{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic tutorial\n", "\n", "This basic tutorial gives a brief overview of some of functionality of the **particles** package. Details are deferred to more advanced tutorials. \n", "\n", "## First steps: defining a state-space model\n", "\n", "We start by importing some standard libraries, plus some modules from the package." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import warnings; warnings.simplefilter('ignore') # hide warnings \n", "\n", "# standard libraries\n", "from matplotlib import pyplot as plt\n", "import numpy as np\n", "import seaborn as sb\n", "\n", "# modules from particles\n", "import particles # core module\n", "from particles import distributions as dists # where probability distributions are defined\n", "from particles import state_space_models as ssm # where state-space models are defined\n", "from particles.collectors import Moments " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's define our first state-space model **class**. We consider a basic stochastic volalitility model, that is: \n", "\\begin{align*}\n", "X_0 & \\sim N\\left(\\mu, \\frac{\\sigma^2}{1-\\rho^2}\\right), &\\\\\n", "X_t|X_{t-1}=x_{t-1} & \\sim N\\left( \\mu + \\rho (x_{t-1}-\\mu), \\sigma^2\\right), &\\quad t\\geq 1, \\\\\n", "Y_t|X_t=x_t & \\sim N\\left(0, e^{x_t}\\right),& \\quad t\\geq 0.\n", "\\end{align*}\n", " \n", "Note that this model depends on fixed parameter $\\theta=(\\mu, \\rho, \\sigma)$. \n", "\n", "In case you are not familiar with the notations above: a state-space model is a model for a joint process $(X_t, Y_t)$, where $(X_t)$ is an unobserved Markov process (the *state* of the system), and $Y_t$ is some noisy measurement of $X_t$ (hence it is observed). For instance, in stochastic volatility, $Y_t$ is typically the log-return of some asset, and $X_t$ its (unobserved) volatility.\n", "\n", "The code below is hopefully transparent." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "class StochVol(ssm.StateSpaceModel):\n", " def PX0(self): # Distribution of X_0\n", " return dists.Normal(loc=self.mu, scale=self.sigma / np.sqrt(1. - self.rho**2))\n", " def PX(self, t, xp): # Distribution of X_t given X_{t-1}=xp (p=past)\n", " return dists.Normal(loc=self.mu + self.rho * (xp - self.mu), scale=self.sigma)\n", " def PY(self, t, xp, x): # Distribution of Y_t given X_t=x (and possibly X_{t-1}=xp)\n", " return dists.Normal(loc=0., scale=np.exp(x))\n", " \n", "my_model = StochVol(mu=-1., rho=.9, sigma=.1) # actual model\n", "true_states, data = my_model.simulate(100) # we simulate from the model 100 data points\n", "\n", "plt.style.use('ggplot')\n", "plt.figure()\n", "plt.plot(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Methods `PX0`, `PX` and `PY` return objects that represent probability distributions (defined in module `distributions`. Parameters $\\mu$, $\\rho$ and $\\sigma$ are defined as **attributes** of a class instance: i.e. `self.mu` and so on. (`self` is the generic name for an instance of a class in Python.)\n", "\n", "If your are not very familiar with OOP (object oriented programming) and related concepts (classes, instances, etc.), here is a simple way to understand them in our context: \n", "\n", "* The **class** `StochVol` represents the parametric class of stochastic volatility models.\n", "\n", "* The object `my_model` (a **class instance** of `StochVol`) defines a particular model, where parameters $\\mu$, $\\rho$ and $\\sigma$ are fixed to certain values. \n", "\n", "In particular, we can inspect the attributes of `my_model` that store the parameter values. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-1.0, 0.9, 0.1)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "my_model.mu, my_model.rho, my_model.sigma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Class `StochVol` is a sub-class of ``StateSpaceModel``. (You can see that from the first line of its definition.) For instance, it inherits a method called `simulate` that generates states and datapoints from the considered model. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Particle filtering\n", "\n", "There are several particle algorithms that one may associate to a given state-space model. Here we consider the simplest option: the **bootstrap filter**. (See next tutorial for how to implement a guided or auxiliary filter.) The code below runs such a bootstrap filter for $N=100$ particles, using stratified resampling." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fk_model = ssm.Bootstrap(ssm=my_model, data=data) # we use the Bootstrap filter\n", "pf = particles.SMC(fk=fk_model, N=100, resampling='stratified', \n", " collect=[Moments()], store_history=True) # the algorithm\n", "pf.run() # actual computation\n", "\n", "# plot\n", "plt.figure()\n", "plt.plot([yt**2 for yt in data], label='data-squared')\n", "plt.plot([m['mean'] for m in pf.summaries.moments], label='filtered volatility')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that a particle filter is a Monte Carlo algorithm: each execution returns a random, slightly different result. Thus, it is useful to run a particle filter multiple times to assess how stable are the results. Say, for instance, that we would like to compare the variability of the log-likelihood estimate provided by a particle filter, when either a standard Monte Carlo algorithm is used, or its QMC variant, called SQMC. The following command runs 30 times each of these two algorithms." