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fix citations and cross-references
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OriolAbril committed Jan 28, 2022
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"## Further topics\n",
"It is also possible to treat the bounds as unknown latent parameters. If these are not known exactly and it is possible to fomulate a prior over these bounds, then it would be possible to infer what the bounds are. This could be argued as overkill however - depending on your data analysis context it may be entirely sufficient to extract 'good enough' point estimates of the bounds in order to get reasonable regression estimates.\n",
"\n",
"The censored regression model presented above takes one particular approach, and there are others. For example, it did not attempt to infer posterior beliefs over the true latent `y` values of the censored data. It is possible to build censored regression models which do impute these censored `y` values, but we did not address that here as the topic of [imputation](https://en.wikipedia.org/wiki/Imputation_(statistics)) deserves its own focussed treatment. The PyMC [Censored Data Models](https://docs.pymc.io/notebooks/censored_data.html) example also covers this topic, with a particular [example model to impute censored data](https://docs.pymc.io/notebooks/censored_data.html#Model-1---Imputed-Censored-Model-of-Censored-Data). "
"The censored regression model presented above takes one particular approach, and there are others. For example, it did not attempt to infer posterior beliefs over the true latent `y` values of the censored data. It is possible to build censored regression models which do impute these censored `y` values, but we did not address that here as the topic of [imputation](https://en.wikipedia.org/wiki/Imputation_(statistics)) deserves its own focussed treatment. The PyMC {ref}`censored_data` example also covers this topic, with a particular {ref}`example model to impute censored data <censored_data/model1>`. "
]
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"## Further reading\n",
"When looking into this topic, I found that most of the material out there focusses on maximum likelihood estimation approaches, with focus on mathematical derivation rather than practical implementation. One good concise mathematical 80 page booklet by :cite:t:`breen1996regression` covers truncated and censored as well as other missing data scenarios. That said, a few pages are given over to this topic in Bayesian Data Analysis by :cite:t:`gelman2013bayesian`, and :cite:t:`gelman2020regression`."
"When looking into this topic, I found that most of the material out there focusses on maximum likelihood estimation approaches, with focus on mathematical derivation rather than practical implementation. One good concise mathematical 80 page booklet by {cite:t}`breen1996regression` covers truncated and censored as well as other missing data scenarios. That said, a few pages are given over to this topic in Bayesian Data Analysis by {cite:t}`gelman2013bayesian`, and {cite:t}`gelman2020regression`."
]
},
{
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],
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"name": "python",
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12 changes: 12 additions & 0 deletions examples/references.bib
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@article{ando2007bayesian,
title={Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models},
author={Ando, Tomohiro},
journal={Biometrika},
volume={94},
number={2},
pages={443--458},
year={2007},
publisher={Oxford University Press},
doi={10.1093/biomet/asm017}
}

@book{breen1996regression,
title={Regression models: Censored, sample selected, or truncated data},
author={Breen, Richard and others},
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6 changes: 4 additions & 2 deletions examples/survival_analysis/censored_data.ipynb
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"cell_type": "markdown",
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"(censored_data)=\n",
"# Censored Data Models"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"(censored_data/model1)=\n",
"### Model 1 - Imputed Censored Model of Censored Data\n",
"\n",
"In this model, we impute the censored values from the same distribution as the uncensored data. Sampling from the posterior generates possible uncensored data sets.\n",
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],
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