mirror of
https://github.com/3b1b/manim.git
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Some finishing tweaks to the med_test video
This commit is contained in:
Grant Sanderson
parent
917ff685bd
commit
c3643cf4e3
1 changed files with 370 additions and 188 deletions
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@ -59,7 +59,93 @@ def get_covid_clipboard(disease_name="SARS\\\\CoV-2", sign="+", report="Detected
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# Scenes
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class Thumbnail(Scene):
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def construct(self):
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title = TextMobject("The Bayes Factor", font_size=96)
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self.clear()
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# New
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bg = FullScreenFadeRectangle()
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bg.set_fill(BLACK, 1)
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bg.set_gloss(0.2)
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self.add(bg)
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pre_pop = VGroup(*(WomanIcon() for x in range(5 * 6)))
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pre_pop.arrange_in_grid(5, 6, fill_rows_first=False)
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pre_pop.set_height(4)
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pre_pop[:5].shift(MED_LARGE_BUFF * LEFT)
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pre_pop[:5].set_fill(YELLOW)
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pre_pop[5:].set_fill(GREY_C)
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post_pop = pre_pop.copy()
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post_pop.set_opacity(0.1)
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for icon in (*post_pop[:4], *post_pop[5::5]):
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rect = SurroundingRectangle(icon, buff=0.01)
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rect.set_stroke(GREEN, 5)
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icon.set_opacity(1)
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plus = TexMobject("+")
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plus.set_color(GREEN)
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plus.set_width(rect.get_width() / 2)
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plus.move_to(rect.get_corner(UR))
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plus.shift(0.05 * UR)
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icon.set_stroke(BLACK, 2, background=True)
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icon.push_self_into_submobjects()
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icon.add_to_back(rect, plus)
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icon.set_stroke(background=True)
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for pop in pre_pop, post_pop:
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colon = TexMobject(":", font_size=96)
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colon.move_to(pop[:10])
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pop.add(colon)
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arrow = Arrow(LEFT, RIGHT, thickness=0.1)
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arrow.scale(1.75)
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group = VGroup(pre_pop, arrow, post_pop)
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group.arrange(RIGHT, buff=1.0)
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group.to_edge(UP)
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post_pop.align_to(pre_pop, DOWN)
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self.add(group)
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clipboard = get_covid_clipboard("Virus")
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clipboard[2][0].set_stroke(GREEN, 8)
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clipboard[2].scale(0.9)
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clipboard.set_width(arrow.get_width() * 1.0)
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clipboard.next_to(arrow, UP)
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VGroup(clipboard, arrow).shift_onto_screen(buff=MED_SMALL_BUFF)
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self.add(clipboard)
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# Or try something else...
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self.remove(group)
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randy = Randolph(color=SICKLY_GREEN, mode="sick")
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randy.set_height(4)
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randy.next_to(ORIGIN, RIGHT, buff=0.5).to_edge(UP)
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clipboard.set_height(4)
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clipboard.next_to(ORIGIN, LEFT, buff=0.5).to_edge(UP)
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self.add(randy)
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self.add(clipboard)
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#
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new_bayes_rule = TextMobject(
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"Post = (Prior)(Bayes factor)",
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tex_to_color_map={
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"(Prior)": YELLOW,
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"(Bayes factor)": BLUE,
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}
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)
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new_bayes_rule.set_width(FRAME_WIDTH - 1)
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new_bayes_rule.move_to(2 * DOWN)
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self.add(new_bayes_rule)
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new_rule_words = TextMobject("Bayes rule redesigned")
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new_rule_words.scale(1.75)
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new_rule_words.next_to(new_bayes_rule, DOWN, MED_LARGE_BUFF)
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new_rule_words.set_fill(GREY_A)
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self.add(new_rule_words)
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self.embed()
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return
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# Old
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title = TextMobject("Interpreting medical tests", font_size=90)
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title.to_edge(UP)
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self.add(title)
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@ -73,20 +159,26 @@ class Thumbnail(Scene):
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)
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factor.scale(2)
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rect = SurroundingRectangle(factor, buff=MED_SMALL_BUFF)
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rect.set_stroke(TEAL, 2)
