From 976c745cf16b9d6248a27714cb1811c554212ec5 Mon Sep 17 00:00:00 2001 From: Benjamin Kenyery Date: Sun, 10 Oct 2021 22:37:41 -0400 Subject: [PATCH] lab-bayesian-statistics[Benjamin Kenyery] --- your-code/main.ipynb | 198 +++++++++++++++++++++++++++++++++++++------ 1 file changed, 174 insertions(+), 24 deletions(-) diff --git a/your-code/main.ipynb b/your-code/main.ipynb index 95bfcb9..0a0368d 100644 --- a/your-code/main.ipynb +++ b/your-code/main.ipynb @@ -11,7 +11,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -31,10 +31,15 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "def bayes_rule(priors, likelihoods):\n", + " marg = sum(np.multiply(priors, likelihoods))\n", + " post = np.divide(np.multiply(priors, likelihoods), marg)\n", + " return post" + ] }, { "cell_type": "markdown", @@ -45,10 +50,12 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "prior_bolw = 1/2" + ] }, { "cell_type": "markdown", @@ -59,10 +66,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.66666667, 0.33333333])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bayes_rule([0.5,0.5], [0.5, 1/4])" + ] }, { "cell_type": "markdown", @@ -93,12 +113,37 @@ "*Hint: For the likelihoods, you will need to multiply the probabilities of drawing yellow from one bag and green from the other bag and vice versa.*" ] }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.74074074, 0.25925926])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "prior = [1/2, 1/2]\n", + "likelihood = [.2*.2, .1*.14]\n", + "\n", + "bayes_rule(prior, likelihood)" + ] + }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "la probabilidad de que se amarillo en la primera bol" + ] }, { "cell_type": "markdown", @@ -112,7 +157,9 @@ "execution_count": null, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "la probabilidad qie el caramelo se amarillo de la segunda es del 26%" + ] }, { "cell_type": "markdown", @@ -126,7 +173,10 @@ "execution_count": null, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "la probabilidad de es el contrario de sacar un caramelo amarillo \n", + "de la primera bolsa es de 26% y 7% bolsa 2" + ] }, { "cell_type": "markdown", @@ -157,10 +207,38 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "n_draws = 100000\n", + "prior = pd.Series(np.random.uniform(0, 1, size=n_draws))\n", + "\n", + "prior.hist()" + ] }, { "cell_type": "markdown", @@ -171,10 +249,57 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "def generative_model(param):\n", + " result = np.random.binomial(100, param)\n", + " return result\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "param = 14\n", + "sample = 100\n", + "\n", + "\n", + "sim_data = list()\n", + "\n", + "for p in prior:\n", + " sim_data.append(generative_model(p))\n", + " \n", + "posterior = prior[list(map(lambda x: x == 14, sim_data))]\n", + "posterior.hist()" + ] }, { "cell_type": "markdown", @@ -185,10 +310,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0.09388519196810907,0.20692609398513295)\n" + ] + } + ], + "source": [ + "# Intervalo de confianza el 90% centrado\n", + "print(f'({posterior.quantile(0.05)},{posterior.quantile(0.95)})')" + ] }, { "cell_type": "markdown", @@ -199,15 +335,29 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 22, "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum Likelihood Estimate: 0.15 | 0.12625250501002003\n" + ] + } + ], + "source": [ + "rounded = posterior.round(2)\n", + "mode = rounded.mode()[0]\n", + "probability = list(rounded).count(mode)/len(rounded)\n", + "print('Maximum Likelihood Estimate: ', mode, '|',probability)\n", + "\n" + ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -221,7 +371,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.2" + "version": "3.9.6" } }, "nbformat": 4,