{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Advanced Tutorial (geared toward state-space models)\n", "\n", "This tutorial covers more or less the same topics as the basic tutorial (filtering and smoothing of state-space models), but in greater detail." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining state-space models\n", "\n", "We consider a state-space model of the form:\n", "\n", "\\begin{align*}\n", "X_0 & \\sim N(0, 1) \\\\\n", "X_t & = f(X_{t-1}) + U_t, \\quad U_t \\sim N(0, \\sigma_X^2) \\\\\n", "Y_t & = X_t + V_t, \\quad V_t \\sim N(0, \\sigma_Y^2)\n", "\\end{align*}\n", "\n", "where function $f$ is defined as follows: $f(x) = \\tau_0 - \\tau_1 * \\exp( \\tau_2 * x)$. This model comes from Population Ecology; there $X_t$ stands for the logarithm of the population size of a given species.\n", "This model may be defined as follows." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# the usual imports\n", "from matplotlib import pyplot as plt\n", "import seaborn as sb\n", "import numpy as np\n", "\n", "# imports from the package\n", "import particles \n", "from particles import state_space_models as ssm\n", "from particles import distributions as dists\n", "\n", "\n", "class ThetaLogistic(ssm.StateSpaceModel):\n", " \"\"\" Theta-Logistic state-space model (used in Ecology). \n", " \"\"\"\n", " default_params = {'tau0':.15, 'tau1':.12, 'tau2':.1, 'sigmaX': 0.47, 'sigmaY': 0.39}\n", "\n", " def PX0(self): # Distribution of X_0\n", " return dists.Normal()\n", " \n", " def f(self, x):\n", " return (x + self.tau0 - self.tau1 * np.exp(self.tau2 * x))\n", " \n", " def PX(self, t, xp): # Distribution of X_t given X_{t-1} = xp (p=past)\n", " return dists.Normal(loc=self.f(xp), scale=self.sigmaX)\n", " \n", " def PY(self, t, xp, x): # Distribution of Y_t given X_t=x, and X_{t-1}=xp\n", " return dists.Normal(loc=x, scale=self.sigmaY)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is most similar to what we did in the previous tutorial (for stochastic volatility models): methods `PX0`, `PX` and `PY` return objects defined in module `distributions`. (See the [documentation](distributions.html) of that module for a list of available distributions). \n", "\n", "The only novelty is that we defined (as a class attribute) the dictionary `default_parameters`, which provides default values for each parameter. When it is defined, each parameter that is not set explicitly when instantiating (calling) `ThetaLogistic` is replaced by its default value:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "my_ssm = ThetaLogistic() # use default values for all parameters\n", "x, y = my_ssm.simulate(100)\n", "\n", "plt.style.use('ggplot')\n", "plt.plot(y)\n", "plt.xlabel('t')\n", "plt.ylabel('data');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Bogus Parameters\" (parameters that do not appear in `PX0`, `PX` and `PY`) are simply ignored:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "just_for_fun = ThetaLogistic(tau2=0.3, bogus=92.) # ok" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This behaviour may look surprising, but it will allow us to define prior distributions that involve hyper-parameters.\n", "\n", "## Automatic definition of `FeynmanKac` objects\n", "\n", "We have seen in the previous tutorial how to run a bootstrap filter: we first define some `Bootstrap` object, and then passes it to SMC. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "fk_boot = ssm.Bootstrap(ssm=my_ssm, data=y)\n", "my_alg = particles.SMC(fk=fk_boot, N=100)\n", "my_alg.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In fact, `ssm.Bootstrap` is a subclass of `FeynmanKac`, the base class for objects that represent \"Feynman-Kac models\" (covered in Chapters 5 and 10 of the book). To make things simple, a Feynman-Kac model is a \"recipe\" for our SMC algorithms; in particular, it tells us: \n", "\n", "1. how to sample each particle $X_t^n$ at time $t$, given their ancestors $X_{t-1}^n$;\n", "2. how to reweight each particle $X_t^n$ at time $t$. \n", "\n", "The bootstrap filter is a particular \"recipe\", where:\n", "\n", "1. we sample the particles $X_t^n$ according to the state transition of the model; in our case a $N(f(x_{t-1}),\\sigma_X^2)$ distribution. \n", "\n", "2. we reweight the particles according to the likelihood of the model; here the density of $N(x_t,\\sigma_Y^2)$ at point $y_t$. \n", "\n", "The class `ssm.Bootstrap` defines this recipe automatically from the supplied state-space model and data. \n", "\n", "The bootstrap filter is not the only available \"recipe\". We may want to run a *guided* filter, where the particles are simulated according to user-chosen proposal kernels. Such proposal kernels may be defined by adding methods `proposal` and `proposal0` to our `StateSpaceModel` class:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "class ThetaLogistic_with_prop(ThetaLogistic):\n", " def proposal0(self, data):\n", " return self.PX0()\n", " def proposal(self, t, xp, data):\n", " prec_prior = 1. / self.sigmaX**2\n", " prec_lik = 1. / self.sigmaY**2\n", " var = 1. / (prec_prior + prec_lik) \n", " mu = var * (prec_prior * self.f(xp) + prec_lik * data[t])\n", " return dists.Normal(loc=mu, scale=np.sqrt(var))\n", "\n", "my_better_ssm = ThetaLogistic_with_prop()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this particular case, we implemented the \"optimal\" proposal, that is, the distribution of $X_t$ given $X_{t-1}$ and $Y_t$. (Check this is indeed this case, this is a simple exercise!). (For simplicity, the proposal at time 0 is simply the distribution of X_0, so this one is not optimal.)