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rect.set_stroke(BLUE, 3)
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factor.add(rect)
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self.add(factor)
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clipboard = get_covid_clipboard("Virus")
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clipboard[2].scale(0.8)
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clipboard[2][0].set_stroke(GREEN, 8)
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clipboard[2].scale(0.9)
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clipboard.set_height(4)
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clipboard.next_to(factor, LEFT, LARGE_BUFF)
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VGroup(clipboard, factor).next_to(title, DOWN, buff=1.0)
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VGroup(clipboard, factor).next_to(title, DOWN, buff=0.7)
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self.add(clipboard)
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brace = Brace(factor, DOWN)
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brace.add(brace.get_text("The one number\\\\you want to know"))
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brace = Brace(factor, DOWN, buff=0.4)
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brace.stretch(1.5, 1, about_edge=UP)
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text = brace.get_text("How much your belief should change", buff=0.4)
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text.scale(1.5, about_edge=UP)
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text.shift_onto_screen()
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text.match_color(rect)
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brace.add(text)
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self.add(brace)
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self.embed()
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@ -207,18 +299,282 @@ class MathAsDesign(Scene):
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self.wait()
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class BayesRuleAndMedicalTests(Scene):
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class NewBayesRuleAndMedicalTests(Scene):
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def construct(self):
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# Add title
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title = TextMobject("Bayes' rule", font_size=72)
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title.to_edge(UP)
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h_line = Underline(title)
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h_line.scale(1.5)
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h_line.set_stroke(GREY_B, 2)
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# Mention paradox
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paradox_name = TextMobject("Medical Test Paradox", font_size=60)
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paradox_name.to_corner(UL)
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paradox_name.shift(MED_SMALL_BUFF * DOWN)
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paradox_line = Underline(paradox_name)
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paradox_line.set_stroke(GREY_B, 2)
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self.add(title)
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clipboard = get_covid_clipboard("Virus", color=BLUE)
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clipboard.set_height(3)
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clipboard.next_to(paradox_line, DOWN, LARGE_BUFF)
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clipboard[2][0].shift(SMALL_BUFF * DOWN)
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clipboard[2][0].set_stroke(BLUE, 4)
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clipboard[2].set_opacity(0)
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self.play(
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FadeIn(paradox_name, lag_ratio=0.1),
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ShowCreation(paradox_line),
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FadeIn(clipboard, DOWN),
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)
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clipboard[2].set_opacity(1)
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self.play(
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Write(clipboard[2], run_time=1)
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)
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self.wait()
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# Show Bayes rule
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bayes_title = TextMobject("Bayes' rule", font_size=60)
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bayes_title.move_to(paradox_name, UL)
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bayes_title.to_edge(RIGHT, buff=1.5)
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bayes_underline = Underline(bayes_title)
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bayes_underline.scale(1.5)
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bayes_underline.set_stroke(GREY_B, 2)
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bayes_underline.match_y(paradox_line)
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formula = TexMobject(
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"P(H|E) = {P(H)P(E|H) \\over P(E)}",
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tex_to_color_map={
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"H": YELLOW,
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"E": BLUE,
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},
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)
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formula.next_to(bayes_underline, DOWN, buff=LARGE_BUFF)
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self.play(
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Write(bayes_title, run_time=1),
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GrowFromCenter(bayes_underline),
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FadeIn(formula, shift=0.5 * DOWN, scale=1.2)
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)
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self.wait()
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# Show high accuracy
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accuracy_words = TextMobject("High accuracy")
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accuracy_words.next_to(paradox_line, DOWN, MED_LARGE_BUFF)
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accuracy_words.set_color(GREEN)
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population = Population(100)
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population.arrange_in_grid(buff=LARGE_BUFF)
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population.set_height(5)
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population.next_to(accuracy_words, DOWN)
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marks = VGroup()
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for icon in population:
