Starting the monty section #6
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This is a start to the monty section - next step will be to write an example in the odin&monty section based on some real world data from the 2009 flu pandemic. I will also add more odin/monty code in the book in the short term as it is quite wordy at the moment. |
monty.qmd
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| ```{r} | ||
| l <- seq(from = 0, to = 10, by = 0.1) | ||
| plot(l, | ||
| exp(Vectorize(l_distribution$density)(l)), |
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@richfitz I need to use Vectorize() here to pass multiple value of the argument - let me know if a better interface can be shown.
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See above. You will need to pass a 1-row matrix in to vectorise , so
l <- matrix(seq(from = 0, to = 10, by = 0.1), 1)
monty_distribution_density(l_distribution, l)Please do not use $density in docs
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Not sure how to make this work. The following code:
fn <- function(l, p, m1, m2) { log(p * dnorm(l, mean = m1) + (1 - p) * dnorm(l, mean = m2)) } l_distribution <- monty_model_function(fn, fixed = list(p = 0.75, m1 = 3, m2 = 7), allow_multiple_parameters = TRUE) l <- matrix(seq(from = 0, to = 10, by = 0.1), 1) monty_model_density(l_distribution, l)
Return the following error,
Error in packer$unpack(): ! Can't unpack a matrix where the unpacker uses 'fixed' Run rlang::last_trace() to see where the error occurred.
that I interpret as a conflict with having some parameters set as fixed. I could pass a 101x4 instead with the fixed argument like this (that works fine),
`l_distribution <- monty_model_function(fn,
allow_multiple_parameters = TRUE)
l <- matrix(c(seq(from = 0, to = 10, by = 0.1), rep(0.75,101), rep(3,101), rep(7,101)),4)
monty_model_density(l_distribution, l)`
but then it makes things quite more complex to understand and it's not the same as the monty model has then 4 "parameters" (with a mixed interpretation, as one is the actual sampling variable of interest, and the others are parameters of the distributions in the statistical sense) instead of one.
advanced_monty.qmd
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| ## Working with other packages | ||
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| Exporting chains to work with other packages |
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this should be basic, not advanced. perhaps just drop this whole file for now
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Removed file for now.
composability.qmd
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| # # Control properties of the combined model: | ||
| # monty_model_combine(likelihood, prior, | ||
| # monty_model_properties(has_gradient = FALSE)) | ||
| ``` |
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not sure what this file is trying to show, drop for now?
| library(monty) | ||
| ``` | ||
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| We can define a simple Gaussian [mixture model](https://en.wikipedia.org/wiki/Mixture_model) of two sub-populations using the `monty_model_function()` from the package. The model represents the distribution of a quantity $l$, sampled with a probability $p$ from a normal distribution of mean $m_{1}$ and with a probability $1-p$ from another normal distribution of mean $m_{2}$. Both subpopulations have variance equal to 1. |
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I am sure we could come up with a less abstract example to help people think about this, but this can be done in the next PR
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I think there might be a nice biology example with antibody titres and positive vs negative subpopulations - but yes can wait for another iteration.
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| While dynamical systems and statistical models serve distinct purposes, they are not strictly separate. In fact, they can be connected through two powerful approaches that bring probabilistic reasoning into dynamical systems: **stochastic processes** and **Bayesian inference**. | ||
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| ### Stochastic processes: adding uncertainty to dynamical models |
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I'm not convinced this belongs here, but leave it here for now. It might belong earlier in some general introduction
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Agree - it touches on odin models, that are upwards in the book.
model.qmd
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| In this way, **stochastic processes** add an uncertainty dimension to the state of dynamical systems, while **Bayesian inference** applies probabilistic modelling to the parameters, merging dynamical and statistical perspectives. Together, these methods provide a rich toolkit for modelling complex systems that evolve over time and accounting for both randomness and uncertainty. | ||
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| ## Parameters and model complexity | ||
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There's a missing paragraph here outlining what you are trying to cover in this section.
