93,807 research outputs found
Applications of Bayesian model selection to cosmological parameters
Bayesian model selection is a tool to decide whether the introduction of a
new parameter is warranted by data. I argue that the usual sampling statistic
significance tests for a null hypothesis can be misleading, since they do not
take into account the information gained through the data, when updating the
prior distribution to the posterior. On the contrary, Bayesian model selection
offers a quantitative implementation of Occam's razor.
I introduce the Savage-Dickey density ratio, a computationally quick method
to determine the Bayes factor of two nested models and hence perform model
selection. As an illustration, I consider three key parameters for our
understanding of the cosmological concordance model. By using WMAP 3-year data
complemented by other cosmological measurements, I show that a non-scale
invariant spectral index of perturbations is favoured for any sensible choice
of prior. It is also found that a flat Universe is favoured with odds of 29:1
over non--flat models, and that there is strong evidence against a CDM
isocurvature component to the initial conditions which is totally
(anti)correlated with the adiabatic mode (odds of about 2000:1), but that this
is strongly dependent on the prior adopted.
These results are contrasted with the analysis of WMAP 1-year data, which
were not informative enough to allow a conclusion as to the status of the
spectral index. In a companion paper, a new technique to forecast the Bayes
factor of a future observation is presented.Comment: v2 to v3: minor changes, matches accepted version by MNRAS. v1 to v2:
major revision. New results using WMAP 3-yr data, scale-invariant spectrum
now disfavoured with moderate evidence. New benchmark test for the accuracy
of the method. Bayes factor forecast methodology (PPOD, formerly called ExPO)
expanded and now presented in a companion paper (astro-ph/0703063
Recommended from our members
Uncertainty explicit assessment of off-the-shelf software: A Bayesian approach
Assessment of software COTS components is an essential part of component-based software development. Poorly chosen components may lead to solutions of low quality and that are difficult to maintain. The assessment may be based on incomplete knowledge about the COTS component itself and other aspects (e.g. vendor’s credentials, etc.), which may affect the decision of selecting COTS component(s). We argue in favor of assessment methods in which uncertainty is explicitly represented (‘uncertainty explicit’ methods) using probability distributions. We provide details of a Bayesian model, which can be used to capture the uncertainties in the simultaneous assessment of two attributes, thus, also capturing the dependencies that might exist between them. We also provide empirical data from the use of this method for the assessment of off-the-shelf database servers which illustrate the advantages of ‘uncertainty explicit’ methods over conventional methods of COTS component assessment which assume that at the end of the assessment the values of the attributes become known with certainty
Why do we need to employ Bayesian statistics and how can we employ it in studies of moral education?: With practical guidelines to use JASP for educators and researchers
ABSTRACTIn this article, we discuss the benefits of Bayesian statistics and how to utilize them in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two data sets previously collected: one small data set collected from a moral educational intervention experiment, and one big data set from a large-scale Defining Issues Test-2 survey. The results suggest that Bayesian analysis of data sets collected from moral educational studies can provide additional useful statistical information, particularly that associated with the strength of evidence supporting alternative hypotheses, which has not been provided by the classical frequentist approach focusing on P-values. Finally, we introduce several practical guidelines pertaining to how to utilize Bayesian statistics, including the utilization of newly developed free statistical software, Jeffrey’s Amazing Statistics Program, and thresholding based on Bayes Factors, to scholars in the field of moral education
Can we disregard the whole model? Omnibus non-inferiority testing for in multivariable linear regression and in ANOVA
Determining a lack of association between an outcome variable and a number of
different explanatory variables is frequently necessary in order to disregard a
proposed model (i.e., to confirm the lack of an association between an outcome
and predictors). Despite this, the literature rarely offers information about,
or technical recommendations concerning, the appropriate statistical
methodology to be used to accomplish this task. This paper introduces
non-inferiority tests for ANOVA and linear regression analyses, that correspond
to the standard widely used -test for and ,
respectively. A simulation study is conducted to examine the type I error rates
and statistical power of the tests, and a comparison is made with an
alternative Bayesian testing approach. The results indicate that the proposed
non-inferiority test is a potentially useful tool for 'testing the null.'Comment: 30 pages, 6 figure
- …