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icon.generate_target()
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if random.random() < 0.025:
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mark = Exmark()
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icon.target.set_opacity(0.5)
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else:
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mark = Checkmark()
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mark.set_height(icon.get_height() / 2)
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mark.move_to(icon.get_corner(UL))
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marks.add(mark)
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accuracy_group = VGroup(accuracy_words, population, marks)
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self.play(
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FadeIn(accuracy_words),
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FadeIn(population, lag_ratio=0.01),
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clipboard.scale, 0.5,
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clipboard.to_corner, DR,
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)
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self.play(
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ShowIncreasingSubsets(marks, run_time=2),
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LaggedStartMap(MoveToTarget, population, run_time=2),
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)
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self.wait()
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# Show test result
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randy = Randolph(height=2)
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randy.next_to(population, RIGHT, MED_LARGE_BUFF, aligned_edge=DOWN)
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clipboard.generate_target()
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clipboard.target.set_height(2)
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clipboard.target.next_to(randy.get_corner(UR), RIGHT)
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self.play(
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VFadeIn(randy),
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randy.change, "guilty", clipboard.target,
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MoveToTarget(clipboard),
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formula.match_width, bayes_underline,
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formula.next_to, bayes_underline, DOWN, MED_SMALL_BUFF,
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)
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self.play(randy.change, "horrified", clipboard)
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self.play(Blink(randy))
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self.wait()
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# Show low predictive value
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prob_expression = TexMobject(
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"P(\\text{Sick} \\text{ given } +) = ",
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tex_to_color_map={
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"+": BLUE,
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"\\text{Sick}": YELLOW,
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}
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)
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prob = DecimalNumber(0.9, font_size=60)
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prob.next_to(prob_expression, RIGHT)
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prob.set_color(WHITE)
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prob.set_opacity(0)
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prob_expression.add(prob)
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p_line = Underline(prob)
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p_line.shift(0.1 * DOWN)
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p_line.scale(1.5)
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p_line.set_stroke(WHITE, 2)
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prob_expression.add(p_line)
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prob_expression.next_to(VGroup(randy, clipboard), UP, aligned_edge=LEFT)
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self.play(
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FadeIn(prob_expression),
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randy.change, "pondering", prob_expression
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)
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self.play(
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ChangeDecimalToValue(prob, 0.09),
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UpdateFromAlphaFunc(prob, lambda m, a: m.set_opacity(a)),
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run_time=2
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)
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self.play(Blink(randy))
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self.play(
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randy.change, "confused", prob,
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ChangeDecimalToValue(prob, 0.01),
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)
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self.play(Blink(randy))
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self.wait()
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predictive_group = VGroup(
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randy, clipboard,
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prob_expression, prob,
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)
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# Accurate does not imply predictive
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implication = TextMobject(
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"Accurate ", "$\\Rightarrow$", " Predictive",
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)
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implication.set_color_by_tex("Accurate", GREEN)
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implication.set_color_by_tex("Predictive", YELLOW)
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implication.match_width(paradox_line)
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implication.next_to(paradox_line, DOWN)
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strike = Line(DL, UR).replace(implication[1], stretch=True)
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strike.set_stroke(RED, 4)
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self.play(
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FadeIn(implication, scale=1.1),
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accuracy_group.scale, 0.8, {"about_edge": DOWN},
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randy.change, 'pondering', implication,
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)
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self.play(ShowCreation(strike))