\n", "\n", "Now we may define our guided Feynman-Kac model: " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "fk_guided = ssm.GuidedPF(ssm=my_better_ssm, data=y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An APF (auxiliarly particle filter) may be implemented in the same way: for this, we must also define method `logeta`, which computes the auxiliary function used in the resampling step; see the documentation and the end of Chapter 10 of the book.\n", "\n", "## Running a particle filter\n", "\n", "Here is the signature of class `SMC`: " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "alg = particles.SMC(fk=fk_guided, N=100, qmc=False, resampling='systematic', ESSrmin=0.5, \n", " store_history=False, verbose=False, collect=None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apart from ``fk`` (which expects a `FeynmanKac` object), all the other arguments are optional. Here is what they do: \n", "\n", "* `N`: the number of particles\n", "* `qmc`: whether to use the QMC (quasi-Monte Carlo) version\n", "* `resampling`: which resampling scheme to use (possible choices: `'multinomial'`, `'residual'`, `'stratified'`, `'systematic'` and `'ssp'`) \n", "* `ESSrmin`: the particle filter resamples at each iteration such that ESS / N is below this threshold; set it to `1.` (resp. `0.`) to resample every time (resp. to never resample)\n", "* `verbose`: whether to print progress information\n", "\n", "The remaining arguments (``store_history`` and ``collect``) will be explained in the following sections. \n", "\n", "Once we have a created a SMC object, we may run it, either step by step, or in one go. For instance: " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "next(alg) # processes data-point y_0\n", "next(alg) # processes data-point y_1\n", "for _ in range(8):\n", " next(alg) # processes data-points y_3 to y_9\n", "# alg.run() # would process all the remaining data-points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At any time, object `alg` has the following attributes:\n", "\n", "* `alg.t`: index of next iteration\n", "\n", "* `alg.X`: the N current particles $X_t^n$; typically a (N,) or (N,d) [numpy array](https://docs.scipy.org/doc/numpy-dev/user/quickstart.html)\n", "\n", "* `alg.W`: the N normalised weights $W_t^n$ (a (N,) numpy array)\n", "\n", "* `alg.Xp`: the N particles at the previous iteration, $X_{t-1}^n$\n", "\n", "* `alg.A`: the N ancestor variables: A[3] = 12 means that the parent of $X_t^3$ was $X_{t-1}^{12}$.\n", "\n", "* `alg.summaries`: various summaries collected at each iteration.\n", "\n", "Let's do for instance a weighted histogram of the particles. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(alg.X, 20, weights=alg.W);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Object alg.summaries contains various lists of quantities collected at each iteration, such as:\n", "\n", " * `alg.summaries.ESSs`: the ESS (effective sample size) at each iteration\n", " * `alg.summaries.rs_flags`: whether or not resampling was triggered at each step\n", " * `alg.summaries.logLts`: estimates of the log-likelihood of the data $y_{0:t}$ \n", " \n", "All this and more is explained in the documentation of the `collectors` module. Let's plot the ESS and the log-likelihood:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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4AAILX43Y64pIdFP4kRNTuQcOVIPPBz1azu0xoVVfCj9yZIfm+0RmsnNz5vymZe8rP8TuKY/464tI9FH4kRMTHPLKycN8aUPIYPhh/SodJilHZEMrvSI02bkZU3ASnDIYAgHsO/Mj/voiEn0UfuSEHJrvc4QfXnm9ICffmdPx708iW5h4QwT3+DkSX9Omh/bdf2Hr61ypQUSih8KPnJgjrPQKMsY0G/rShofSkq2vg7Ji58KFYS8Aho6Cblmwfy922Xvu1CAiUUPhR07Il/f4+bJQ+Fm9DBvGw2AlBpTugEAAUrtAejdXSjAJCZhxXwHALnxNy95F4pzCjxyXtRZKmlZ6HW133v6nQNd0qKmGz7SkWA4JBeeevTHGuFaHOfdS8CfC5xth8wbX6hAR9yn8yPHt2QUHD0BCAvTIO+JTjC8BM8TZ88eu0qovaaY4wjs7H4XpmoY56zzA2fRQROKXwo8cX2ilVz7Gn3jUp5nhTbs9f/KhhhUkxO44xmT5CDMXTATArnhfm3KKxDGFHzkue4zJzi2cOtTZTXdPOXyxJQKViSe4uMfPl5k+/aH/QGhsxL77L7fLERGXKPzI8QV7fo4zbGGSkuG04YDO+hKHPVgDu8uciwid5n48od6fd+djG+pdrkZE3KDwI8d1wj0/gBmuJe/STNORKKR3w3RJc7eWJuaMMc6qs6oK7IolbpcjIi5Q+JFjsoHAoZ6fEwk/g0eC8cEXW7DB3/glbjVf6RUtjN+PGXcZAHbRay5XIyJuUPiRY9tdBnW14PdDzpFXejVnuqbByacB6v0Rmm2O6f5k5+bMeZdCgh82fYr9fKPb5YhIhCn8yLEFhy169MQkJJzQl2i3ZwmKxp4fAJOeiRkxFgD7lpa9i8QbhR85ptbM9wkKHXRatBZbva8jyhKvKHb3TK9jMcHzvpa9h91X5XI1IhJJCj9ybK2Y7xNksnOdlWGBAHbN8g4qTKKd3bcXqiqci7xe7hZzJP1OgT4DoKFey95F4ozCjxyTbeNv7hr6klBwzuqB6ZTibi1HYIw5tOz9nfnYxkaXKxKRSFH4kaOygUYobZrz08o9WoK7PbP2Y+dUb4k7tjg43yf6hryCzMhznTPpKnaBgrpI3FD4kaPbtRPq6iAxCbJ7tO5re/eHzCyoPQifru6Y+iS6BXd2jpLNDY/EJCY6B54CAZ33JRI3FH7k6ILDFrk9Mb4TW+kVZIzBDD0LcM76kvgTOtMrint+AGfPH5/PmaC/XceyiMQDhR85quAPr7b+5h7a7XnVUmezRIkb1tpmp7lHb88PgOmWhRl+NgB2oTY9FIkHCj9ydMVtm+8TUjgIUlJhbyVsKQpbWeIBlXugptrpUelR4HY1xxVa9v7R29qeQSQOKPzIUbVlj5/mjD8RM/hM516aTBpfgpsb9uiJSUx0t5YTcfLpUHAS1NVhF7/pdjUi0sEUfuSInJVe252L9kxY1ZL3uBRc6RXNk52ba7HsfdFrzvtfRGKWwo8cWVkpNNRDUhJktXKlVzNm0AjnDKXS7dhgmJLY55HJzs2Zs8ZBahfnPLs1K9wuR0Q6kMKPHFlwpVdeb4yv7W8Tk5IKAwcD6v2JJ8EzvaJ9snNzJjkZc+7FgJa9i8Q6hR85okPDFu0/lkC7PccXGwhASfBYFO/0/ACY8ZeD8cG6ldgS9VSKxCqFHzmy9q70asYMbTrodPMG7N6Kdt9Polxwc0x/IuTkul1Nq5isHjB0JAB2kXp/RGKVwo8cUXtXejVnMrvDSSeDtdhVy9p9P4lywWMt8nu1enPMaOALTnxesgh7oMblakSkIyj8yGFsQwOU7nAuwrRaJzT0pd2eY15oc0wPTXZuYeAQ5xT62gPYJW+5XY2IdACFHzlceQk0NkByJ+iWHZZbmmFNB52uX4U9eCAs95QotSP6DzQ9FmMM5vymTQ8XvqbdyUVikMKPHC640iu/fSu9WsjvBdm5zvL5f38SnntKVAqt9PLYZOfmzNnnO7uTlxXDOr1fRWKNwo8c5tCZXu1f6RVkjMEMd3p/tOordtmGetjZNGTqoWXuX2Y6pWDGXAhAQOd9icQchR85jA1NWA3vD6/gqi+7ehm2UTvoxqSdxdDY6PSaZGa5XU27BIe+WLsCW1bibjEiElYKP3K4pmXuYT+aYMBA6JIGNfvhs3+H994SFYJDXuT3xhjjbjHtZHrkw6ARzirFRfPcLkdEwkjhR1qwDfXOPAcIf8+PLwET3ENFQ1+xyesrvb4ktOz9/Tc1UV8khvjdLqA1AoEAM2fO5L333qOyspJu3boxbtw4rrzyytBvmdZaZs6cyVtvvUV1dTUDBw5k6tSp5OXluVy9R3TwsIUZNgr7/lvYlR9hr53q+d4BaenQkGlshB9OHw45eVBWgv3wbcz4r7hdkYiEgad6fubOncuCBQv4zne+w8MPP8w3v/lNXn75ZV5//fXQc1566SVef/11brnlFh544AGSk5O5//77qaurc7Fy77ChM716dUwwOXW4c1jq7jLYvjX89xd3efBMr2MxPh/m/MuBptPerXW5IhEJB0/1/BQVFXHmmWdyxhlnAJCTk8PixYvZuHEj4PT6zJs3jyuuuIKRI53hldtuu41bbrmFZcuWMXbs2CPet76+nvr6+tC1MYaUlJTQx+ESvFdU93YUHxq26Ig6TadO2NOGO8Neqz7C9O4X9tc44Vq80B4eYmsPOkdbAKbgpDb9vUZjm/jGXkzj3H843xsb1mBOHep2SRETje0Rz9Qe4eOp8FNYWMhbb71FcXEx+fn5bN26lQ0bNvDtb38bgLKyMiorKxkyZEjoa1JTUxkwYABFRUVHDT9z5sxh1qxZoeu+ffvy4IMPkp0dng3+viw3N3rPO9q1p4wDQPrAQXTtoKHC/eMvpWLlRySsXUHud2/vkNdojWhuDy+p+2wdO63Fl9GN/MKB7bpXtLXJngsnUj1vFslL3iTrgsvcLifioq094p3ao/08FX6+/vWvc+DAAX7yk5/g8/kIBAJcd911nHvuuQBUVlYCkJ6e3uLr0tPTQ587ksmTJzNx4sTQdTBVl5eX09DQELb6jTHk5uZSWloatd3nDZuKANjbJYP9JR2zvNf2KQTjo37TBorXrsJ0z+mQ1zkeL7SHlwRWrQDA5hZQ0sb3TrS2iR19PsybxYEP33X1PRtp0doe8UrtcXx+v/+EOi48FX4++OADFi9ezA9/+EN69erF1q1beeqpp8jMzGT8+PFtvm9iYiKJiYlH/FxHvMGstVH5xrX1dRDczyS/V8fV2CXNWfb+2ToCn3yE78KJx/+aDhSt7eE1ttmxFu39+4y6NsnrBacOhfWrCCyah+/KKW5XFFFR1x5xTu3Rfp6a8PzMM88wadIkxo4dS+/evTnvvPOYMGECc+fOBSAjIwOAqqqqFl9XVVUV+pwcQ+kOsAFI7Qzp3Tr0pYJnfdlVWvIeK5rv8ROLfBc0nff13hvYulqXqxGR9vBU+KmtrcX3pbOmfD5fKAHn5OSQkZHBmjVrQp+vqalh48aNFBYWRrRWL7LNz/Tq4Al1wVPeKVqLrd7foa8lERJje/wcZshI6J4D1fuwS991uxoRaQdPhZ8RI0Ywe/ZsPv74Y8rKyli6dCmvvvpqaGWXMYbLL7+c2bNns3z5crZt28YjjzxCZmZm6DlyDMGVXhH4zd3k5Dk9BI2N2DXLO/z1pGPZ6v1Qudu5iNGeH+NLOLTsfeGrGnYQ8TBPzfm5+eabeeGFF3j88cepqqqiW7duXHzxxVx11VWh50yaNIna2loee+wxampqGDhwIHfddRdJSUkuVu4Nh3p+IvObuxk22nnNlR/B6PEReU3pIMH3TrdsTEqqu7V0IHPOxdiXnoUvtsDG9XDyaW6XJCJt4Knwk5KSwo033siNN9541OcYY7j22mu59tprI1dYrCgO/2nux2KGjcLOm4ld+zG2vh5zlEnnEv2aT3aOZaZzV8yocdjFC7ALX8Uo/Ih4kqeGvaTj2NpaKC91LiK1O2+f/pDRHWoPwKerI/Oa0jGajrWIxJCp20zwvK+Pl2ArdrtcjYi0hcKPOEq3g7XQpSt0zYjISxqfDzPsLEAHnXqdbZrsHOs9PwCmV19nuCsQwL473+1yRKQNFH4EiOxKr+bMUGfVl131ETYQiNjrSvhYaw/1/MTImV7HEzrt/Z352GZH44iINyj8iCOCK71aGDjYOUG+qgK2fhbZ15bw2FsJ+/eB8UFugdvVRMaw0c6Q7b4q7IrFblcjIq2k8CNAy56fSDL+RMygEU4NKz+M6GtLmAQnO+fkYZKS3a0lQozfjxn/FQDswtfcLUZEWk3hRxxu9fwANG14aFcujfxrS7vZ4uBKr/gY8goy514Cfj9sKcJuKXK7HBFpBYUfwdYehF07nQsXwo8ZNAIS/FDyBbZ0R8RfX9opuLNzhPaHihYmLQMz0jlU2S581eVqRKQ1FH4ESr5w/t81HdM1PeIvb1I7wymDAJ315UXBPX7iZbJzc+b8ponPyxZj91a4XI2InCiFHzm0TNnFPVpCB51qybun2EAAipvCcxwsc/8y0/dk6FsIjQ3Yd99wuxwROUEKP+LufJ8mZqiz3w+bPtVv0F6yp9zZpNLvh+w8t6txRWjTw3dexzY0uFyNiJwIhR9xbaVXc6ZbFvQZANZiVy1zrQ5ppWCvYW4Bxu+p03LCxpw5FtIyoHIP9hOtWBTxAoUfiYqeH3DO+gKwq7Tqyyts6FiL+BvyCjL+RMx5lwGa+CziFQo/cc4erHGGLsD1pcrB8MO6lc4KNIl+O+JzmfuXmXGXQkICbFyH3bbZ7XJE5DgUfuJdcLJqejdM567u1tKzD2TnQn0d/PsTd2uRExKcLG/icLJzcyajO+aMMYB6f0S8QOEnzh2a79PL3UIAY8yhs76023PUs42NUNoUnuPgNPfjCU18Xvoudv9el6sRkWNR+Il3O6Jjvk+QGd4UflYvd364SvQqK4GGBkjuBN1z3K7Gff0HQu/+UF+HfW+B29WIyDEo/MS5aFjp1UL/U6FLV6jeBxvXu12NHEvwWIv83hif/ikxxmAumACAfXseNqDwLhKt9C9WvIuSlV5BJiEBM3gkoKGvaBfa2TlK3jvRwIw81wnve8pBWzaIRC2Fnzhma/ZD5W7nIgrm/ASZ4Yd2e7bWulyNHE1oZ/A4n+zcnElKdg48BQKzn8bu09wfkWik8BPPgiu9MrpjUru4W0tzpw2DxCTnsNUdW92uRo6mOH7P9DoWc9HXIDMLSncQ+MO92AM1bpckIl+i8BPHQvN9ouyHl0nu5AQgdNZXtLL1dbCzxLmI4w0Oj8SkZeL7yS+hSxp8vpHAo/dj62rdLktEmlH4iWdRNt+nudBuzyu123NUKtkONgCdu0J6ptvVRB2TV4Dvx/dBpxTYsIbA//5W536JRBGFnzgWdSu9mjFDRoIx8PlGbHAHaokawWMt6NkbY4y7xUQp06c/vtvucYZwVy3FPv0nbCDgdlkigsJPfIvmnp+0DGfZOzrrKyqF9ofSkNexmFMG4fveneDzYT9chH3hcU3iF4kCCj9xylbvg6oK5yKKVno1Fxr60knZUcfqTK8TZoaOxNz0Y8A5+sK+8ry7BYmIwk/cCi5T7paN6ZTqbi1HETrotGitsyxfokexen5awzd6POYb3wXAvvIcgbdecbkikfim8BOnonm+T5DpkQ95vaCxEbtmhdvlSBN7oAZ2lzkX6vk5Yb4LJmImXQ+Aff7/CHywyOWKROKXwk+8iuL5Ps2Fen+05D16BINzRjdM567u1uIxZsK1zj5AgH3qD9rFXMQlCj9xKlr3+Pmy0G7Pa1dg6+tdrkagea+hhrxayxiDufpmzJgLIRAg8NhvsZ+udrsskbij8BOvPNLzQ58BkN4NDh6ADfohERV2aGfn9jA+H+bbt8Gw0dBQT+CR+7FbP3O7LJG4ovATh+y+KthX5VzkRedKryDj82GGnQVot+docajXUD0/bWUSEvB99w4YOARqDzjHYJR84XZZInFD4SceBX94ZfVwjpKIcqEl76uWapO4aBA6zV3hpz1MYhK+W++Ck06G/fsI/O7n2OBEchHpUAo/ccgLK71aOGWIc0xA5R74fKPb1cQ1u68K9lY6F1G6P5SXmE6p+H70C6cHtnK3E4D2VrhdlkjMU/iJR16Z79PEJCZiBo0ANPTlumBwzs71RK+hF5guac5BqN1zoKyYwMP3al8rkQ6m8BOHPNfzA6DdnqNCaGdnL713PMBkdsd3+y8hLQO2byHwp19ha3USvEhHUfiJM9baQz0/HlqtYwaPgIQEKPkCW1bsdjnxK3imlyY7h53JyXdOgk/tDBvXE/jrf2MbtL2DSEdQ+Ik3+yph/z4wPsgtcLuaE2ZSu0DhIEBDX24Kneaunp8OYXr1xfcfP4ekJFi7Avvk77GBRrfLEok5Cj/xJnimV3YPTFKyu7W00qGDThV+3GCtVc9PBJgBp+L7wV2Q4Mcuew/77GM6CV4kzPxuF9Bat956K+Xl5Yc9fskllzB16lTq6uqYMWMGS5Ysob6+nqFDhzJ16lQyMjIiX2wU8uR8nyZm2Cjsc/8Lmz7F7q3EpGW4XVJ8qdgNB6qd4cfcnm5XE9PMoDMw37kd+3+/xb4zHzp3xUz+lttlicQMz4Wf3/zmNwSa7fWybds2fv3rX3P22WcD8PTTT/Pxxx9z++23k5qayhNPPMH06dP51a9+5VbJ0cVjK72aM92yoXd/2LYJu3oZ5pyL3S4pvgSHvHLyMf5Ed2uJA76R5xA4sB/79z9j5/2TQGoXfJdOdrsskZjgufCTlpbW4nru3Ln06NGD0047jZqaGhYuXMiPfvQjBg1y5odMmzaNn/zkJxQVFVFYWHjEe9bX11Pf7NwoYwwpKSmhj8MleK9w3rO1bLPJzm7W0Va+4aMJbNsEq5Zizr2kXfeKhvbwkkPvnT4d9nemNmkpYdxXCNRUE3jxaeysv2E7d8HXzvd9a6g9oovaI3w8F36aa2ho4L333mPChAkYY9i8eTONjY0MHjw49JyePXuSlZV1zPAzZ84cZs2aFbru27cvDz74INnZ2R1Sd25ubofc93istewo2Y4FsoeMICkvz5U62qPu4onsfOkfsG4lPTIz8HVKafc93WoPr9m9p5waoOvAQaR38HtHbdLMzf9BJZZ9L84g8PdHyczvSeo5F0W0BLVHdFF7tJ+nw8/SpUuprq5m/PjxAFRWVuL3++ncuXOL56Wnp1NZWXnU+0yePJmJEyeGroOpury8nIaGhrDVa4whNzeX0tJSVyYw2srd2Op94POxy5+MKSmJeA3tZZM7Q1YOdlcZJQtfxzf87Dbfy+328JqGjZ8CsD+tGzUd9N5RmxyZvewqTPlO7Lv/Yvf//IyKg3X4Th/e4a+r9oguao/j8/v9J9Rx4enws2jRIoYNG0a3bt3adZ/ExEQSE488h6Ej3mDWWnfCT3CDupw88Cd69pvHDBuNffNl7CcfYYeNbvf93GoPL7GBRig5NFm+o/++1CaHM9/8PlTvx654n8Cj98Ptv8L0HxiR11Z7RBe1R/t5dql7eXk5q1ev5sILLww9lpGRQUNDA9XV1S2eW1VVpdVegN3h3ZVezYWWvK9eim3UHigRsWsn1NVBYhJk93C7mrhkfAmYqbfDacOhrpbAH3+J3b7V7bJEPMmz4WfRokWkp6dzxhlnhB7r168fCQkJrFmzJvRYcXExu3btOup8n7ji4ZVeLQw4DTp3dTZr3LTe7WriQzA45/XC+BLcrSWOGX8ivmn/Bf0HQs1+Ar//Bba81O2yRDzHk+EnEAjw9ttvM27cOBISDv1DnJqaygUXXMCMGTNYu3Ytmzdv5s9//jOFhYUKP3h7j5/mTEICZsiZgDY8jJTgkKmXjkSJVSa5k7MLdM8+UFVB4Hf3YCt3u12WiKd4MvysWbOGXbt2cf755x/2uSlTpnDGGWcwffp0fvGLX5CRkcEdd9zhQpXRxVoLJV8AMdDzQ7Ohr1Ufaew7EoLBWTs7RwXTuYtzDlh2LuzaSeD39zqLGUTkhHhywvPQoUOZOXPmET+XlJTE1KlTmTp1aoSrinIVu+BAjbM7b498t6tpv9PPcOaflJc6P5j1Q7lDhXp+8vX3HC1MRjd8P/klgQf/E3Z8TuAP9+G7/VeYMGz/IBLrPNnzI20Q/M09RnbnNcmd4NShANhPPnS5mthmG+ph5w7nQsNeUcVk5+L7yS+dOXBbigj8+QFsvU6CFzkehZ84YWNlsnMzoaEvnfLesXYWQ2MjpKRCZpbb1ciXmJ698f3oF5DcCdavIvD4Q1oFKXIcCj/xIkYmOzdnho4EY+Dzjdg9u9wuJ2aF9ofK9+aRKPHA9C3Ed+vd4PfDxx9g//6o5sKJHIPCT5wI7vETS6t1TFom9DsFALtqqcvVxLAdh870kuhlTh2K75b/D4wP+/6bzllgCkAiR6TwEwdsIBBa6RVLPT8AZrizw7OGvjqODZ7mrsnOUc+ccTZmym0A2DfmYuf90+WKRKKTwk882FMOtQchwQ/Z3jvM9FjMUGfeDxvWYGuqj/1kaRvt8eMpvrEXYa75DgB27jME3p7nckUi0UfhJx4E5/vk9sT4Pbm7wVGZ3J6Q1wsaG7BrV7hdTsyxtQedoy1A2wl4iO/iSZgJ1wBgn32MwEfvuFyRSHRR+IkDsbjSqzkz7CznAw19hV/JF2AtdE3HdE13uxppBTPpm5jzLwdrsX/7PXbNcrdLEokaYQ0/e/fu5d133+Wll15i2bJlBAKBcN5e2ioGV3o1Fxz6smtXOHvSSNiEDsNVr4/nGGMw130Xc9Y4aGwk8Jf/xhb92+2yRKJCq8dAFi9ezMKFC/nxj39MWlpa6PGioiIefPBB9u/fH3pswIAB3HPPPXTq1Ck81Uqb2OLYOdbiiPoWQnomVFXAhrVw+nC3K4odxcH5Pgo/XmR8PrjpR9gD1bBmOYFHfoXvjvsxvfu7XZqIq1rd8/P+++/T2NjYIvhYa/nTn/5ETU0NV111FXfeeScXX3wxGzdu5OWXXw5rwdI6zkqvGO/58fkwQ52hL7tSuz2HU/M9fsSbjN+P7/t3QuHpcKDGOQesdIfbZYm4qtXh5/PPP+fUU09t8diGDRsoKyvj4osv5uqrr+aMM85g6tSpnHHGGXz0keZhuGrXTqirA38i5OS6XU2HMcOCS96XOoFPwkN7/MQEk5SM79afQe9+sK+KwMM/x+4pd7ssEde0OvxUVVWRk5PT4rHVq1cDMGbMmBaPDxkyhLKysnaUJ+0WWulVgPEluFtLRxo4BJJToHI3fL7J7Wpigq3e7/x9gnp+YoBJ7YzvR/dCj56wp5zAw7/A7qtyuywRV7Q6/HTt2rXFvB6ATz/9FL/fT79+/Vo8npyc3L7qpN1ifaVXkElMhEHOXB9teBgmweDcLRuTkupuLRIWJi3DOQg1MwtKtxP4w33YAzVulyUSca0OP3369GHJkiU0Nh2ct2fPHjZs2MDpp59OUlJSi+fu3LmTbt26hadSaZvQSq9e7tYRAaGhr1UKP+EQmu+jIa+YYrpnOwGoSxp8vpHAI7/G1tW6XZZIRLU6/EyePJktW7Zw55138pe//IV77rmHhoYGJk6ceNhzV6xYQf/+WlXgplDPTxz8ADODzwSfD3Z8ji0rcbsc7wuu9IrxXsN4ZPIK8P34XuiUAkVrCfzvb7ENDW6XJRIxrQ4/AwcO5Mc//jHWWhYvXkxiYiLf//73GTJkSIvnrV27lrKyMs4888ywFSutYwONULLduYiDH2Cmcxc4ZTCgoa9w0B4/sc30GYDvtnsgMQlWLcU+/SctFpC40aazDs4++2zOPvvsYz5n0KBBzJgxo01FSZiUlUJDPSQlQVYPt6uJCDN0FHb9KmfJ+yVfd7scz7LWNtvjJ/aDc7wypwzC9707Cfz5fuyHiyC1M1x3C8YYt0sT6VA63iKWhVZ69XI2O4sDoaMuNn6K3bfX3WK8bG8l7N8Hxge5BW5XIx3IDB2JuenHANiFr2Jfec7dgkQioNU9P5WVlRQXF9OvX78WOzc3NDTw4osvsnjxYioqKujZsydXX321hr1cFC8rvZoz3XOcvUy2bcauXoYZe6HbJXlTcLJzTh4mSas2Y51v9HgCNfuxz/0v9pXnCaR2wXfR19wuS6TDtLo7YO7cuTz88MP4v3Q6+IwZM5g9ezb79++nV69eFBcXM336dNatWxe2YqWVYvxMr6MJnfWl3Z7bzBYHV3rF13snnvkumIiZdD0A9oXHCSxZ6HJFIh2n1eFn3bp1jBgxokX42bt3L2+88QYFBQU88sgj/OY3v+F3v/sdaWlpvPrqq2EtWE5cPPb8AJjhzpJ31n2CrdUS3jYJ7uycr8nO8cRMuBbT1ONjn/4jgU/0C4TEplaHn927d1NQ0HIOwIoVK7DW8tWvfpXOnTsDkJ2dzfjx4/nss8/CU6m0im1shJ1N5/fE22/vBSdB9xznWI/1n7hdjScF9/jRZOf4YozBXH0zZsyFEAgQeOx/OLDiA7fLEgm7Voefurq6w05pX79+PeCs8GquR48eVFdXt6M8abOyEmhogORO0C3b7WoiyhiDGRYc+tKS99aygQAUf+FcaJl73DE+H+bbt8Gw0dBQz66f/weNTz6M3VvhdmkiYdPq8JOTk8PWrVtbPPbvf/+b7OxssrKyWjx+8OBBunTp0q4CpY2Cczby4melV3Oh8LNqmbPfkZy4PeVQewD8fsjOc7sacYFJSMD33Tsw514CgF2ykMDPfkDgzZe0GaLEhFb/VBw1ahTvvPMOS5YsYdeuXcyePZtdu3Ydcd+fzz77jB494mN/mWhjd8TnfJ+Qk0+H1C6wfy9s/NTtarwluLlhbgHG36atwCQGmMQkEqb8BznTn4KTBsCBGuwLTxD49U+wG9a4XZ5Iu7T6X7avfe1rrFixgj/84Q+hx/Lz87niiitaPG/fvn0sX76cr31NyyVdEacrvYJMQgJmyEjsh4uwqz7CFJ7udkmeYUPHWmjISyB54CAS7ppO4L03sHNmwI7PCTx0N2bkuZirbsJ0yzr+TUSiTKvDT6dOnXjggQdYunQpO3fuJDs7m5EjRx52qOmePXu45pprGD16dNiKlRMXryu9mjPDRjnh55MPsVfdpF1rT9QOLXOXlozPh++8S7EjxmDn/gP7znzssvecvbSaVoiZxES3yxQ5Ya0OPxs3biQ3N/e4x1v06dOHlJQU1q1bx7hx49pcoLSebaiHsmLnIo7DD6cPB38ilJc6E3j1w/yEhIZMNdlZvsR07or55vex515M4NnHYNOn2NlPY99/E991t2AGneF2iSInpNVzfu6++25WrlwZut6/fz833HDDETcz3LBhA3/+85/bVaC0wc4SaGx0TmyO4y5p0ykFTh0KaMPDE2UbG6G0aaVXPAdnOSbTuz++Ox/E3PwTSMuAnTsI/OFeGh99AFte6nZ5IsfV7mVA1lrq6+sJ6DTgqGGbzfeJ96EeLXlvpeZbJHTPcbsaiWLGGHxnn4/v13/FXDwJfD5Y+SGBX9xG4OXnsHXaYFSiV/ytgY4Hmu8TYoaeBcbA1s+wFbvdLif6BbdIyO8dl1skSOuZlFR813wH38//CAOHQH0d9pXnCPz8VuzKD7HWul2iyGH0r1sMss1+gMU7k54J/U4BwK5S78/xHNrZWfN9pHVMz974bv8Vvu/9FDKzYHcZgUcfIPDH+7ClO9wuT6QFhZ9YpJ6fFg4ddKrwczzByc6aHC5tYYzBnHkOvl/9GXP51c5GmWs/JnDvfxCY/TT24AG3SxQB2rDaC6CsrIzNmzcDUFNTA0BJSQmpqamHPU8iy9bXO/M2QD0/TczwUdjZT8Ona7AHajApqcf/onilPX4kDExyJ8zkb2HHXEjg+f+DtSuwr7+I/eBtzDU3Y848J+7nI4q72hR+XnjhBV544YUWjz3++ONhKUjaaed2CAQgpTNkdHO7mqhgcgsgtyeU7sCuXYEZea7bJUUlW1/nrBQEneklYWF65OP74c9h9TInBO3aif3f32LfmY/vG9/V8Kq4ptXh5wc/+EFH1CFhEhq2yO+l36yaMcNGY+e/CCs/AoWfIyv5AmwAunR1li+LhIExBoaehe/Uodg35mDnzYINawj88keYC76K+ep1mNTObpcpcabV4Wf8+PEdUIaETdNp3PqNqiUzbBR2/ovYNcuxDfUYv3aj/bJDwbmPgrOEnUlKxky8Djv6fAIzn4BPPsS++RJ26TuYK2/EjB6vFYYSMZ47tXDPnj0888wzrFy5ktraWnJzc5k2bRr9+/cHnH2HZs6cyVtvvUV1dTUDBw5k6tSp5OXFx+nUNs7P9DqqvoVOb8beSihaC6cNd7ui6BNa6aX3jnQck9WDhGl3Ydd+7AyF7dyB/dvvse/Ox3f99zC9+7tdosQBT8Xs/fv3c8899+D3+7nrrrt4+OGH+fa3v03nzoe6TF966SVef/11brnlFh544AGSk5O5//77qaurc7HyCApNWNUPsOaMz+fs+YNWfR3NoeCsXkPpeGbQGfju/SPmyinOppqbPiXw69sJ/OMv2Op9bpcnMc5TPT8vvfQS3bt3Z9q0aaHHcnIO7UJrrWXevHlcccUVjBw5EoDbbruNW265hWXLljF27Ngj3re+vp76+vrQtTGGlJSU0MfhErxXRw0p2Lpa5xwrnGEvDV20ZIaPxr73BnblUrj++x3eHp7T1PPjK3DvvaM2iS4d3R4mMQm+cpUzFPbPJ7FL38W+/Tp2+WJ8k7+NOfdijC+hQ17bi/T9ET6eCj/Lly9n6NCh/O53v2PdunV069aNSy65hIsuughwltZXVlYyZMiQ0NekpqYyYMAAioqKjhp+5syZw6xZs0LXffv25cEHHyQ7O7tD/hy5ubkdct+6TZ+y01p8XdPJO+VUfYN8ie1+KTv+97fYil1kVVeRdPKpQMe1h5cEavazY085ALnDz8LXNc3VetQm0aXD2yMvD37xOw6uXk7lX39L/eebCPz9URI/XETm939K8sBBHfv6HqPvj/bzVPgpKytjwYIFTJgwgcmTJ7Np0yb+9re/4ff7GT9+PJWVlQCkp6e3+Lr09PTQ545k8uTJTJw4MXQdDA3l5eU0NDSErX5jDLm5uZSWlnbIlu+BVR87/88toLRUhwse0enDYcUSyt58FX/XzA5tDy+xmz51Psjszs791bC/2pU6Ovp7RFon4u2R3RP7Xw/he3segZf+Qf1n6yj7fzdizrkY3xXfxsT5KkR9fxyf3+8/oY4LT4WfQCBA//79uf766wGnh2bbtm0sWLCgXavQEhMTSUw88uqfjniDWWs75r6h+T699I1xNENHwYol2E8+xH79BqDj2sNLAtu3Oh/k946Kvwu1SXSJaHskJGAu/Cq+kedgX5yBXfIWdvECGlcswUz6Jmb8VzAJ8T0Upu+P9vNU+MnMzKSgoKDFYwUFBXz0kTOBNSMjA4CqqioyMzNDz6mqquKkk06KVJmusU3L3LVB3dGZIWdifT7Y8Tm2vNTpbpdDR6LovSNRwqRlYm76Efa8Swk8+xhs24R9/n+x7/3LWRVWGPtDYfZgDZTswJZsg5LtULqd3Vk5BIadDYWna2pDO3gq/JxyyikUFxe3eKy4uDjUxZWTk0NGRgZr1qwJhZ2amho2btzIJZdcEulyI09neh2X6dwVTj4dNqzBfvIhDNGSdzh0oKlWekm0Mf0H4rv7Iex7C7Bz/g47Pifw27swZ43DXH0jJqO72yW2m91XBcVfYEu+gNLtzv9LtkPFrsOeWwPw5iuQk4c55xLMmAucA5ylVTwVfiZMmMA999zD7NmzGTNmDBs3buStt97iu9/9LuCMh15++eXMnj2bvLw8cnJyeP7558nMzAyt/opVtvZgaKWX9vg5NjN8NHbDGgIrP4Ip2rEc0B4/EtWMLwEz7jLsiDHYuc9g3/0Xduk72FVLMV+9FnPhV6N+41JrLezZBSXbsCXboeQL5/+lX8D+YyztT8+E3AJMXi9MXgEpFeVUL5oPZSXY2U9j5/4dhpyF77xL4PThWh13gjwVfgYMGMAdd9zBs88+y4svvkhOTg5Tpkzh3HMPHVcwadIkamtreeyxx6ipqWHgwIHcddddJCUluVh5BJQ0DXl1Tcd0TT/2c+OcGTYK+/z/wWfraKyqdLsc19m9lbCvCoyBvF5ulyNyVKZLGuaGadhzLyXw7F9h8wbsrKewixc4Z4VFwealtrERyku+1JPjDFlRe/DIX2QMdM+BpoATDDvk9cJ07tLsaYZueXkcnPgNAssXY997AzZ9Cis/JLDyQ8jMwoy9EDP2IkxWjwj9ib3JU+EHYMSIEYwYMeKonzfGcO2113LttddGsCr3aWfnE2e650BBX9i+hYPLFsPpR38/xYXgeyerBya5k7u1iJwA06c/vjsfxH64CDvrKSjdQeDhX8AZZ+O75jvO93gHs3W1zmHJJV8c6sUp+QLKSqDxKKuEExIgJ/9QyAn+v0cBJjn5hF/bdErBN/YiGHsRdsc27OIF2A8XQsUu7KsvYF+bCacOw3fuxTBsVNT3irnBc+FHjiI030e/uZ8IM3wUdvsWDnz4TtyHn9CZXprsLB5ifD7MmAuxw0ZjX3kOu/BV+PgDAmtXYL5yFebSK5xNFNvJ1uyHku3OL5jBXpySL2B3GRxtxVVS8hF7ccjOxfjD+2PX9OyNufY72Cu+jV35odMbtH4VrPuEwLpPoEuaMy/onIudOgRQ+IkZoZVe6vk5IWbYKOwrz3Pw4w/wfasWwvCPpGeFtkhQ+BHvMamdMddOxZ5zsbMqrGgt9qVnsUsW4rt2auhYm2Ox1kJVRVMPjjPZODhkRVXF0b+wc9fDe3HyejnDTxE+pNUkJmJGngsjz8WWl2IXv4ld8iZU7sG+MRf7xlwYcCrm3EswI8bGfS+vwk+s0Eqv1unVD7plY/eUY//9MWbYaLcrck1opZcmO4uHmZ598N1xP3b5YuzMJ6G8lMAjv4bBZ+K7biomJx8baITd5c1CTnC4ajscOMbGnhndIb+X03MS6skpcOZYRuFyc5Odi5l8A/Zr34C1HxN471+wZjlsXI/duB77/P9hzjoPc+6lmD7xeZCswk8MsAcPOF2woJ6fE2SMwYw8F/uv2QReeQHfkLMi/ptaNLDWao8fiRmh7+vBZ2Jfm4ld8BKsWU5g/UrILYCdxVB/lEOujQ+yezT14DjhJhR2UlIj+ucIF5OQAENHkjB0JLZyN3bJQuziBVBein1nPvad+dC7n7NkftR5mNQux79pjFD4iQXBlV7pmZgu7p7J5CW+y64g8N6/sNs2YZe+ixk93u2SIq9iFxyocSZi9sh3uxqRsDCdUjBXTsGOvZDAc/8H6z6B4C7m/kToke/0kuc2n3ScH5Y5QtHKZHTHXH419rIrnX3OFi/AfrwEtm3GPvtX7KwnneGwcy6Bk0+Lyh6tcFL4iQGHNqhTr09rmK7ppF19I1VPP+rsHTJiTEz/43dEwcnOPXpqRYjEHJNbgO/H98LG9VCz3xmqyuoR13vhGJ8PTh2KOXUodv9e7IdvO5Oki7dhP1iE/WAR5PZ0eoPOPj9mz1NT+IkFmu/TZl2+9g2qXn4edpdhF76GuXSy2yVFVOg8OA15SYwyxsDJp7ldRlQyXdIwF30Ne+FXYUuR0xu09F1nCf+sv2HnzICho5wl86cNi6nQqPATAw7t8aNljK3l69QJ39dvIPC3P2DnzcSec5FzBEa8UK+hSNwzxkC/UzD9TsFeczN2WdMGiluK4OMlBD5eAt2ync0Tx16E6X78U9OjXfzN8IxFTcvc1fPTNubs8509bmqqnc3B4khwjx/1/IgIgOmUiu/cS0i46yF8v/gD5sKvQmoX2FOOfeU5Av81lcY/3Iv9eAm24SibOXqAwo/H2ZrqQ4ffKfy0ifEl4LvqJgDsotec097jgA00Hposr2XuIvIlpqAvvutuwffQU5ip/w9OGexs7Lj2YwJ/+W8CP72JwKy/YUt3uF1qq2nYy+uCP7wyusfVMsWwO304nDoU1q/Czn0Gc8sdblfU8cp3Ost+k5JA5wCJyFGYxCTMqHEwahy2rLhpA8W3oKoC+6852H/NgcLTnUnSI8Zgkk78qA63qOfH43SmV3gYY5zeH2OwS9/Fbv3M7ZI6XnC+T17vmJrIKCIdx+Tk47vi2/j++wl8t94FQ0Y6eyQV/Rv75MME7riRwLN/xW7b7Hapx6SeH6/bETyaQOGnvUzvfpjR47EfLCLwz7/hu+P+mN7rIrTSS+8dEWkl4/fDsNEkDBuNrdiNff9NZwPF3WXYRfOwi+ZBnwHOcRpnnRd1G0Uq/HicVnqFl5l0A3bZYihaC6uXw9CRbpfUcXSgqYiEgcnsjpl4Lfbyq+HT1dj33sB+8iF8vhH7+UbszCcwZ56DOfcS6D8wKn6pVPjxOq30CivTPdvZ92L+iwRefArfoDOcLeJjUHBzTKPJziISBsbnc/YDOm0Ydt9e7IeLnCXzJV9gl7zlzBPK6+WcMH/2+Ziu6a7Vqjk/Hmar90PVHudC4SdszFeuhC5dnW/Y9990u5wOYevroazYudBp7iISZqZrGr6LJ+G77xF8dz6IGXshJCU7/67+80kC/99N2PWrXKtP4cfLgkNe3bKibjzVy0xqF8yEawGwLz+LrT3ockUdYOcOaGyElM6Q2d3takQkRhljMANOxXfjj/A99DTmhmnQZ4BzxlrfQtfq0rCXhx2a76Pf3MPNjP8KduGrzunHb8zFfPU6t0sKq9B5cD17R8X4u4jEPpOSihl3GYy7DFu5G9MpxbVa1PPjZTrTq8MYfyJm8rcBsP+aja2qcLmiMAu9dxScRSTyTIa7Pc4KPx6m09w7ljlzrNMtW3sQ+8pzbpcTVs17fkRE4o3Cj5ep56dDhTY+BGfpZsl2lysKo2Kd6SUi8Uvhx6Psvr2wr8q5yCtwt5gYZgpPh2GjIBAgMPtpt8sJC1t7EILnlyk4i0gcUvjxquBk5+45rk4aiwe+K6aAzwcrP8IW/dvtctqvaW8o0jJc3WdDRMQtCj8epTO9IsfkFTg7k4JzgrG1LlfUPsFjLbSzs4jEK4Ufr9KcjYgyX/sGJHeCLUXY5e+7XU776Dw4EYlzCj8epZ6fyDJpmZhLrwDAzpnh7JDsUVZneolInFP48SBrLehE7ogzl3wd0jOdjQ/fed3tctpO7x0RiXMKP160rxL27wNjIFcrvSLFJHfCfO16AOyrL2Br9rtcUevZ6n1QqfPgRCS+Kfx4UXDYIqsHJjnZ3VrijBl7EeT1gup92NdfdLuc1tvRbJWgzoMTkTil8ONBNrhUWb+5R5xJSMB35Y0A2Ddfxu4ud7egVgqt9NJ7R0TimMKPF2lnZ3cNORNOGQwN9di5z7hdTevs0CpBERGFHw/SSi93Ocde3AiA/eht7LZN7hbUCof2+NF7R0Til8KPxzgrvfTbu9vMSSdjzjoPrCUw6ylPbHxorT3U86PT3EUkjin8eE1VBdTsB+OD3J5uVxPXzNdvAL8f1q+Cf3/idjnHV1UB1fuc947OgxOROKbw4zXBYYucPExikru1xDmTnYs5fwLQdOxFoNHlio4j+N7pofeOiMQ3hR+POTTfp5e7hQgAZsI1kNoZdnyO/WCR2+UcU2hnZw15iUicU/jxmqZl7lrpFR1M566Yy68BwM79B7a21uWKjiF4ppcmO4tInFP48Rit9Io+5oIJ0D0HKndj33zJ7XKOymqivIgIAH63C2iNmTNnMmvWrBaP5efn8/vf/x6Auro6ZsyYwZIlS6ivr2fo0KFMnTqVjIyMyBfbAVqs9FL4iRomMQkz+VvYx6dj57+IPe9STNd0t8tqwQYCofeOhr1EJN55KvwA9OrVi3vuuSd07fMd6rx6+umn+fjjj7n99ttJTU3liSeeYPr06fzqV79yo9Twq9gNB2ogIUErvaKMGXku9o25sG0T9pXnMdd/z+2SWtpdBrUHndVpOXluVyMi4irPDXv5fD4yMjJC/6WlpQFQU1PDwoULmTJlCoMGDaJfv35MmzaNDRs2UFRU5HLVYRL8zT0nH+NPdLcWacH4fPiuvgkA++587M5ilyv6kuB7J7cXJiHB3VpERFzmuZ6f0tJSvve975GYmEhhYSHXX389WVlZbN68mcbGRgYPHhx6bs+ePcnKyqKoqIjCwsKj3rO+vp76+vrQtTGGlJSU0MfhErxXW+9pmw15hbOueNXe9jjsfqcOxQ4+E7tmOXbODHw/+K+w3Dccms/3ieb3TrjbRNpH7RFd1B7h46nwc/LJJzNt2jTy8/OpqKhg1qxZ/PznP2f69OlUVlbi9/vp3Llzi69JT0+nsrLymPedM2dOi7lEffv25cEHHyQ7O7sj/hjk5ua26ev2VJZTDXQ95TTS8zR0ES5tbY8jqfv+Hez8j+uxK5bQraKM5NOGhu3e7bF7Txk1QNrAQaR54L0TzjaR9lN7RBe1R/t5KvwMHz489HGfPn1CYeiDDz4gKantm7ZNnjyZiRMnhq6Dqbq8vJyGhoa2F/wlxhhyc3MpLS1t03EIDRs3ALA/rRs1JSVhqytetbc9jii5M2bMhdjFCyj760Mk/OeDUfFbWsPGTwHYl5ZJdRS/dzqkTaTN1B7RRe1xfH6//4Q6LjwVfr6sc+fO5OfnU1paypAhQ2hoaKC6urpF709VVdVxV3slJiaSmHjkOTQd8Qaz1rb6vs5KL2ePH/J66Y0fRm1pj2Mxk67HLn0XNq3HfrwEzhgTtnu3hW1ogNLtzkV+b0+8d8LdJtI+ao/oovZoP89NeG7u4MGDlJaWkpGRQb9+/UhISGDNmjWhzxcXF7Nr165jzvfxjD3lUHsAEvyQk+92NXIMJqM75pKvAxB4cYYTPtxUXgINDZCcAt06ZihXRMRLPNXzM2PGDM4880yysrKoqKhg5syZ+Hw+zjnnHFJTU7nggguYMWMGXbp0ITU1lSeffJLCwsLYCD+h1To9MX5PNVtcMpdOxr4zH8qKse/9K3QGmCuadnYmvxfG5+nfd0REwsJTP0X37NnDH/7wB/bt20daWhoDBw7k/vvvDy13nzJlCsYYpk+fTkNDQ2iTw1hgtbmhp5hOqZivfQP7j79iX3keO/p8TEqqK7UEz/TSzs4iIg5PhZ8f//jHx/x8UlISU6dOjZnA00Kz397FG8w5l2DffAV27sDOn42ZfIMrddjgae4600tEBPD4nJ94YnWgqecYvx/flVMAsG/OxVbsdqeQYM+PjrUQEQEUfjzBBgJQ0rTSS+HHW4aNggGnQV0d9qV/RPzlbV0tlDUtbdewl4gIoPDjDbvLoK7WOZcpO/o3qJNDjDH4rroRALvkLez2rZEtoHQ72AB06QppGZF9bRGRKKXw4wWhlV4FOpfJg0z/gZgRY8FaAi8+HdHXDk52Jj+6j7UQEYkkhR8P0Eov7zNXfMvZo2ntCuz6VZF74aaJ8kaTnUVEQhR+vCDY86Pw41kmJx8z/isABGb9zZnHFQG2+FDPj4iIOBR+PODQidwKP15mJlwLKamwbTN26TuRedFQz4/Cj4hIkMJPlLOBRig5dC6TeJfpmob5ylUA2DnPYOvrOvT17IEa51gU0HtHRKQZhZ9oV74T6usgMQmyerhdjbSTufCrkJkFe8qxC1/t2BcLDnlldMd07tKxryUi4iEKP9Eu+AMsrwDj00ovrzNJyZivfxMA+9o/sfv3dthr2R3a2VlE5EgUfqKcVnrFHjN6PBT0hQPV2NdmdtwLFetMLxGRI1H4iXZa6RVzjC/h0MaHi+Zhy0s75HVCPT9a6SUi0oLCT5Q71POjH2CxxJw+HE4bDo0N2Dl/75gX0R4/IiJHpPATxWxjo3M8Aeg09xjku+pGMAa77D3slqKw3tvurYR9VWAM5Om9IyLSnMJPNCsrgYYGSEqG7jluVyNhZnr1xYw+H2ja+NDa8N08OFya1QOT3Cl89xURiQEKP9EstNKrF8anpopF5uvfdLYxKPo3rF4WtvuGzvTSZGcRkcPoJ2oU00qv2Ge6ZWMu+ioAgVlPOUOd4VDcNN9Hc8VERA6j8BPNgj0/mrAa08xlV0GXrlC6Hbt4QVjuqT1+RESOTuEniqnnJz6Y1M6YidcBYF9+FnvwQLvuZ63VHj8iIseg8BOlbEMD7Cx2LjR0EfPMuMsgOxf2VmLfmNO+m1XsggM1kJAAPfLDU6CISAxR+IlWZcXQ2ACdUqBbltvVSAcz/kR8V3wbAPvGXGzlnrbfLDjZuUdPjD8xDNWJiMQWhZ8oFVqtk9cLY4y7xUhkjBgL/U6B2oPYV55r821scLKzhrxERI5I4Sdaab5P3DHG4LvqJgDsewtCc75aLXSshd47IiJHovATpazO9IpL5uTTYNhosAECs2e06R7BXkP1/IiIHJnCT7RSz0/c8l35bfD5YNVS7Ia1rfpaG2iEki+cCy1zFxE5IoWfKGTr650Jz6Cenzhkcgsw510KQOCfT2IDgRP/4vKdUF8HSUmQ1aODKhQR8TaFn2i0cwcEApDSGTK7u12NuMB89TpIToHPN2KXLz7xLwzO98nrjfEldExxIiIep/AThQ7N99FKr3hl0jIxl10BgJ3zd6c38ASEVnqpx1BE5KgUfqKR5vsIYC6eBOndYNdO7NvzTuyLdKCpiMhxKfxEodAePwo/cc0kd8JMuh4A++oL2Or9x/2a4JleRpOdRUSOSuEnGqnnR5qYsRc6IbhmP/b1fx7zuS0nyqvnR0TkaBR+ooytr4PyUudC4SfuGV8CvqtuBMC+9Sp2d9nRn7xzBzQ2aqK8iMhxKPxEm5LtYAOQ2gXSM92uRqLBoBFwymBoqMfOfeaoTwsOedGzjybKi4gcg8JPlGm+s7N+gAk0HXtxddOxFx++jf1805GfGBwu1XwfEZFjUviJNvoBJkdg+gzAjBoHQGDW37DWHvac5j0/IiJydAo/UUZnesnRmK/fAH4/fLoa1n58+BNCE+UVfkREjkXhJ9popZcchcnqgbngqwAEXnzKOceria09qInyIiInSOEnitjaWti107nQDzA5AnP51c5k+B2fY5csPPSJ4qbDTNMzMV3T3ClORMQjPB1+5s6dyzXXXMNTTz0Veqyuro7HH3+cm2++mW9961s89NBDVFZWulZjq5R+AdZClzRMWobb1UgUMp27YCZcA4B96R9Ojw+HjrVQaBYROT7Php+NGzeyYMEC+vRpOb/h6aefZsWKFdx+++3cd999VFRUMH36dJeqbB3t7Cwnwpw/AbrnQOUe7JsvOw9uD+7srPk+IiLH48nwc/DgQf70pz/xve99j86dO4cer6mpYeHChUyZMoVBgwbRr18/pk2bxoYNGygqKnKx4hOk+T5yAkxiImbytwCw81/E7q1Uz4+ISCv43S6gLR5//HGGDx/OkCFDmD17dujxzZs309jYyODBg0OP9ezZk6ysLIqKiigsLDzi/err66lvdmq2MYaUlJTQx+ESvNdR71kSXOauTeoi4bjtEcV8Z51H45svwdaN2FefDx1o6is4yZN/niAvt0ksUntEF7VH+Hgu/Lz//vts2bKF3/zmN4d9rrKyEr/f36I3CCA9Pf2Y837mzJnDrFmzQtd9+/blwQcfJDs7O2x1N5ebm3vEx4t3FtMIdB8ynE55eR3y2nK4o7VHtDv4vTso/6/vY9/5FzSt/ModPhJfaufjfGX082qbxCq1R3RRe7Sfp8LPrl27eOqpp/jZz35GUlJS2O47efJkJk6cGLoOpury8nIaGhrC9jrGGHJzcyktLT1skzp78ACNO51DKfckd8aUlITtdeXIjtUenpDdEzNkJHb1Muc6K4edVXuhaq+7dbWD59skxqg9oova4/j8fv8JdVx4Kvxs3ryZqqoq7rzzztBjgUCA9evXM3/+fO6++24aGhqorq5u0ftTVVVFRkbGUe+bmJhIYmLiET/XEW8wa+3h4Se4uWFaBnTuqjd2BB2pPbzCXDkFu2aFcx5cfh/P/jm+zMttEovUHtFF7dF+ngo/gwcP5qGHHmrx2F/+8hfy8/OZNGkSWVlZJCQksGbNGkaPHg1AcXExu3btOup8n2ihnZ2lLUx+b8y5l2DfnY/pd4rb5YiIeIKnwk9KSgq9e7cMB8nJyXTt2jX0+AUXXMCMGTPo0qULqampPPnkkxQWFkZ9+NFKL2kr843vYoaPck5+FxGR4/JU+DkRU6ZMwRjD9OnTaWhoYOjQoUydOtXtso5LPT/SVsbvh0Ej3C5DRMQzPB9+7r333hbXSUlJTJ061ROBpwWd5i4iIhIRntzkMNbYAzWwZ5dzoZ4fERGRDqXwEw2CQ14Z3TCpXdytRUREJMYp/EQBzfcRERGJHIWfaKCVXiIiIhGj8BMF1PMjIiISOQo/0UA9PyIiIhGj8OMyW7MfKvc4F3m93C1GREQkDij8uC045NUtCxMDp3GLiIhEO4Ufl2m+j4iISGQp/Lhth+b7iIiIRJLCj8vU8yMiIhJZCj9u00ovERGRiFL4cZHdvxf2VjoXWuklIiISEQo/bgoOeXXPwXRKcbcWERGROKHw4yLN9xEREYk8hR83ab6PiIhIxCn8uMjuUM+PiIhIpCn8uCnY89NT4UdERCRSFH5cYvdWwv69YAzkaqWXiIhIpCj8uCU42TmrByY52d1aRERE4ojCj0u00ktERMQdCj9u0UovERERVyj8uEQ9PyIiIu5Q+HGBtVanuYuIiLhE4ccNVRVQsx+MD/IK3K5GREQkrij8uCA05JWdi0lMcrcYERGROKPw4wbN9xEREXGNwo8LrFZ6iYiIuEbhxwWHzvTSzs4iIiKRpvATYdbaZmd69XG5GhERkfij8BNhjbvL4UA1+HzQo6fb5YiIiMQdhZ8Iq/98k/NBTj4mMdHdYkREROKQwk+ENWxrCj+a7CwiIuIKhZ8Iq/98M6CVXiIiIm5R+Imw+m1O+FHPj4iIiDsUfiLIWkv9ti2Aen5ERETcovATSXvKsQeqIcEPPfLcrkZERCQuKfxEUOhMrx75GL9WeomIiLjB73YBrfHGG2/wxhtvUF5eDkBBQQFXXXUVw4cPB6Curo4ZM2awZMkS6uvrGTp0KFOnTiUjI8PFqpvZoWMtRERE3Oapnp9u3bpx/fXX89///d/85je/YdCgQfzP//wPX3zxBQBPP/00K1as4Pbbb+e+++6joqKC6dOnu1z1Ibb4cwBMT4UfERERt3gq/Jx55pmcccYZ5OXlkZ+fzze+8Q06derEZ599Rk1NDQsXLmTKlCkMGjSIfv36MW3aNDZs2EBRUZHbpQPNhr3U8yMiIuIaTw17NRcIBPjggw+ora2lsLCQzZs309jYyODBg0PP6dmzJ1lZWRQVFVFYWHjUe9XX11NfXx+6NsaQkpIS+jgcrLXQ0ADG4OvZB8J0X2m7YNuGq42l/dQm0UXtEV3UHuHjufCzbds27r77burr6+nUqRN33HEHBQUFbN26Fb/fT+fOnVs8Pz09ncrKymPec86cOcyaNSt03bdvXx588EGys7PDW/xjswgcPIhJSsL4PNXpFtNyc3PdLkG+RG0SXdQe0UXt0X6eCz/5+fn89re/paamhg8//JBHH32U++67r133nDx5MhMnTgxdB1N1eXk5DQ0N7bp3c8YYcnNzKS0tdXqCxFVqj+ijNokuao/oovY4Pr/ff0IdF54LP36/P5R6+/Xrx6ZNm5g3bx5jxoyhoaGB6urqFr0/VVVVx13tlZiYSOJRDhntiDeYtVZv3Cii9og+apPoovaILmqP9vP82EsgEKC+vp5+/fqRkJDAmjVrQp8rLi5m165dx5zvIyIiIvHFUz0/zz77LMOGDSMrK4uDBw+yePFi1q1bx913301qaioXXHABM2bMoEuXLqSmpvLkk09SWFio8CMiIiIhngo/VVVVPProo1RUVJCamkqfPn24++67GTJkCABTpkzBGMP06dNpaGgIbXIoIiIiEuSp8PODH/zgmJ9PSkpi6tSpCjwiIiJyVJ6f8yMiIiLSGgo/IiIiElcUfkRERCSuKPyIiIhIXFH4ERERkbii8CMiIiJxReFHRERE4orCj4iIiMQVT21yGGl+f8f89XTUfaVt1B7RR20SXdQe0UXtcXQn+ndjrI6GFRERkTiiYa8IOnDgAHfeeScHDhxwuxRB7RGN1CbRRe0RXdQe4aPwE0HWWrZs2YI626KD2iP6qE2ii9ojuqg9wkfhR0REROKKwo+IiIjEFYWfCEpMTOSqq64iMTHR7VIEtUc0UptEF7VHdFF7hI9We4mIiEhcUc+PiIiIxBWFHxEREYkrCj8iIiISVxR+REREJK7ogJAImj9/Pq+88gqVlZX06dOHm2++mQEDBrhdVtyZM2cOS5cuZceOHSQlJVFYWMgNN9xAfn6+26UJMHfuXJ599lkuv/xybrzxRrfLiUt79uzhmWeeYeXKldTW1pKbm8u0adPo37+/26XFpUAgwMyZM3nvvfeorKykW7dujBs3jiuvvBJjjNvleZLCT4QsWbKEGTNmcMstt3DyySfz2muvcf/99/P73/+e9PR0t8uLK+vWrePSSy+lf//+NDY28txzz/HrX/+a3/3ud3Tq1Mnt8uLaxo0bWbBgAX369HG7lLi1f/9+7rnnHk4//XTuuusu0tLSKCkpoXPnzm6XFrfmzp3LggULuPXWWykoKGDz5s38+c9/JjU1lcsvv9zt8jxJw14R8uqrr3LhhRdy/vnnU1BQwC233EJSUhKLFi1yu7S4c/fddzN+/Hh69erFSSedxK233squXbvYvHmz26XFtYMHD/KnP/2J733ve/pB66KXXnqJ7t27M23aNAYMGEBOTg5Dhw4lNzfX7dLiVlFREWeeeSZnnHEGOTk5jB49miFDhrBx40a3S/MshZ8IaGhoYPPmzQwePDj0mM/nY/DgwRQVFblYmQDU1NQA0KVLF5criW+PP/44w4cPZ8iQIW6XEteWL19Ov379+N3vfsfUqVP56U9/yptvvul2WXGtsLCQtWvXUlxcDMDWrVvZsGEDw4cPd7ky79KwVwTs3buXQCBARkZGi8czMjJCb2ZxRyAQ4KmnnuKUU06hd+/ebpcTt95//322bNnCb37zG7dLiXtlZWUsWLCACRMmMHnyZDZt2sTf/vY3/H4/48ePd7u8uPT1r3+dAwcO8JOf/ASfz0cgEOC6667j3HPPdbs0z1L4kbj2xBNP8MUXX/DLX/7S7VLi1q5du3jqqaf42c9+RlJSktvlxL1AIED//v25/vrrAejbty/btm1jwYIFCj8u+eCDD1i8eDE//OEP6dWrF1u3buWpp54iMzNTbdJGCj8RkJaWhs/no7KyssXjlZWVh/UGSeQ88cQTfPzxx9x33310797d7XLi1ubNm6mqquLOO+8MPRYIBFi/fj3z58/n2WefxefTCH2kZGZmUlBQ0OKxgoICPvroI5cqkmeeeYZJkyYxduxYAHr37k15eTlz585V+GkjhZ8I8Pv99OvXj7Vr13LWWWcBzj/ua9eu5bLLLnO5uvhjreXJJ59k6dKl3HvvveTk5LhdUlwbPHgwDz30UIvH/vKXv5Cfn8+kSZMUfCLslFNOOWw4vri4mOzsbJcqktra2sO+D3w+Hzqas+0UfiJk4sSJPProo/Tr148BAwYwb948amtrldpd8MQTT7B48WJ++tOfkpKSEuqRS01N1bCLC1JSUg6bb5WcnEzXrl01D8sFEyZM4J577mH27NmMGTOGjRs38tZbb/Hd737X7dLi1ogRI5g9ezZZWVkUFBSwdetWXn31Vc4//3y3S/MsneoeQfPnz+fll1+msrKSk046iZtuuomTTz7Z7bLizjXXXHPEx6dNm6YwGiXuvfdeTjrpJG1y6JIVK1bw7LPPUlpaSk5ODhMmTOCiiy5yu6y4deDAAV544QWWLl1KVVUV3bp1Y+zYsVx11VX4/erDaAuFHxEREYkrGkwXERGRuKLwIyIiInFF4UdERETiisKPiIiIxBWFHxEREYkrCj8iIiISVxR+REREJK4o/IiIiEhcUfgRERGRuKLwIyJxY8OGDcycOZPq6mq3SxERFyn8iEjc2LBhA7NmzVL4EYlzCj8iIiISV3SwqYjEhZkzZzJr1qzDHn/kkUfIyclxoSIRcYvf7QJERCJh1KhRlJSU8P777zNlyhS6du0KQFpamsuViUikKfyISFzo06cPffv25f3332fkyJHq7RGJY5rzIyIiInFF4UdERETiisKPiIiIxBWFHxGJG8YYt0sQkSig8CMicSM5ORmAmpoalysRETdptZeIxI1+/foB8NxzzzF27FgSEhIYMWIEnTp1crkyEYkkbXIoInHlxRdfZMGCBVRUVGCt1SaHInFI4UdERETiiub8iIiISFxR+BEREZG4ovAjIiIicUXhR0REROKKwo+IiIjEFYUfERERiSsKPyIiIhJXFH5EREQkrij8iIiISFxR+BEREZG4ovAjIiIicUXhR0REROLK/w/4eHTDJTAnhAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(alg.summaries.ESSs)\n", "plt.xlabel('t')\n", "plt.ylabel('ESS');" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(alg.summaries.logLts)\n", "plt.xlabel('t')\n", "plt.ylabel('log-likelihood');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Running many particle filters in one go\n", "\n", "Function multiSMC accepts the same arguments as `SMC` plus the following extra arguments: \n", "\n", "* `nruns`: number of runs \n", "* `nprocs`: if >0, number of CPU cores to use; if <=0, number of cores *not to* use; i.e. `nprocs=0` means use all cores\n", "* `out_func`: a function that is applied to each resulting particle filter (see below). \n", "\n", "To explain how exactly `multiSMC` works, let's try to compare the bootstrap and guided filters for the theta-logistic model we defined at the beginning of this tutorial:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "outf = lambda pf: pf.logLt\n", "results = particles.multiSMC(fk={'boot':fk_boot, 'guid':fk_guided}, \n", " nruns=20, nprocs=1, out_func=outf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The command above runs **40** particle algorithms (on a single core): 20 bootstrap filters, and 20 guided filters. The output, ``results``, is a list of 40 dictionaries; each dictionary contains the following (key, value) pairs:\n", "\n", "* `'model'`: either `'boot'` or `'guid'` (according to whether a bootstrap or guided filter has been run)\n", "* `'run'`: a run indicator (between 0 and 19)\n", "* `'output'`: the result of `outf(pf)` where pf is the SMC object that was run. (If `outf` is set to None, then the SMC object is returned.)\n", "\n", "The rationale for function `outf` is that SMC objects may take a lot of memory in certain cases (especially if you set `store_history=True`, see section on smoothing below), so we may want to save only some results of interest rather than the complete object itself. Here the output is simply the estimate of the log-likelihood of the (complete) data computed by each particle filter. Let's check if the guided filter provides lower-variance estimates, relative to the bootstrap filter." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sb.boxplot(x=[r['fk'] for r in results], y=[r['output'] for r in results])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is indeed the case. To understand this line of code, you must be a bit familiar with [list comprehensions](http://www.secnetix.de/olli/Python/list_comprehensions.hawk). \n", "\n", "More generally, function `multiSMC` may be used to run multiple SMC algorithms, while varying any possible arguments; for more details, see the documentation of `multiSMC` and of the module `particles.utils`. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Collectors, on-line smoothing\n", "\n", "We have said that `alg.summaries` (where `alg` is a SMC object) contains **lists** that contains quantities computed each iteration (such as the ESS, the log-likelihood estimates). It is possible to compute extra such quantities such as: \n", "\n", "* moments: at each time $t$, a dictionary with keys 'mean', and 'var', which stores the component-wise weighted means and variances. \n", "\n", "* on-line smoothing estimates (naive, and $O(N^2)$, see module ``collectors`` for more details)\n", "\n", "by providing a list of `Collector` objects to parameter `collect`. For instance, to collect moments:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from particles.collectors import Moments\n", "\n", "alg_with_mom = particles.SMC(fk=fk_guided, N=100, collect=[Moments()])\n", "alg_with_mom.run()\n", "\n", "plt.plot([m['mean'] for m in alg_with_mom.summaries.moments], \n", " label='filtered mean')\n", "plt.plot(y, label='data')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Off-line smoothing\n", "Off-line smoothing is the task of approximating, at some final time $T$ (i.e. when we have stopped acquiring data), the distribution of all the states, $X_{0:T}$, given the full data, $Y_{0:T}$. \n", "\n", "To run a particular off-line smoothing algorithm, one must first run a particle filter, and save its **history**: " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "alg = particles.SMC(fk=fk_guided, N=100, store_history=True)\n", "alg.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now `alg` has a `hist` attribute, which is a `ParticleHistory` object. Basically, `alg.hist` recorded, at each time $t$:\n", "\n", " * the N particles $X_t^n$\n", " * their weights $W_t^n$\n", " * the N ancestor variables\n", " \n", "Smoothing algorithms are implemented as methods of class `ParticleHistory`. For instance, the FFBS (forward filtering backward sampling) algorithm, which samples complete smoothing trajectories, may be called as follows:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "trajectories = alg.hist.backward_sampling_ON2(5)\n", "plt.plot(trajectories);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The output of `backward_sampling_ON2` is a list of 100 arrays: `trajectories[t][m]` is the $t$-component of trajectory $m$. (If you want to turn it into a numpy array, simply do: `np.array(trajectories)`.)\n", "\n", "**Remark**: `particles` implement several FFBS algorithms; `backward_sampling_ON2` implements the most basic one, which has complexity $\\mathcal{O}(N^2)$ if you want to generate $N$ trajectories (where $N$ is the initial number of particles). There are faster variants, the recommended one, based on Dau & Chopin (2023), is `backward_sampling_mcmc`, which relies on MCMC. This is fast, and has a deterministic running time, $\\mathcal{O}(N)$, contrary to some other rejection-based schemes (which are also implemented). To learn more about this, see again [Dau & Chopin (2023)](https://arxiv.org/abs/2207.00976)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Remark**: Two-filter smoothing is also available. The difficulty with two-filter smoothing is that it requires to design an \"information filter\", that is a particle filter that computes recursively (backwards) the likelihood of the model. Since this is not trivial for the model considered here, we refer to Section 12.5 of the book and the documentation of package `smoothing`." ] } ], "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 }