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The whole section has been reworked, for hopefully adding flow and clarity.
model.qmd
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| ## Bayesian or non-Bayesian modelling | ||
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| Many statistical modelling tools, such as `stan`, `mcstate`, and `BayesTools`, are inherently Bayesian. However, the `monty` package is **Bayesian-agnostic**: it does not require a Bayesian interpretation. This flexibility allows users to work with probabilistic models either within a Bayesian framework or outside of it, depending on the needs of the analysis. |
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We should drop mcstate from this, it will just be confusing to people
model.qmd
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| A key concept in Bayesian inference and Monte Carlo methods is the distinction between **normalised** and **unnormalised** probability densities. | ||
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| ### Unnormalised density |
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these are just paragraphs, not sections - it would read more smoothly without the headings I think
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| Many statistical modelling tools, such as `stan`, `mcstate`, and `BayesTools`, are inherently Bayesian. However, the `monty` package is **Bayesian-agnostic**: it does not require a Bayesian interpretation. This flexibility allows users to work with probabilistic models either within a Bayesian framework or outside of it, depending on the needs of the analysis. | ||
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| ## Probability densities: normalised vs. unnormalised |
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This does not feel like it belongs here? Perhaps it belongs in a details section and then linked back to where you want to refer to it?
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This has been reworked.
Co-authored-by: edknock <47318334+edknock@users.noreply.github.com>
Co-authored-by: edknock <47318334+edknock@users.noreply.github.com>
Co-authored-by: edknock <47318334+edknock@users.noreply.github.com>
Co-authored-by: edknock <47318334+edknock@users.noreply.github.com>
…Bayesian orientated softwares.
…BayesianTransform sections into paragraphs as suggested in review to improve flow
…ut back with some potential reorganising of the content in a follow-up iteration
…n of matrix and value of variance of proposal distribution
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I should have covered all points in the review apart from the one linked with the Vectorize treatment of the density. See comments there: #6 (comment) |
monty.qmd
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| Hmm, there really is quite a bit of ground to cover here! | ||
| The most basic method to define a `monty` model is through a simple R function, as shown in this chapter. More advanced examples are covered in the @sec-monty-models in particular in the context of Bayesian statistics. @sec-monty-dsl introduces the monty DSL for more versatile model building using a small probabilistic DSL similar to BUGs. @sec-monty-combine explains how to compose new monty models by combining two existing ones. The last part of this book starting from @sec-inference demonstrates how to incorporate `odin` models into `monty` workflows. |
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Referring to sec-monty-combine here, doesn't seem to exist currently
monty.qmd
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| We've discussed a little bit about the philosophy of `monty` and built a simple model using an R function with `monty_function`. The example introduces the basics of defining and sampling from a `monty` model. | ||
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| For more advanced applications, refer to @sec-monty-dsl for constructing models using `monty`'s domain-specific language, which enables greater flexibility for complex structures. To combine multiple models, see @sec-monty-combine, which demonstrates how to compose and integrate existing `monty` models. Lastly, @sec-inference illustrates how to incorporate `odin` models into `monty` workflows, expanding the package’s potential for Bayesian inference with more sophisticated, system-based models. Each section provides detailed examples to guide you in leveraging `monty`’s full capabilities. |
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Again, referring to sec-monty-combine here when it doesn't seem to exist
monty.qmd
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| ## Sampling from our example distribution | ||
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| We now want to sample from this model, using the `monty_sample()` function. For this we need to tell `monty` which sampler we want to use to explore our distribution. There are a variety of samplers avalaible and you can learn about them in @sec-samplers. One of the simplest is the random walk [Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) algorithm that should work almost out of the box (though not necesseraly efficiently) in most cases. |
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| We now want to sample from this model, using the `monty_sample()` function. For this we need to tell `monty` which sampler we want to use to explore our distribution. There are a variety of samplers avalaible and you can learn about them in @sec-samplers. One of the simplest is the random walk [Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) algorithm that should work almost out of the box (though not necesseraly efficiently) in most cases. | |
| We now want to sample from this model, using the `monty_sample()` function. For this we need to tell `monty` which sampler we want to use to explore our distribution. There are a variety of samplers avaliable and you can learn about them in @sec-samplers. One of the simplest is the random walk [Metropolis-Hastings](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) algorithm that should work almost out of the box (though not necesseraly efficiently) in most cases. |
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Good spot - but still not the right spelling due to malignant typo
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Corrected though ;)
monty-dsl.qmd
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| source("common.R") | ||
| ``` | ||
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| The `monty` DSL provides a more intuitive way to define statistical models with `monty`. It is currently relatively basic and focus on providing support for defining priors in Bayesian models. It fully support differentiability allowing to use gradient based samplers on these models. |
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"focuses on" or "focused on"?
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I went for focuses on :)
…into monty-general
Co-authored-by: edknock <47318334+edknock@users.noreply.github.com>
Co-authored-by: edknock <47318334+edknock@users.noreply.github.com>
…into monty-general
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