start populating references

06_Monte_Carlo.ipynb

@@ -6,7 +6,7 @@
    "source": [
     "# The Monte Carlo method\n",
     "\n",
-    "The Monte Carlo method is a computational technique that uses <font color='orange'>random sampling</font> to estimate complex mathematical outcomes or solve problems that might be <font color='orange'>deterministic</font> in nature.\n",
+    "The Monte Carlo {cite}`metropolis1949monte, robert1999monte` method is a computational technique that uses <font color='orange'>random sampling</font> to estimate complex mathematical outcomes or solve problems that might be <font color='orange'>deterministic</font> in nature.\n",
     "\n",
     "The name “Monte Carlo” for the Monte Carlo methods has an origin that ties back to the famous Monte Carlo Casino located in Monaco. This name was not chosen because of any direct association with the mathematical principles behind these methods, but rather for its metaphorical connection to randomness and chance, which are central elements in both gambling and Monte Carlo simulations.\n",
     "\n",
@@ -449,6 +449,11 @@
     "$$"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": []
+  },
   {
    "cell_type": "markdown",
    "metadata": {},

07_MCMC.ipynb

@@ -42,7 +42,7 @@
    "source": [
     "## Metropolis-Hastings algorithm\n",
     "\n",
-    "The Metropolis-Hastings algorithm is particularly useful when direct sampling from the distribution is difficult or impossible, but evaluating the probability density function (PDF) up to a constant of proportionality is feasible. It's useful for sampling from <font color='orange'>high-dimensional</font>, complex distributions. The algorithm iteratively generates samples from a target distribution by constructing a Markov chain.\n",
+    "The Metropolis-Hastings algorithm {cite}`robert2004metropolis` is particularly useful when direct sampling from the distribution is difficult or impossible, but evaluating the probability density function (PDF) up to a constant of proportionality is feasible. It's useful for sampling from <font color='orange'>high-dimensional</font>, complex distributions. The algorithm iteratively generates samples from a target distribution by constructing a Markov chain.\n",
     "\n",
     "Let $\\pi(x)$ be the target probability density function (pdf) from which we want to sample. The steps of the Metropolis-Hastings algorithm are as follows:\n",
     "\n",
@@ -615,7 +615,7 @@
    "source": [
     "## Hamiltonian Monte Carlo\n",
     "\n",
-    "Hamiltonian Monte Carlo algorithm introduces gradient information in improving efficiency on the proposals and reduce random walk behavior of the sampling. The gradients help the algorithm to find high probability states. HMC can potentially improve sampling efficiently, but the gradients of the distribution need to be tractable. Additional parameters need to be tuned, which makes its implementation more difficult than other MCMC methods. However, methods have been developed for automatic adaptation of the parameters, such as no-U-turn sampler (NUTS)."
+    "Hamiltonian Monte Carlo {cite}`betancourt2017conceptual` algorithm introduces gradient information in improving efficiency on the proposals and reduce random walk behavior of the sampling. The gradients help the algorithm to find high probability states. HMC can potentially improve sampling efficiently, but the gradients of the distribution need to be tractable. Additional parameters need to be tuned, which makes its implementation more difficult than other MCMC methods. However, methods have been developed for automatic adaptation of the parameters, such as no-U-turn sampler (NUTS)."
    ]
   },
   {

09_intro_to_Numpyro.ipynb

@@ -8,7 +8,7 @@
    "source": [
     "# Introduction to NumPyro\n",
     "\n",
-    "[NumPyro](https://num.pyro.ai/en/latest/index.html#) is a probabilistic programming library that combines the flexibility of `numpy` with the probabilistic modeling capabilities of `pyro`, making it an excellent choice for researchers and data scientists. In this introductory tutorial, we'll explore the basics of `numpyro` and how to get started with probabilistic programming in a hands-on manner."
+    "[NumPyro](https://num.pyro.ai/en/latest/index.html#) {cite}`phan2019composable,bingham2019pyro` is a probabilistic programming library that combines the flexibility of `numpy` with the probabilistic modeling capabilities of `pyro`, making it an excellent choice for researchers and data scientists. In this introductory tutorial, we'll explore the basics of `numpyro` and how to get started with probabilistic programming in a hands-on manner."
    ]
   },
   {

