bridgesampling: An R Package for Estimating Normalizing Constants

Statistical procedures such as Bayes factor model selection and Bayesian model averaging require the computation of normalizing constants (e.g., marginal likelihoods). These normalizing constants are notoriously difficult to obtain, as they usually involve high-dimensional integrals that cannot be solved analytically. Here we introduce an R package that uses bridge sampling (Meng & Wong, 1996; Meng & Schilling, 2002) to estimate normalizing constants in a generic and easy-to-use fashion. For models implemented in Stan, the estimation procedure is automatic. We illustrate the functionality of the package with three examples

Informed Bayesian T-Tests

Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t-test. In contrast, the Bayesian versions of the t-test have languished in obscurity. In recent years, however, the theoretical and practical advantages of the Bayesian t-test have become increasingly apparent and various Bayesian t-tests have been proposed, both objective ones (based on general desiderata) and subjective ones (based on expert knowledge). Here we propose a flexible t-prior for standardized effect size that allows computation of the Bayes factor by evaluating a single numerical integral. This specification contains previous objective and subjective t-test Bayes factors as special cases. Furthermore, we propose two measures for informed prior distributions that quantify the departure from the objective Bayes factor desiderata of predictive matching and information consistency. We illustrate the use of informed prior distributions based on an expert prior elicitation effort

Fitting the Cusp Catastrophe in R: A cusp Package Primer

Of the seven elementary catastrophes in catastrophe theory, the âÂÂcuspâ model is the most widely applied. Most applications are however qualitative. Quantitative techniques for catastrophe modeling have been developed, but so far the limited availability of flexible software has hindered quantitative assessment. We present a package that implements and extends the method of Cobb (Cobb and Watson'80; Cobb, Koppstein, and Chen'83), and makes it easy to quantitatively fit and compare different cusp catastrophe models in a statistically principled way. After a short introduction to the cusp catastrophe, we demonstrate the package with two instructive examples.

A Tutorial on Fisher Information

In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different statistical paradigms. First, in the frequentist paradigm, Fisher information is used to construct hypothesis tests and confidence intervals using maximum likelihood estimators; second, in the Bayesian paradigm, Fisher information is used to define a default prior; lastly, in the minimum description length paradigm, Fisher information is used to measure model complexity

Development of microdialysis methodology for interstitial insulin measurement in rodents.

INTRODUCTION: Accurate assessment of muscle insulin sensitivity requires measurement of insulin concentration in interstitial fluid (ISF), but has proved difficult. We aimed to optimise measurement of ISF insulin concentrations in rat muscles in vivo using microdialysis. METHODS: Factorial experimental design experiments were performed in vitro to determine optimal conditions for insulin recovery with microdialysis probes. These conditions were tested in vivo, adjusted appropriately and used in lean and obese Zucker rats to compare ISF insulin concentrations basally and during hyperinsulinaemic-euglycaemic (HE) clamp. RESULTS: Optimal conditions in vivo were: a 100kDa microdialysis probe inserted in muscle, perfused with 1% BSA, 1.5mM glucose in 0.9% sodium chloride at 1μl/min. Samples were collected into siliconised glass microvials. As a reference for insulin, we established a protocol of inulin infusion, beginning at -80min and reaching equilibrium within 60min. HE clamp, beginning at 0min, increased ISF insulin concentration from 122±56 basally to 429±180pmol/l (P<0.05) in lean rats and from 643±165 to 1087±243pmol/l (P=0.07) in obese rats; ISF insulin concentrations were significantly higher throughout in obese rats. The difference between ISF and plasma insulin concentration (ISF:plasma ratio) was substantially higher in obese rats, but fell to similar values in obese and lean rats during HE clamp. DISCUSSION: Optimising insulin recovery with microdialysis allowed accurate measurement of basal ISF insulin in muscle of lean and obese Zucker rats and indicates insulin transport across capillaries is impaired in obese rats, basally and during hyperinsulinaemia