diff --git a/notebooks/Normal and t-Distribution/BIND_2_5.ipynb b/notebooks/Normal and t-Distribution/BIND_2_5.ipynb index e2364e926a30f7d8f60bf6d2fd46ebcb1490262c..bced5debd9ec91516572c364611d90b9b9b0a735 100644 --- a/notebooks/Normal and t-Distribution/BIND_2_5.ipynb +++ b/notebooks/Normal and t-Distribution/BIND_2_5.ipynb @@ -307,9 +307,16 @@ "Diese Beziehung für den Bayes-Faktor gilt nur, wenn $H_0$ ein Spezialfall von $H_1$ ist. " ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Als erstes betrachten wir das Beispiel zum Altersunterschied zwischen Ehemännern und Ehefrauen. Wir nehmen als erstes eine uniforme Prior-Verteilung von 0 bis 10 Jahren für die Altersdifferenz zwischen Ehemännern und Ehefrauen an.\n" + ] + }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -338,23 +345,13 @@ "text": [ "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1 seconds.\n", "Sampling: [y, μ]\n", - "The reference value is outside of the posterior. This translate into infinite support for H1, which is most likely an overstatement.\n" + "The reference value is outside of the posterior. This translate into infinite support for H1, which is most likely an overstatement.\n", + "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n" ] }, { "data": { - "text/plain": [ - "({'BF10': 7.7022598539738, 'BF01': 0.12983202578968736},\n", - " <Axes: title={'center': 'The BF_10 is 7.70\\nThe BF_01 is 0.13'}, xlabel='μ', ylabel='Density'>)" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] @@ -373,9 +370,32 @@ "az.plot_bf(trace_h, var_name=\"μ\", ref_val=0)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Mit `az.plot_bf` können wir den Plot für die Darstellung des Savage-Dickey Verhältnisses darstellen.\n", + "`ref_val=...` bezieht sich auf den Nullwert, an welchem Prior- und Posterior-Dichte ausgewertet werden sollen." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In obiger Abbildung ist das Savage-Dickey Verhältnis für die Altersdifferenzen für eine uniforme Prior-Verteilung dargestellt. Die beiden schwarzen Punkte zeigen, dass wir die beiden Wahrscheinlichkeitsdichten an der Stelle $\\mu_0=0$ ausgewertet haben. Wir stellen fest, dass der Bayes Faktor zu Gunsten der\n", + " Nullhypothese $\\text{BF}_{01}\\approx 0.06$ ist, während der Bayes-Faktor zu Gunsten der Alternativ-Hypothese $\\text{BF}_{01}\\approx 16$ ist. Dies können wir als starke Evidenz zu Gunsten der Alternativ-Hypothese interpretieren. Mit anderen Worten, wir können mit grosser Wahrscheinlichkeit davon ausgehen, dass es einen relevanten Altersunterschied zwischen Ehemännern und Ehefrauen gibt." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Betrachten wir nun eine normalverteilte Prior-Verteilung mit Mittelwert $2$ und Standardabweichung $2$, so finden wir:" + ] + }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 21, "metadata": {}, "outputs": [ { @@ -408,18 +428,7 @@ }, { "data": { - "text/plain": [ - "({'BF10': 0.20072838426921713, 'BF01': 4.9818564705766715},\n", - " <Axes: title={'center': 'The BF_10 is 0.20\\nThe BF_01 is 4.98'}, xlabel='μ', ylabel='Density'>)" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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"text/plain": [ "<Figure size 640x480 with 1 Axes>" ] @@ -435,15 +444,24 @@ " y = pm.Normal('y', mu=μ, sigma=σ, observed=diff)\n", " trace_h = pm.sample(1000)\n", " trace_h.extend(pm.sample_prior_predictive(8000))\n", - "az.plot_bf(trace_h, var_name=\"μ\", ref_val=2)" + "az.plot_bf(trace_h, var_name=\"μ\", ref_val=2)\n", + "plt.savefig('savage_dickey_couples_age_informed.pdf', dpi=300)" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "source": [] + "source": [ + "In der obigen Abbildung ist das Savage-Dickey Verhältnis für die Altersdifferenzen für eine normale Prior-Verteilung mit Erwartungswert 2 und Standardabweichung 2 dargestellt. Die beiden schwarzen Punkte zeigen, dass wir die beiden Wahrscheinlichkeitsdichten an der Stelle $\\mu_0=2$ ausgewertet haben. Wir stellen fest, dass der Bayes Faktor zu Gunsten der\n", + " Nullhypothese nun $\\text{BF}_{01}\\approx 5$ ist, während der Bayes-Faktor zu Gunsten der Alternativ-Hypothese $\\text{BF}_{01}\\approx 0.2$ ist. Dies können wir als moderate Evidenz zu Gunsten der Nullhypothese interpretieren. Mit anderen Worten, eine Altersunterschied von 2 Jahren zwischen Eheleuten kann nicht ausgeschlossen werden und erscheint plausibel." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Der Bayes-Faktor misst, welches Modell als ganzes die Daten erklärt. Dies beinhaltet auch den Prior, selbst wenn die Prior-Verteilung einen relativ kleinen Einfluss auf die Berechnung der Posterior-Verteilung hat. In obigem Beispiel wäre der Bayes-Faktor noch kleiner ausgefallen, wenn die Standardabweichung der Prior-Verteilung kleiner angenommen worden wäre. 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