09a_JAX_patterns.ipynb

@@ -6,7 +6,7 @@
    "source": [
     "# JAX patterns\n",
     "\n",
-    "Since Numpyro uses JAX as a backend, it is important to know how to work with JAX efficiently. JAX is a high-performance numerical computing library designed for machine learning research, which leverages XLA (Accelerated Linear Algebra) for optimizing and compiling numerical computations. This combination enables JAX to efficiently execute large-scale mathematical operations on hardware accelerators, boosting performance and scalability."
+    "Since Numpyro uses JAX {cite}`jax2018github` as a backend, it is important to know how to work with JAX efficiently. JAX is a high-performance numerical computing library designed for machine learning research, which leverages XLA (Accelerated Linear Algebra) for optimizing and compiling numerical computations. This combination enables JAX to efficiently execute large-scale mathematical operations on hardware accelerators, boosting performance and scalability."
    ]
   },
   {

999_bibliography.md

@@ -0,0 +1,4 @@
+# Bibilography
+
+```{bibliography}
+```

_toc.yml

@@ -28,4 +28,5 @@ chapters:
 - file: 22_ODEs.ipynb
 - file: 23_ID_modelling.ipynb
 - file: 24_other.ipynb
-- file: 999_acknowledgements.md
+- file: 999_acknowledgements.md
+- file: 999_bibliography.md

assets/references.bib

@@ -3,4 +3,72 @@ @article{gelman2020bayesian
   author={Gelman, Andrew and Vehtari, Aki and Simpson, Daniel and Margossian, Charles C and Carpenter, Bob and Yao, Yuling and Kennedy, Lauren and Gabry, Jonah and B{\"u}rkner, Paul-Christian and Modr{\'a}k, Martin},
   journal={arXiv preprint arXiv:2011.01808},
   year={2020}
+}
+
+@article{metropolis1949monte,
+  title={The monte carlo method},
+  author={Metropolis, Nicholas and Ulam, Stanislaw},
+  journal={Journal of the American statistical association},
+  volume={44},
+  number={247},
+  pages={335--341},
+  year={1949},
+  publisher={Taylor \& Francis}
+}
+
+@misc{robert1999monte,
+  title={Monte Carlo Statistical Methods},
+  author={Robert, CP},
+  year={1999},
+  publisher={Springer-Verlag New York}
+}
+
+@article{robert2004metropolis,
+  title={The metropolis—hastings algorithm},
+  author={Robert, Christian P and Casella, George and Robert, Christian P and Casella, George},
+  journal={Monte Carlo statistical methods},
+  pages={267--320},
+  year={2004},
+  publisher={Springer}
+}
+
+@article{betancourt2017conceptual,
+  title={A conceptual introduction to Hamiltonian Monte Carlo},
+  author={Betancourt, Michael},
+  journal={arXiv preprint arXiv:1701.02434},
+  year={2017}
+}
+
+@article{phan2019composable,
+  title={Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro},
+  author={Phan, Du and Pradhan, Neeraj and Jankowiak, Martin},
+  journal={arXiv preprint arXiv:1912.11554},
+  year={2019}
+}
+
+@article{bingham2019pyro,
+  author    = {Eli Bingham and
+               Jonathan P. Chen and
+               Martin Jankowiak and
+               Fritz Obermeyer and
+               Neeraj Pradhan and
+               Theofanis Karaletsos and
+               Rohit Singh and
+               Paul A. Szerlip and
+               Paul Horsfall and
+               Noah D. Goodman},
+  title     = {Pyro: Deep Universal Probabilistic Programming},
+  journal   = {J. Mach. Learn. Res.},
+  volume    = {20},
+  pages     = {28:1--28:6},
+  year      = {2019},
+  url       = {http://jmlr.org/papers/v20/18-403.html}
+}
+
+@misc{jax2018github,
+  author = {James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and George Necula and Adam Paszke and Jake Vander{P}las and Skye Wanderman-{M}ilne and Qiao Zhang},
+  title = {{JAX}: composable transformations of {P}ython+{N}um{P}y programs},
+  url = {http://github.com/jax-ml/jax},
+  version = {0.3.13},
+  year = {2018},
 }