Using a Simple Binomial Model to Assess Improvement in Predictive Capability: Sequential Bayesian Inference, Hypothesis Testing, and Power Analysis

2012 ◽  
Author(s):  
David E. Sigeti ◽  
Robert A. Pelak
Keyword(s):  
Bayesian Inference ◽  
Hypothesis Testing ◽  
Power Analysis ◽  
Binomial Model ◽  
Predictive Capability

scholarly journals Bayesian Inference and Testing Any Hypothesis You Can Specify

2018 ◽  
Vol 1 (2) ◽  
pp. 281-295 ◽  
Author(s):  
Alexander Etz ◽  
Julia M. Haaf ◽  
Jeffrey N. Rouder ◽  
Joachim Vandekerckhove
Keyword(s):  
Bayesian Inference ◽  
Model Selection ◽  
Hypothesis Testing ◽  
Likelihood Ratio ◽  
Special Form ◽  
Null Hypothesis ◽  
Bayes Factor ◽  
Alternative Hypotheses ◽  
Competing Models

Hypothesis testing is a special form of model selection. Once a pair of competing models is fully defined, their definition immediately leads to a measure of how strongly each model supports the data. The ratio of their support is often called the likelihood ratio or the Bayes factor. Critical in the model-selection endeavor is the specification of the models. In the case of hypothesis testing, it is of the greatest importance that the researcher specify exactly what is meant by a “null” hypothesis as well as the alternative to which it is contrasted, and that these are suitable instantiations of theoretical positions. Here, we provide an overview of different instantiations of null and alternative hypotheses that can be useful in practice, but in all cases the inferential procedure is based on the same underlying method of likelihood comparison. An associated app can be found at https://osf.io/mvp53/ . This article is the work of the authors and is reformatted from the original, which was published under a CC-By Attribution 4.0 International license and is available at https://psyarxiv.com/wmf3r/ .

scholarly journals An introductory tutorial on Bayesian inference using a simple pedagogical tool

2017 ◽  
Author(s):  
Guillermo CAMPITELLI
Keyword(s):  
Probability Theory ◽  
Bayesian Inference ◽  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Traditional Approach ◽  
Postgraduate Students ◽  
Data Table ◽  
Null Hypothesis Testing ◽  
Testing Approach ◽  
Hypothesis Testing Approach

This tutorial on Bayesian inference targets psychological researchers who are trained in the null hypothesis testing approach and use of SPSS software. There a number ofexcellent quality tutorials on Bayesian inference, but their problem is that, they assume mathematical knowledge that most psychological researchers do not possess. Thistutorial starts from the idea that Bayesian inference is not more difficult than the traditional approach, but before being introduced to probability theory notation is necessary for the newcomer to understand simple probability principles, which could be explained without mathematical formulas or probability notation. For this purpose in this tutorial I use a simple tool-the parameter-data table-to explain how probability theory can easily be used to make inferences in research. Then I compare the Bayesian and the null hypothesis testing approach using the same tool. Only after having introduced these principles I show the formulas and notations and explain how they relate to the parameter-data table. It is to be expected that this tutorial will increase the use of Bayesian inference by psychological researchers. Moreover, Bayesian researchers may use this tutorial to teach Bayesian inference to undergraduate or postgraduate students.

The logic of null hypothesis testing

1998 ◽  
Vol 21 (2) ◽  
pp. 197-198 ◽  
Author(s):  
Edward Erwin
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Power Analysis ◽  
Meta Analysis ◽  
Significance Testing ◽  
Null Hypothesis Significance Testing ◽  
Null Hypothesis Testing

In this commentary, I agree with Chow's treatment of null hypothesis significance testing as a noninferential procedure. However, I dispute his reconstruction of the logic of theory corroboration. I also challenge recent criticisms of NHSTP based on power analysis and meta-analysis.

scholarly journals Survey estimates of king crab (Paralithodes camtschaticus) abundance off Northern Norway using GLMs within a mixed generalized gamma-binomial model and Bayesian inference

2012 ◽  
Vol 69 (8) ◽  
pp. 1416-1426 ◽  
Author(s):  
C. Hvingel ◽  
M. C. S. Kingsley ◽  
J. H. Sundet
Keyword(s):  
Bayesian Inference ◽  
Skewed Distribution ◽  
Binomial Model ◽  
Paralithodes Camtschaticus ◽  
King Crab ◽  
Northern Norway ◽  
Generalized Gamma ◽  
Wide Range ◽  
Compound Model ◽  
Survey Estimates

Abstract Hvingel, C., Kingsley, M.C.S., and Sundet, J.H. 2012. Survey estimates of king crab (Paralithodes camtschaticus) abundance off Northern Norway using GLMs within a mixed generalized gamma-binomial model and Bayesian inference. – ICES Journal of Marine Science, 69: . A trawl survey provides information on number and biomass of introduced king crab (Paralithodes camtschaticus) to the management of a fishery off the coast of Northern Norway; the annual catch quotas are largely set as a percentage of the survey estimate. A specially built sledge trawl was designed for the survey. It needs only small areas of trawlable bottom, performs well on a wide range of bottoms, and appears to have good catchability for benthic organisms. Many survey hauls catch no crabs and the non-zero catches have a highly skewed distribution. Data were therefore analysed with a compound model, in which separate predictors were fitted for the proportion of zero catches and for the catch size of the non-zero catches. The compound model was fitted by Bayesian methods using WinBUGS. The distribution of non-zero catches fitted well to a generalized gamma distribution, but with parameter values that made it approximate a lognormal distribution. Numbers of fishable crabs peaked in 2003, and total numbers in 2010 were about two-fifths of the 2003 maximum.

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