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self.wait()
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implication.add(strike)
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paradox_group = VGroup(paradox_name, paradox_line, implication)
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# Get rid of medical test stuff
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p_rect = SurroundingRectangle(paradox_group, buff=MED_SMALL_BUFF)
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p_rect.set_stroke(WHITE, 2)
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p_rect.set_fill(GREY_E, 1)
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self.add(p_rect, paradox_group),
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self.play(
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FadeOut(accuracy_group, DL),
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FadeOut(predictive_group, 2 * DL),
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DrawBorderThenFill(p_rect)
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)
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paradox_group.add_to_back(p_rect)
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self.wait()
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# Alternate framing
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odds_formula = TexMobject(
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"O(H|E) = O(H){P(E|H) \\over P(E|\\neg H)}",
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tex_to_color_map={
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"H": YELLOW,
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"E": BLUE,
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"\\neg": RED,
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}
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)
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odds_formula.match_height(formula)
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odds_formula.next_to(formula, DOWN, LARGE_BUFF)
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odds_formula.shift_onto_screen()
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bf_rect = SurroundingRectangle(odds_formula[7:], buff=0.025)
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bf_rect.set_stroke(TEAL, 2)
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bf_name = TextMobject("Bayes\\\\factor", font_size=36)
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bf_name.match_color(bf_rect)
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bf_name.next_to(bf_rect, DOWN, buff=0.2)
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odds_formula.add(bf_rect, bf_name)
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arrow = Vector(1.5 * RIGHT)
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arrow.next_to(formula, LEFT)
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self.play(
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paradox_group.next_to, arrow, LEFT,
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GrowArrow(arrow),
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)
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self.wait()
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self.play(
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VGroup(paradox_group, arrow).next_to, odds_formula[0], LEFT,
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FadeIn(odds_formula, DOWN)
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)
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self.wait()
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# Reflections on this formula
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morty = Mortimer(height=2.2)
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morty.to_corner(DR)
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morty.shift(2 * LEFT)
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randy = Randolph(height=2)
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randy.next_to(morty, LEFT, LARGE_BUFF, aligned_edge=DOWN)
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bubble = ThoughtBubble()
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bubble.pin_to(morty)
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self.play(
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LaggedStart(*(
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ShowCreationThenFadeOut(SurroundingRectangle(mob, color=BLUE))
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for mob in (formula, odds_formula)
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), lag_ratio=0.4, run_time=3),
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VFadeIn(randy),
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randy.change, "confused", formula,
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)
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self.play(Blink(randy))
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self.wait()
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self.add(bubble, odds_formula)
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odds_formula.save_state()
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self.play(
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VFadeIn(morty),
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morty.change, "maybe", bubble[-1],
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randy.look_at, bubble,
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FadeIn(bubble, lag_ratio=0.5),
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odds_formula.move_to, bubble.get_bubble_center(),
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odds_formula.shift, 0.2 * LEFT + 0.1 * DOWN,
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FadeOut(arrow, scale=0.5),
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paradox_group.scale, 0.5,
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paradox_group.to_corner, DL,
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)
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self.play(Blink(morty))
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self.play(Blink(randy))
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self.wait(2)
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self.play(randy.change, "pondering")
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self.play(Blink(randy))
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self.wait()
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paradox_group.generate_target()
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paradox_group.target.scale(1.5)
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paradox_group.target.next_to(randy.get_corner(UL), UP)
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paradox_group.target.shift(LEFT)
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self.play(
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FadeOut(bubble, lag_ratio=0.4),
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Restore(odds_formula),
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morty.change, 'tease', paradox_group.target,
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randy.change, 'raise_left_hand', paradox_group.target,
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MoveToTarget(paradox_group),
