{ "cells": [ { "cell_type": "markdown", "id": "6460d2b9d26b1e20", "metadata": {}, "source": [ "# Chapter 5 - Priors" ] }, { "cell_type": "markdown", "id": "dd762fd1", "metadata": {}, "source": [ "## What is a prior\n", "In Bayesian statistics, a **prior** is a concept that is used in order to combine prior knowledge with new data/measurement in order to get a *posterior distribution*. Here the prior determines how much new data will influence the final distribution. The prior encodes all the knowledge known, or assumed about a certain parameter before new data is collected, into a probability distribution. The information used for the prior can come from previous experiments, knowledge or other logical reasoning. As a result different priors can be chosen for the same experiments, based on prior knowledge or beliefs. Not all options for priors are as objective as others and can cause different results.\n", "\n", "In some cases the choice for a prior is obvious, take for example the age of the universe. It this point in time we know the age of the universe quite well, but there was a time that this was different. At that time there was only one thing for sure and that was the it must be positive. This is an example of one of the simplest prior possible, an uniform distribution from 0 to infinity." ] }, { "cell_type": "markdown", "id": "b020ba8f", "metadata": {}, "source": [ "### Frequentists view on priors\n", "Frequentist do not use the mathematical flexibility of priors used in bayesian statistics. Frequentists assign a long-run frequency to a specific fixed value of the parameter $\\theta$, which is often seen as objective. Whereas bayesian statistics assigns a certain subjective belief to $\\theta$.\n", "\n", "This is not to say that the frequentist perspective is not able to introduce a previous result to improve the current data/measurement. This can be done by:\n", "* Assigning a single value to the most likely value of $\\theta$.\n", "* The null hypothesis is often tested against values derived from previous results.\n", "* Prior information can be used to determine what data is worth collecting for the next experiment.\n", "\n", "These lacks the benefits of a full prior distribution used in Bayesian statistics. To simulate your full range and intervals of belief for $\\theta$." ] }, { "cell_type": "markdown", "id": "1ce0afc1", "metadata": {}, "source": [ "## Strength of a prior\n", "Priors can be strong and weak. **Strong priors** show a high level of certainty in the parameter's values before looking at the data, while **weak priors** show a low level of certainty. This is shown in the plots below. The weak prior distribution is more spread out than the strong prior distribution. \n", "\n", "Do note that the prior is not bound by gaussians, and can take any shape or form. It does not even require a proper normalized probability density as further explained in the [next subchapter](#Improper-prior)" ] }, { "cell_type": "code", "execution_count": 9, "id": "9955abca-9435-4850-a1e2-476a7e0f96c8", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import norm\n", "\n", "plt.style.use(\"seaborn-v0_8-colorblind\")\n", "\n", "# Parameters\n", "theta = np.linspace(-10, 10, 1000)\n", "\n", "# Strong prior\n", "strong_prior_mean = 0 \n", "strong_prior_std = 0.5\n", "strong_prior = norm.pdf(theta, strong_prior_mean, strong_prior_std)\n", "\n", "# Weak prior\n", "weak_prior_mean = 0\n", "weak_prior_std = 2.5\n", "weak_prior = norm.pdf(theta, weak_prior_mean, weak_prior_std)\n", "\n", "# Plot figures\n", "fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n", "\n", "# Strong Prior plot\n", "axs[0].plot(theta, strong_prior)\n", "axs[0].set_title('Strong Prior')\n", "axs[0].set_xlabel('θ')\n", "axs[0].set_ylabel('Density')\n", "axs[0].grid()\n", "\n", "# Weak Prior plot\n", "axs[1].plot(theta, weak_prior)\n", "axs[1].set_title('Weak Prior')\n", "axs[1].set_xlabel('θ')\n", "axs[1].set_ylabel('Density')\n", "axs[1].grid()\n", "\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "02851c27-eec7-43b5-8b93-1b3797461da5", "metadata": {}, "source": [ "### Weak Priors\n", "You can use a weak prior when the prior information is uncertain, vague, not trustworthy or not precise. The prior will exert minimal influence on the posterior distribution, which means that the prior is not very informative about the parameters that are being estimated. Weak priors have broad distributions, so the probability is widely spread out over the parameter values and they do not strongly favor a specific value or range. The use of weak priors can lead to less precise estimates of the data, but the use also allows for flexibility because it will not impose strong assumptions about the parameter values. It is also used to minimize the influence of subjective beliefs, thus letting the data \"speak for itself\".\n", "\n", "### Strong Priors\n", "Strong priors are used when the prior information is certain, precise and confident. The prior will exert influence on the posterior distribution, so the prior is informative about the parameters that are being estimated. Strong priors have narrow distributions, so they assign a higher probability to a specific value or range. Using strong priors can improve estimates when the data is limited. However, if a strong prior based on incorrect prior information is used, then the results will be biased." ] }, { "cell_type": "markdown", "id": "413323dc", "metadata": {}, "source": [ "## Type of priors\n", "### Informative prior\n", "An **informative prior** conveys information about one or more variables in your statistical model. Often the posterior of previous experiments/analyses is used as the prior of current future experiments/analyses.\n", "\n", "This has the goal that over time the posterior will be dominated by data, rather then the underlying assumptions made by a weakly informing prior.\n", "\n", "In short, an informative prior can be setup if substantial existing information is present, improving the estimate and inference about parameter $\\theta_i$, in prior distribution $p \\left(\\theta_i\\right)$\n", "\n", "### Weakly informative prior\n", "Rather then building upon an informative prior, a **weakly informative prior** only builds on rough estimates and information known about the aforementioned parameters.\n", "\n", "It is important to take into account the inherent objectivity that choosing such a prior brings. And during the process of choosing a prior it is important to not constrain the result and prevent extremities.\n", "\n", "**Example:** Choosing $\\theta \\ge 6$ introduces a purely objective argument to your prior. Whether or not this is valid is still a topic of discussion among statisticians. But it does allow for some useful tricks to apply to Bayesian statistics, as a prior is a requirement for the posterior probability.\n", "\n", "As such the construction of a weakly informative prior is as follows (Gelman et al., 2021):\n", "* Start with some version of a noninformative prior distribution and then add enough information so that inferences are constrained to be reasonable.\n", "* Start with a strong, highly informative prior and broaden it to account for uncertainty in one’s prior beliefs and in the applicability of any historically based prior distribution to new data.\n", "\n", "### Uninformative prior\n", "If insufficient knowledge is available for the model, a flat or a diffuse prior can also be applied.\n", "\n", "#### Flat prior\n", "A **flat prior** gives a fixed probability to $\\theta$ for the entire interval. This is often used when you have no information about parameter $\\theta$.\n", "\n", "#### Diffusie prior\n", "A **diffuse prior** can be chosen when there is a certain expected value, but in reality is not trustworthy enough, or has a very large confidence interval.\n", "\n", "A common shape of a diffuse prior is a gaussian with a high relative standard deviation, which essentially corresponds to a flat prior.