• Corpus ID: 118565424

Data analysis recipes: Probability calculus for inference

@article{Hogg2012DataAR,
  title={Data analysis recipes: Probability calculus for inference},
  author={David W. Hogg},
  journal={arXiv: Data Analysis, Statistics and Probability},
  year={2012}
}
  • D. Hogg
  • Published 20 May 2012
  • Computer Science
  • arXiv: Data Analysis, Statistics and Probability
In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the operations performed in probabilistic data analysis. Dimensional analysis is emphasized as a valuable tool for helping to construct non-wrong probabilistic statements. The applications of probability calculus in constructing likelihoods, marginalized likelihoods… 
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References

SHOWING 1-5 OF 5 REFERENCES
Data analysis recipes: Fitting a model to data
We go through the many considerations involved in fitting a model to data, using as an example the fit of a straight line to a set of points in a two-dimensional plane. Standard weighted
Data analysis : a Bayesian tutorial
TLDR
This tutorial jumps right in to the power ofparameter estimation without dragging you through the basic concepts of parameter estimation.
Is cosmology just a plausibility argument
I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration
INFERRING THE ECCENTRICITY DISTRIBUTION
Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As
2010b, “Inferring the eccentricity
  • 2010