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)
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self.play(Blink(morty))
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self.wait()
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return
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# Unprocessed
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# Show rule
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formula = TexMobject(
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"P(H|E) = {P(H)P(E|H) \\over P(E)}",
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@ -291,181 +647,7 @@ class BayesRuleAndMedicalTests(Scene):
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FadeOut(pis, DOWN),
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)
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# Mention paradox
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paradox_name = TextMobject("Medical Test Paradox")
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paradox_name.to_corner(UL)
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paradox_name.shift(MED_SMALL_BUFF * DOWN)
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paradox_line = Underline(paradox_name)
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paradox_line.set_stroke(GREY_B, 2)
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self.play(
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FadeIn(paradox_name, lag_ratio=0.1),
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ShowCreation(paradox_line),
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)
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self.wait()
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# Show high accuracy
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accuracy_words = TextMobject("High accuracy")
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accuracy_words.next_to(paradox_line, DOWN, MED_LARGE_BUFF)
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accuracy_words.set_color(GREEN)
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population = Population(100)
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population.arrange_in_grid(buff=LARGE_BUFF)
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population.set_height(5)
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population.next_to(accuracy_words, DOWN)
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marks = VGroup()
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for icon in population:
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icon.generate_target()
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if random.random() < 0.05:
|
||||
mark = Exmark()
|
||||
icon.target.set_opacity(0.5)
|
||||
else:
|
||||
mark = Checkmark()
|
||||
mark.set_height(icon.get_height() / 2)
|
||||
mark.move_to(icon.get_corner(UL))
|
||||
marks.add(mark)
|
||||
|
||||
accuracy_group = VGroup(accuracy_words, population, marks)
|
||||
|
||||
self.play(
|
||||
FadeIn(accuracy_words),
|
||||
FadeIn(population, lag_ratio=0.01)
|
||||
)
|
||||
self.play(
|
||||
ShowIncreasingSubsets(marks, run_time=2),
|
||||
LaggedStartMap(MoveToTarget, population, run_time=2),
|
||||
)
|
||||
self.wait()
|
||||
|
||||
# Show test result
|
||||
randy = Randolph(height=2)
|
||||
randy.move_to(DOWN)
|
||||
clipboard = get_covid_clipboard("Virus", color=YELLOW)
|
||||
clipboard.set_height(2)
|
||||
clipboard.next_to(randy.get_corner(UR), RIGHT)
|
||||
|
||||
self.play(
|
||||
VFadeIn(randy),
|
||||
randy.change, "guilty", clipboard,
|
||||
FadeIn(clipboard, shift=0.25 * UL, scale=1.5)
|
||||
)
|
||||
self.play(randy.change, "horrified", clipboard)
|
||||
self.play(Blink(randy))
|
||||
self.wait()
|
||||
|
||||
# Show low predictive value
|
||||
prob_expression = TexMobject(
|
||||
"P(\\text{Sick} | +) = ",
|
||||
tex_to_color_map={
|
||||
"+": YELLOW,
|
||||
"\\text{Sick}": GREY_A,
|
||||
}
|
||||
)
|
||||
prob = DecimalNumber(0.9, font_size=60)
|
||||
prob.next_to(prob_expression, RIGHT)
|
||||
prob.set_color(WHITE)
|
||||
prob.set_opacity(0)
|
||||
prob_expression.add(prob)
|
||||
p_line = Underline(prob)
|
||||
p_line.shift(0.1 * DOWN)
|
||||
p_line.scale(1.5)
|
||||
p_line.set_stroke(WHITE, 2)
|
||||
prob_expression.add(p_line)
|
||||
prob_expression.next_to(VGroup(randy, clipboard), UP)
|
||||
|
||||
self.play(
|
||||
FadeIn(prob_expression),
|
||||
randy.change, "pondering", prob_expression
|
||||
)
|
||||
self.play(
|
||||
ChangeDecimalToValue(prob, 0.09),
|
||||
UpdateFromAlphaFunc(prob, lambda m, a: m.set_opacity(a)),
|
||||
run_time=2
|
||||
)
|
||||
self.play(Blink(randy))
|
||||
self.play(
|
||||
randy.change, "confused", prob,
|
||||
ChangeDecimalToValue(prob, 0.01),
|
||||
)
|
||||
self.play(Blink(randy))
|
||||
self.wait()
|
||||
|
||||
predictive_group = VGroup(
|
||||
randy, clipboard,
|
||||
prob_expression, prob,
|
||||
)
|
||||
|
||||
# Accurate does not imply predictive
|
||||
implication = TextMobject(
|
||||
"Accurate ", "$\\Rightarrow$", " Predictive",
|
||||
)
|
||||
implication.set_color_by_tex("Accurate", GREEN)
|
||||
implication.set_color_by_tex("Predictive", YELLOW)
|
||||
implication.next_to(paradox_line, DOWN)
|
||||
|
||||
strike = Line(DL, UR).replace(implication[1], stretch=True)
|
||||
strike.set_stroke(RED, 4)
|
||||
|
||||
self.play(
|
||||
FadeIn(implication, scale=1.1),
|
||||
accuracy_group.scale, 0.8, {"about_edge": DOWN},
|
||||
randy.change, 'pondering', implication,
|
||||
)
|
||||
self.play(ShowCreation(strike))
|
||||
self.wait()
|
||||
implication.add(strike)
|
||||
|
||||
paradox_group = VGroup(paradox_name, paradox_line, implication)
|
||||
|
||||
# Get rid of medical test stuff
|
||||
p_rect = SurroundingRectangle(paradox_group, buff=MED_SMALL_BUFF)
|
||||
p_rect.set_stroke(WHITE, 2)
|
||||
p_rect.set_fill(GREY_E, 1)
|
||||
self.add(p_rect, paradox_group),
|
||||
self.play(
|
||||
FadeOut(accuracy_group, DL),
|
||||
FadeOut(predictive_group, 2 * DL),
|
||||
VGroup(title, formula).to_edge, UP,
|
||||
DrawBorderThenFill(p_rect)
|
||||
)
|
||||
paradox_group.add_to_back(p_rect)
|
||||
self.wait()
|
||||
|
||||
# Alternate framing
|
||||
odds_formula = TexMobject(
|
||||
"O(H|E) = O(H){P(E|H) \\over P(E|\\neg H)}",
|
||||
tex_to_color_map={
|
||||
"H": YELLOW,
|
||||
"E": BLUE,
|
||||
"\\neg": RED,
|
||||
}
|
||||
)
|
||||
odds_formula.match_height(formula)
|
||||
odds_formula.next_to(formula, DOWN, LARGE_BUFF)
|
||||
odds_formula.shift_onto_screen()
|
||||
|
||||
bf_rect = SurroundingRectangle(odds_formula[7:], buff=0.025)
|
||||
bf_rect.set_stroke(TEAL, 2)
|
||||
bf_name = TextMobject("Bayes\\\\factor", font_size=36)
|
||||
bf_name.match_color(bf_rect)
|
||||
bf_name.next_to(bf_rect, DOWN, SMALL_BUFF)
|
||||
odds_formula.add(bf_rect, bf_name)
|
||||
|
||||
arrow = Vector(1.5 * RIGHT)
|
||||
arrow.next_to(odds_formula[0], LEFT)
|
||||
|
||||
self.play(
|
||||
paradox_group.next_to, arrow, LEFT,
|
||||
GrowArrow(arrow),
|
||||
FadeIn(odds_formula, DOWN)
|
||||
)
|
||||
self.wait()
|
||||
|
||||
# Question the formulas
|
||||
morty = Mortimer(height=2)
|
||||
morty.to_corner(DR)
|
||||
|
||||
self.play(FadeIn(morty))
|
||||
self.play(morty.change, "hesitant", formula)
|
||||
self.play(Blink(morty))
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue