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arm61 committed Feb 25, 2020
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"source": [
"# Markov chain Monte Carlo\n",
"\n",
"In the [previous tutorial](./max_likelihood.html), you we introduced to the idea of the **likelihood**, $L$. \n",
"In the [previous tutorial](./max_likelihood.html), you were introduced to the idea of the **likelihood**, $L$. \n",
"This parameter is just one of the components of Bayes theorem, the foundation of Bayesian inference, \n",
"\n",
"$$ p = \\frac{P L}{Z}, $$ \n",
"\n",
"where, $p$ is the posterior probability, $P$ is the prior probability, and $Z$ is the evidence (more about these latter two factors in the [custom priors](./custom_priors.html) and [nested sampling](nested_sampling.html) tutorials). \n",
"This tutorial will show how Markov chain Monte Carlo may be used to evaluate the shape of the posterior probability, and show what this means for our understanding of a models inverse uncertainties. \n",
"\n",
"Let's start where we left of the previous tutorial, with a set of variables that maximise the likelihood of some model."
"Let's start where we left the previous tutorial, with a set of variables that maximise the likelihood of some model."
]
},
{
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