* *

**Sections**

- Surf
- Liddle, AT 6: Direct link.
- Wikipedia: Graphical timeline from Big Bang to Heat Death but note that the left-hand vertical scale is tricky, for greater than about > 0, it is x=100*log(log(t_year)) and so t_year=10**(10**(x/100)))
- Wikipedia: Graphical timeline of the Big Bang: Redundant to the timeline above.
- Wikipedia: Chronology of the universe: Redundant to timeline above.
- Thomas Bayes (1701?--1761)
- Pierre-Simon Laplace (1749--1827): He developed a good deal of what we now consider Bayesian inference (see Wikipedia: Pierre-Simon Laplace (1749--1827): Analytic theory of probabilities). Did Laplace know of Bayes? Someone must know. Wikipedia doesn't say! But France had already had a long tradition of statistics going back to Blaise Pascal (1623--1622) who invented may have invented the roulette wheel.
- Harold Jeffreys (1891--1989): The key mid- 20th century. Images: Harold Jeffreys:
- Bayes' theorem
- Bayesian probability
- Bayesian inference: Inferring from data in hand what is the reality. Images.
- Bayesian statistics
- Bayes factor (AKA Bayes K factor):
The formula is correct: see Kass & Raftery, p. 776.
The Bayes factor is
**NOT**the odds ratio: the prior and posterior odds ratio are producted in the last expression. See also Bayes factor table. - Hagen proof
of the Gaussian distribution: Scroll through p. 80--87, but
the proof is
**NOT**complete. The Hagen proof is hard to find online it seems, but it was common in textbooks once. - ** | Bayesian Methods in Cosmology:
Roberto Trotta,
arXiv,
2017,
Jan05,
86 pages:
Review: On
Bayesian inference
in cosmology.
Probably pretty useful. I should teach it to make up half the course.
A more compact intro (without cosmology) is
Kass & Raftery, 1995.

--- Keywords: anthropic principle, Bayesian inference (see also Bayes' theorem, Bayes factor (AKA Bayes K factor), Bayesian probability, Bayesian statistics, marginalization, nuisance parameter, priors, posteriors), Boltzmann brain, cold dark matter (CDM), concordance model, concordance model distance measures graph, cosmological redshift, cosmology, dark energy, dark matter, expansion of the universe, fine-tuned universe, fundamental constants, IceCube Neutrino Observatory, IOP cosmological parameters summary: bit dated, metaphysical naturalism, multiverse, philosophical cosmology, philosophy, pocket universe, Universe in Problems: lots of solutions, etc. - * | Testing the Multiverse: Bayes, Fine-Tuning and Typicality:
Luke A. Barnes,
arXiv,
2017,
Apr06,
19 pages:
Research: On Bayesian inference
in cosmology.
This is the philosophical complement to
Bayesian Methods in Cosmology:
Roberto Trotta (see below).
See also
Barnes, L., 2012, The Fine-Tuning of the Universe for Intelligent Life, 77 pages
for discussion of
the fine-tuned universe.
To an arguable extent the
observable universe has been
fine-tuned for life as we know it, but
**NOT**over-fined-tuned as Martin Rees (1942--) and others have pointed out. Over-fine-tuning would falsify the multiverse. So the multiverse has passed one significant falsification test. How many falsification tests does a theory have to pass to be deemed a scientific theory?

--- Keywords: anthropic principle, Bayesian inference (see also Bayes' theorem, Bayesian probability, Bayesian statistics, Bayes factor (AKA Bayes K factor)), Boltzmann brain, cold dark matter (CDM), concordance model, concordance model distance measures graph, cosmological redshift, cosmology, dark energy, dark matter, expansion of the universe, fine-tuned universe, fundamental constants, IceCube Neutrino Observatory, IOP cosmological parameters summary: bit dated, metaphysical naturalism, multiverse, philosophical cosmology, philosophy, pocket universe, Universe in Problems: lots of solutions, etc. - Kass & Raftery, 1995, Bayes Factors

For the time being, mainly what we have is just Liddle, AT 6: Direct link.

Plus some supplements/complements.