\n", "\n", "### Improper prior\n", "An **improper prior**, or rather a non-informative prior, is a prior which cannot be a proper probability density. As for prior probability density $p\\left(\\theta_i\\right)$ the following can be said:\n", "\n", "$$ \\int p \\left(\\theta\\right) \\text{d} \\theta \\neq 1 $$\n", "\n", "**Example:** An example for which this is the case is a flat prior, where $p\\left(\\theta_i\\right) \\propto \\text{constant}$.\n", "\n", "Improper priors are usually unproblematic, as the resulting posterior will be a proper probability density.\n", "\n", "### Conjugate prior\n", "A **conjugate prior** is a good choice if you have a concrete idea of the model at hand, and as such it falls under the family of strong priors.\n", "\n", "Priors are called conjugate when the statistical model $p\\left(y |\\theta\\right)$, the prior $p\\left( \\theta \\right)$, and posterior $p \\left( \\theta | y_1, y_2, \\ldots , y_n \\right)$ belong to the same parametric family, with parameter $\\theta$.\n", "\n", "An example of a conjugate prior in action can be found on the [manual example 2](#Example-2:-Normal-likelihood-and-prior)." ] }, { "cell_type": "markdown", "id": "895f76c4-f0f7-4d9b-aeed-67090102c5e8", "metadata": {}, "source": [ "## Computational examples of priors\n", "### Example 1: Flipping coins\n", "Suppose we have a coin and we want to know the probability that the coin will land on heads when we flip it. Before us, our friends have also flipped this coin. They had 9 times heads and 11 times tails. We use this as our prior belief. We will also flip the coin 20 times. " ] }, { "cell_type": "code", "execution_count": 10, "id": "ea1b090d-b4cb-47d0-a225-43ac8521bd8d", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import beta, binom\n", "\n", "heads_prior = 9\n", "tails_prior = 11 \n", "\n", "theta = np.linspace(0,1,100)\n" ] }, { "cell_type": "markdown", "id": "66d262e7-536e-40f8-9a7a-03916695e27d", "metadata": {}, "source": [ "We flip the coin 1, 10, 20 and 100 times and we write down our results. After one time, we saw 1 head and zero tails, after 10 times we saw 6 heads and 4 tails, after 20 times we saw 14 heads and 6 tails, and after 100 times we saw 65 heads and 35 tails." ] }, { "cell_type": "code", "execution_count": 11, "id": "dc4d65b1-3afd-429c-af8a-853f743083bf", "metadata": {}, "outputs": [], "source": [ "heads_or_tails = [(1, 0), (6, 4), (14, 6), (65, 35)]\n" ] }, { "cell_type": "markdown", "id": "ebe4a740-6613-4f4f-a7f6-023aa6783f02", "metadata": {}, "source": [ "Now we can determine the prior, likelihood and posterior distributions. To calculate the likelihood we use the binomial probability mass function. We plot all three distributions for flipping 1, 10, 20 and 100 times." ] }, { "cell_type": "code", "execution_count": 12, "id": "8e4a44ff-6ab7-4e69-a901-2037bd12e21f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.style.use(\"seaborn-v0_8-colorblind\")\n", "\n", "titles = [\"1 time flipping\", \"10 times flipping\", \"20 times flipping\", \"100 times flipping\"]\n", "\n", "fig, axes = plt.subplots(2, 2, figsize=(12, 10))\n", "\n", "for i, (heads_observed, tails_observed) in enumerate(heads_or_tails):\n", " \n", " heads_posterior = heads_prior + heads_observed\n", " tails_posterior = tails_prior + tails_observed\n", " \n", " prior_distribution = beta.pdf(theta, heads_prior, tails_prior) # the prior follows a Beta distribution\n", " posterior_distribution = beta.pdf(theta, heads_posterior, tails_posterior) # the posterior follows a Beta distrbution\n", " likelihood_distribution = binom.pmf(heads_observed, heads_observed + tails_observed, theta)\n", " \n", " # Plot\n", " ax = axes[i // 2, i % 2]\n", " ax.fill_between(theta, prior_distribution, alpha=0.3, label=\"Prior\")\n", " ax.fill_between(theta, likelihood_distribution / likelihood_distribution.max(), alpha=0.3, label=\"Scaled likelihood\")\n", " ax.fill_between(theta, posterior_distribution, alpha=0.3, label=\"Posterior\")\n", " ax.set_title(titles[i])\n", " ax.set_xlabel(r\"$\\theta$\")\n", " ax.set_ylabel(\"Density\")\n", " ax.legend()\n", " ax.grid()\n", "\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "57eef121-d954-40c0-a6da-b43d76769b76", "metadata": {}, "source": [ "### Example 2: Estimating the mass of an exoplanet\n", "Exoplanets can be discovered using the radial velocity method. Astronomers found a wobbling star, and based on this wobbling, they want to estimate the mass of the exoplanet. \n", "\n", "Before the astronmers collected data, they looked at earlier researches and found that exoplanet masses follow a log-normal distribution, with a mean mass of 3 Earth masses. They use this posterior distribution as their prior." ] }, { "cell_type": "code", "execution_count": 13, "id": "ff855564-27ae-4674-b448-0e4db1434755", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import norm, lognorm\n", "\n", "mu_prior = np.log(3) # mean mass of 3 Earth masses\n", "sigma_prior = 0.6 # standard deviation\n", "prior_distribution = lognorm(s=sigma_prior, scale=np.exp(mu_prior)) \n", "mass_values = np.linspace(0.1, 15, 1000) # mass range in Earth masses\n", "prior_pdf = prior_distribution.pdf(mass_values) # make the PDF of the prior\n" ] }, { "cell_type": "markdown", "id": "bfdf44e2-abf3-4b9e-a012-8d381a9b1ab8", "metadata": {}, "source": [ "The astronomers conducted their research and found a mass of 5 Earth masses. They use this to make the likelihood." ] }, { "cell_type": "code", "execution_count": 14, "id": "62af6743-f093-4e9b-b593-da6ce5539dff", "metadata": {}, "outputs": [], "source": [ "observed_mass = 5.0\n", "likelihood = norm(loc=observed_mass)\n", "likelihood_pdf = likelihood.pdf(mass_values) # make the PDF of the likelihood\n" ] }, { "cell_type": "markdown", "id": "8f7b67f4-9022-4acb-9fea-adcb9c6a66d6", "metadata": {}, "source": [ "Now, the astronomers can combine the prior with the likelihood, using Bayes' theorem, to determine the posterior distribution. " ] }, { "cell_type": "code", "execution_count": null, "id": "3e3408a9-8a18-4bd7-b0a5-86053faf177e", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_5889/1969620551.py:1: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.\n", " posterior_pdf = (prior_pdf * likelihood_pdf) / np.trapz(prior_pdf * likelihood_pdf, mass_values) # make the PDF of the posterior\n" ] } ], "source": [ "posterior_pdf = (prior_pdf * likelihood_pdf) / np.trapezoid(prior_pdf * likelihood_pdf, mass_values) # make the PDF of the posterior\n" ] }, { "cell_type": "markdown", "id": "718fcda3-f9a2-4dde-b84d-b04a4769fef0", "metadata": {}, "source": [ "The astronomers can now plot the prior, likelihood and posterior distributions." ] }, { "cell_type": "code", "execution_count": 16, "id": "00e54fda-58c8-4fd2-a79c-71245da319cf", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.style.use(\"seaborn-v0_8-colorblind\")\n", "\n", "plt.figure(figsize=(10, 6))\n", "plt.fill_between(mass_values, prior_pdf, alpha=0.3, label=\"Prior\")\n", "plt.fill_between(mass_values, likelihood_pdf, alpha=0.3, label=\"Likelihood\")\n", "plt.fill_between(mass_values, posterior_pdf, alpha=0.3, label=\"Posterior\")\n", "plt.xlabel(\"Exoplanet Mass (Earth masses)\")\n", "plt.ylabel(\"Probability density\")\n", "plt.legend()\n", "plt.grid()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "f84d22e7", "metadata": {}, "source": [ "## Manual examples of (conjugate) priors\n", "\n", "There are some special cases where these calculations can even be done by hand. In these cases the likelihood function and the prior distribution are both from the same family of functions, resulting in a relatively easy calculation. These priors, of the same family of functions, are often called conjugate priors. We will look at two different examples, one where two poisson distributions will lead to a gamma function and one where two normal distributions will result in another normal distribution." ] }, { "cell_type": "markdown", "id": "22ab50aa", "metadata": {}, "source": [ "### Example 1: Poisson likelihood and prior\n", "For the first example we will look at a situation where both the likelihood function and the prior distribution are a poisson distribution. We will first define both functions, where it is, in this case, not really important which one is which:\n", "\n", "$$ f(x) = \\frac{\\lambda_1^xe^{-\\lambda_1}}{x!}, g(x) = \\frac{\\lambda_2^xe^{-\\lambda_2}}{x!}\\ $$\n", "\n", "In order to get the posterior distribution we will multiply these functions to get:\n", "\n", "$$ P(x) = f(x)g(x) $$\n", "$$ = \\frac{1}{(x!)^2}\\lambda_1^x\\lambda_2^xe^{-\\lambda_1}e^{-\\lambda_2} $$\n", "$$ = \\frac{1}{(x!)^2}(\\lambda_1\\lambda_2)^xe^{-(\\lambda_1+\\lambda_2)} $$\n", "\n", "This result can be recognised as a gammafunction. One small detail for this example is that is not yet normalized, which of course needs to be done before using it.\n" ] }, { "cell_type": "markdown", "id": "5793ed3c", "metadata": {}, "source": [ "\n", "### Example 2: Normal likelihood and prior\n", "Another example is a situation where both the likelihood function and the prior distribution are a normal distribution. This works similar as the first example, but it is a bit more work to recognise the final distribution (Smith, 2011). Again we will start by defining both functions:\n", "\n", "$$ f(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma_f}e^{-\\frac{(x-\\mu_f)^2}{2\\sigma_f^2}}, g(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma_g}e^{-\\frac{(x-\\mu_g)^2}{2\\sigma_g^2}} $$\n", "\n", "After which we will be able to multiply them:\n", "\n", "$$ f(x)g(x) = \\frac{1}{2\\pi\\sigma_f\\sigma_g}e^{-\\left(\\frac{(x-\\mu_f)^2}{2\\sigma_f^2}+\\frac{(x-\\mu_g)^2}{2\\sigma_g^2}\\right)} $$\n", "\n", "In order to see what is going on, we will define $\\alpha$ as\n", "\n", "$$ \\alpha = -\\left(\\frac{(x-\\mu_f)^2}{2\\sigma_f^2}+\\frac{(x-\\mu_g)^2}{2\\sigma_g^2}\\right) $$\n", "\n", "Which we can expand to get:\n", "\n", "$$ \\alpha = -\\frac{(\\sigma_f^2+\\sigma_g^2)x^2-2(\\mu_f\\sigma_g^2+\\mu_g\\sigma_f^2)x+\\mu_f^2\\sigma_g^2+\\mu_g^2\\sigma_f^2}{2\\sigma_f^2\\sigma_g^2} $$\n", "\n", "This can then be rewritten to:\n", "\n", "$$ \\alpha = -\\frac{x^2-2\\frac{\\mu_f\\sigma_g^2+\\mu_g\\sigma_f^2}{\\sigma_f^2+\\sigma_g^2}x+\\frac{\\mu_f^2\\sigma_g^2+\\mu_g^2\\sigma_f^2}{\\sigma_f^2+\\sigma_g^2}}{\\frac{2\\sigma_f^2\\sigma_g^2}{\\sigma_f^2+\\sigma_g^2}} $$\n", "\n", "When looking at this carefully, we see that this is equal to:\n", "\n", "$$ \\alpha = -\\frac{(x-\\mu_{fg})^2}{2\\sigma_{fg}^2} -\\gamma $$\n", "\n", "With:\n", "\n", "$$ \\sigma_{fg} = \\sqrt{\\frac{\\sigma_f^2\\sigma_g^2}{\\sigma_f^2+\\sigma_g^2}}, \\mu_{fg} = \\frac{\\mu_f\\sigma_g^2+\\mu_g\\sigma_f^2}{\\sigma_f^2+\\sigma_g^2} $$\n", "\n", "Putting this in for the posterior distribution $P(x) = f(x)g(x)$, we will see that it is not important what $\\gamma$ exactly is, since it is independent of $x$. Therefore $\\gamma$ will only be a scaling factor. We get:\n", "\n", "$$ P(x) = \\frac{e^{-\\gamma}}{\\sqrt{2\\pi}\\sigma_{f}\\sigma_g}e^{-\\frac{(x-\\mu_{fg})^2}{2\\sigma_{fg}^2}} $$\n", "\n", "We know that the integral of the posterior distribution over all values of $x$ must be 1, thus we can use this to normalize the expression we found:\n", "\n", "$$ \\int_{-\\infty}^{\\infty}P(x) = \\frac{e^{-\\gamma}}{\\sqrt{2\\pi(\\sigma_f^2+\\sigma_g^2)}} = 1 $$\n", "\n", "So we end up with:\n", "\n", "$$ P(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma_{fg}}e^{-\\frac{(x-\\mu_{fg})^2}{2\\sigma_{fg}^2}} $$\n", "\n", "This can be easily recognised as a normal distribution, which beautifully shows the elegance of conjugate priors. \n" ] }, { "cell_type": "markdown", "id": "394ba30e", "metadata": {}, "source": [ "## Sources\n", "Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman and Hall/CRC. https://doi.org/10.1201/b16018 \n", "\n", "Smith, J. O. S., III. (2011). Spectral Audio signal processing. W3K Publishing. ISBN 978-0-9745607-3-1" ] }, { "cell_type": "code", "execution_count": null, "id": "ba44760a-89a7-4f3e-943d-c4794ee56290", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "bayes24", "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": "3.9.19" } }, "nbformat": 4, "nbformat_minor": 5 }