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = particles.multiSMC(fk=fk_model, N=100, nruns=30, qmc={'SMC':False, 'SQMC':True})\n", "plt.figure()\n", "sb.boxplot(x=[r['output'].logLt for r in results], y=[r['qmc'] for r in results]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the variance of SQMC estimates is quite lower. \n", "\n", "Command `multiSMC` makes it possible to run several particle filters, with varying options. Parallel execution is also possible, as explained in next tutorial." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing\n", "\n", "So far, we have only considered filtering; let's try smoothing, that is, approximating the distribution of the whole trajectory $X_{0:T}$, given data $Y_{0:T}=y_{0:T}$, for some fixed time horizon $T=100$. In particular, we are going to sample smoothing trajectories from the output of the first particle filter we ran a few steps above." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "smooth_trajectories = pf.hist.backward_sampling(10) \n", "plt.figure()\n", "plt.plot(smooth_trajectories);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we used the standard version of the FFBS (forward filtering, backward sampling) algorithm, which generates smoothing trajectories from the particle **history** (which we generated when running pf above). Other smoothing algorithms are available, see the next tutorial." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## (Bayesian) Parameter estimation\n", "\n", "Finally, we consider how to estimate the parameter $\\theta=(\\alpha, \\rho, \\sigma)$ from a given data-set. First, we set up a prior as follows." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "prior_dict = {'mu':dists.Normal(), \n", " 'sigma': dists.Gamma(a=1., b=1.), \n", " 'rho':dists.Beta(9., 1.)}\n", "my_prior = dists.StructDist(prior_dict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, the code above should be fairly readable: the prior for $\\mu$ is $N(0,1)$, the one for $\\sigma$ is a Gamma(1,1) and so on. \n", "(As before, probability distributions are represented by objects defined in the `distributions` module.)\n", "\n", "This may not be a sensible prior distribution; for instance it restricts $\\rho$ to $[0,1]$. However, this will suffice for our purposes. \n", "A popular way to simulate from the posterior distribution of the parameters of a state-space model is PMMH, a particular instance of the PMMC framework. Basically, this is a MCMC algorithm that runs at each iteration a particle filter so as to evaluate the likelihood. \n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "%%capture\n", "from particles import mcmc # where the MCMC algorithms (PMMH, Particle Gibbs, etc) live\n", "pmmh = mcmc.PMMH(ssm_cls=StochVol, prior=my_prior, data=data, Nx=50, niter = 1000)\n", "pmmh.run() # Warning: takes a few seconds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, the code above is hopefully readable: PMMH is run for 1000 iterations (`niter`), the particle filter run at each iteration have $N_x=50$ particles, and so on. One point worth mentioning is that we pass as an argument the *class* `StochVol`. Again, remember that this class indeed represents the considered parametric class (as opposed to `my_model`, which was a stochastic volatility model, for certain fixed parameter values). \n", "\n", "OK, we have waited long enough, let's plot the results." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the marginals \n", "burnin = 100 # discard the 100 first iterations\n", "for i, param in enumerate(prior_dict.keys()):\n", " plt.subplot(2, 2, i+1)\n", " sb.distplot(pmmh.chain.theta[param][burnin:], 40)\n", " plt.title(param)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These results might not be very reliable, given that we used a fairly small number of MCMC iterations. If you are familiar with MCMC, you may wonder how the Metropolis proposal was set: by default, PMMH uses an adaptive Gaussian random walk proposal, such that the covariance matrix of the random step is iteratively adapted to the running simulation. \n", "\n", "The library also implements SMC$^2$, and Particle Gibbs, but that will be covered in the next tutorial.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The end\n", "\n", "That's all, folks! This very basic tutorial is over. If you crave for more, head to the other tutorials: \n", "\n", "* [Advanced tutorial for state-space models](advanced_tutorial_ssm.html): covers the same topics as above (filtering, smoothing, parameter estimation for state-space models) but with more details.\n", "* [Tutorial on Bayesian estimation](Bayes_estimation_ssm.html): covers PMCMC and SMC^2 algorithms that may be used to estimate the parameters of a state-space model. \n", "* [Tutorial on SMC samplers](SMC_samplers_tutorial.html): a tutorial on how to run a SMC sampler (such as IBIS or tempering SMC) for a given static target distribution. \n", "* [How to define manually Feynman-Kac models](Defining_Feynman-Kac_models_manually.html): an advanced tutorial on how to define your own Feynman-Kac models.\n", "\n" ] } ], "metadata": { "celltoolbar": "Edit Metadata", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.4" } }, "nbformat": 4, "nbformat_minor": 1 }