhD students, post-docs.

**When can I register? **September 25 – October 22, 2017.

**How** **can I register? **Please send an email to: hsennhenn-reulen(at)dpz.eu

**What is the maximum number of participants? **15 (minimum number: 5).

**What are the contents I can expect? **A hierarchical regression model does not only include model terms that explain variation in the (expectation of) the response by products of covariates *x**k *and regression coefficients β_{k} (this is supposed to describe the data generating mechanism across observation units, often denoted as fixed model terms), but also coefficients γ_{i} that explain variation between the observation units *i **∈ {*1*,* *. . . , n**} *(this is often denoted as a random term of the model). Other terminologies for hierarchical regression models are mixed effects regression model (fixed and random model terms), or multilevel regression model (referring to primary observation units being nested within higher order units). During this workshop, we will lay the emphasis on the Bayesian approach to this class of regression models. This is why this workshop is called Hierarchical Regression instead of Mixed Effects Regression Models: by the possibility to naturally incorporate the assumption that γ_{i} *∼ *N (0*, σ*^{2}) into a Bayesian framework, there is no need anymore to distinct between fixed and random model terms.

**But why should I learn how to use a Bayesian inference approach to hierarchical regression models? **In the classical statistical inference framework, mixed model regression parameters do not have nice asymptotic distributions to test against (this is in contrast to ordinary least squares and generalized linear models parameters, which asymptotically converge to known distributions), which complicates the inferences that can be made from mixed models in this classical framework. The main source of this added complexity is a shrinkage factor that is applied to the random effects by the usual assumption γ_{i} *∼ *N (0*, σ*^{2}), leading to complications in the determination of degrees of freedom associated with this model term. In an applied example, the variance parameter* γ *may be estimated from *n *levels of a variable, and a design matrix used to estimate the parameters of this variable incorporates *n *indicator variables for these *n *levels. If we would include this variable in the usual way (taking it as a fixed coefficients variable), we would associate one degree of freedom with one estimated value, and so we would usually associate *n *degrees of freedom with these *n *indicators. But since these *n *indicators have a shrinkage factor applied to them (this results in the so-called *partial pooling*), we do not really need *n *degrees of freedom. So what would be the correct degrees of freedom to use for the cost to estimate this random effects model term? Is it one (we only estimate one variance parameter), or *n *(we explain variation in the expectation of the response by the use of *n *coefficients), or something in between (partial pooling)? The latter option must be correct, but, unfortunately, there is no generally accepted theory that can provide us with an exact value to answer this question. Moreover, assuming we can find a good value for the degrees of freedom, we still can not count on our test statistic (from likelihood ratio tests and the like) to be *F *or *χ*2 distributed, now that we added this shrinkage part to the model. However, if we now move on towards a Bayesian framework in order to estimate this model, we see that the shrinkage is just a very natural consequence of the model assumptions – here seen as prior formulations. This is a major benefit that comes with the use of a Bayesian approach, and it can be assumed that Bayesian approaches to multilevel/hierarchical/mixed models will become the standard in the next years to come, moreover since recent great improvements in software solutions made this approach much easier applicable now (see STAN based R add-ons rstanarm and brms).

# Kontakt

Dr. Christian Schloegl Koordinator +49 551 3851-480 +49 551 3851-489 Kontakt

# Anmeldung

Mitglieder des WissenschaftsCampus können sich jeweils bis zu der genannten Anmeldefrist für Kurse registrieren, wobei die Plätze in der Reihenfolge der Anmeldungen vergeben werden. Falls im Anschluss an die Anmeldefrist Restplätze verfügbar sind, so stehen diese anderen Studierenden und Post-Docs aus Göttingen offen. Auch hierbei erfolgt die Vergabe in der Reihenfolge der Anmeldungen. Interessenten, die nicht in Göttingen tätig sind, sollten vorab Kontakt aufnehmen.