{"id":103073,"date":"2023-05-28T11:16:20","date_gmt":"2023-05-28T15:16:20","guid":{"rendered":"https:\/\/www.shortform.com\/blog\/?p=103073"},"modified":"2023-05-28T13:16:58","modified_gmt":"2023-05-28T17:16:58","slug":"bayesian-theory","status":"publish","type":"post","link":"https:\/\/www.shortform.com\/blog\/bayesian-theory\/","title":{"rendered":"How Bayesian Theory Helps Us Predict the Future"},"content":{"rendered":"\n<p>What is Bayesian Theory? How does it help forecasters make better predictions?<\/p>\n\n\n\n<p>Named after Thomas Bayes, Bayesian Theory is one of the best ways to determine the probability of an event in the future. In his book <em>The Signal and the Noise<\/em>, Nate Silver shares two lessons you can use to correctly apply Bayesian Theory to any situation.<\/p>\n\n\n\n<p>Let&#8217;s take a look at Bayesian Theory in detail.<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-better-predictions-through-bayesian-logic\"><strong>Better Predictions Through Bayesian Logic<\/strong><\/h2>\n\n\n\n<p>Although prediction is inherently difficult\u2014and made more so by the various thinking errors we\u2019ve outlined\u2014Silver argues that it\u2019s possible to make consistently more accurate predictions by following the principles of a statistical formula known as Bayesian Theory. Silver explains that it encourages us to <em>think<\/em> while making predictions. According to Silver, Bayesian Theory suggests that <strong>we make better predictions when we consider the prior likelihood of an event and update our predictions in response to the latest evidence<\/strong>.<\/p>\n\n\n\n<p>Here, we\u2019ll briefly describe Bayesian Theory, then we\u2019ll explore the broader lessons Silver draws from it and offer concrete advice for improving the accuracy of your predictions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-the-principles-of-bayesian-statistics\"><strong>The Principles of Bayesian Statistics<\/strong><\/h3>\n\n\n\n<p>Bayesian Theory\u2014named for Thomas Bayes, the English minister and mathematician who first articulated it\u2014posits that <strong>you can calculate the probability of event A with respect to a specific piece of evidence B<\/strong>. To do so, Silver explains, you need to know (or estimate) three things:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The prior probability of event A, regardless of whether you discover evidence B\u2014mathematically written as P(A)<\/li><li>The probability of observing evidence B <em>if <\/em>event A occurs\u2014written as P(B|A)<\/li><li>The probability of observing evidence B if event A <em>doesn\u2019t<\/em> occur\u2014written as P(B|not A)<\/li><\/ul>\n\n\n\n<p>Bayes\u2019 Theorem uses these values to calculate the probability of A given B\u2014P(A|B)\u2014as follows:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shortform.com\/blog\/wp-content\/uploads\/2023\/05\/image-6.png\" alt=\"\" class=\"wp-image-103074\" width=\"387\" height=\"60\"\/><\/figure>\n\n\n\n<p>(Shortform note: This formula may look complicated, but in less mathematical terms, what it\u2019s calculating is [the probability that you observe B <em>and<\/em> A is true] divided by [the probability that you observe B at all <em>whether or not<\/em> A is true\u2014or P(B)]. In fact, Silver\u2019s version of the formula (as written above) is <a href=\"https:\/\/www.mathsisfun.com\/data\/bayes-theorem.html\" target=\"_blank\" rel=\"noreferrer noopener\">a very common special case used when you don\u2019t directly know P(B)<\/a>; that lengthy denominator is actually just a way to calculate P(B) using the information we\u2019ve listed above.)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Bayesian Lesson #1: Consider All Possibilities<\/strong><\/h3>\n\n\n\n<p>Now that we\u2019ve explored the mathematics of Bayesian Theory, let\u2019s look at the broader implications of its underlying logic. First, building on the principle of considering prior probabilities, Silver argues that <strong>it\u2019s important to be open to a wide range of possibilities<\/strong>, especially when you\u2019re dealing with noisy data. Otherwise, you might develop blind spots that hinder your ability to predict accurately.<\/p>\n\n\n\n<p>To illustrate this point, Silver argues that the US military\u2019s failure to predict the Japanese attack on Pearl Harbor in 1941 shows that <strong>it\u2019s dangerous to commit too strongly to a specific theory when there\u2019s scant evidence for <em>any<\/em> particular theory<\/strong>. He explains that in the weeks before the attack, the US military noticed a sudden dropoff in intercepted radio traffic from the Japanese fleet. According to Silver, most analysts concluded that the sudden radio silence was because the fleet was out of range of US military installations\u2014they didn\u2019t <a href=\"https:\/\/www.shortform.com\/blog\/consider-the-possibilities\/\">consider the possibility<\/a> of an impending attack because they believed the main threat to the US Navy was from domestic sabotage by Japanese Americans.<\/p>\n\n\n\n<p>Silver explains that <strong>one reason we sometimes fail to see all the options is that it\u2019s common to mistake a lack of precedence for a lack of possibility<\/strong>. In other words, when an event is extremely uncommon or unlikely, we might conclude that it will <em>never<\/em> happen, even when logic and evidence dictate that given enough time, it will. For example, Silver points out that before the attack on Pearl Harbor, the previous foreign attack on US territory came in the early 19th century\u2014a fact that made it easy to forget that such an attack was even possible.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Bayesian Lesson #2: Follow the Evidence, Not Emotions or Trends<\/strong><\/h3>\n\n\n\n<p>In addition to emphasizing the importance of considering all possibilities, Bayesian logic also highlights the need to stay focused on the evidence rather than getting sidetracked by other factors such as your emotional responses or the trends you observe.<\/p>\n\n\n\n<p>For one thing, Silver argues that <strong>when you give in to strong emotions, the quality of your predictions suffers<\/strong>. He gives the example of poker players <em>going on tilt<\/em>\u2014that is, losing their cool due to a run of bad luck or some other stressor (such as fatigue or another player\u2019s behavior). Poker depends on being able to accurately predict what cards your opponent might have\u2014but Silver argues that when players are on tilt, they begin taking ill-considered risks (such as betting big on a weak hand) based more on anger and frustration than on solid predictions.&nbsp;<\/p>\n\n\n\n<p>(Shortform note: To help keep your emotions in check, remember that getting a prediction wrong (such as by losing to an unlikely poker hand) doesn\u2019t mean you <em>did <\/em>anything wrong\u2014it\u2019s not uncommon for the best possible predictions to fail simply due to luck. In fact, in <a href=\"https:\/\/www.shortform.com\/app\/book\/fooled-by-randomness\/\" target=\"_blank\" rel=\"noreferrer noopener\"><em>Fooled By Randomness<\/em><\/a>, <a href=\"https:\/\/www.shortform.com\/blog\/nassim-nicholas-taleb\/\">Nassim Nicholas Taleb<\/a> argues that luck is more important than skill in determining outcomes. He says that this is especially true because, in many situations, <a href=\"https:\/\/www.shortform.com\/app\/book\/fooled-by-randomness\/part-1#randomness-allows-less-qualified-competitors-to-win\" target=\"_blank\" rel=\"noreferrer noopener\">early success leads to future success<\/a>, such as when a startup experiences some early good fortune that allows it to survive long enough to benefit from more good fortune down the road.)<\/p>\n\n\n\n<p>Furthermore, Silver says, it\u2019s important not to be swayed by trends because <strong>psychological factors such as herd mentality distort behaviors in unpredictable ways<\/strong>. For instance, the stock market sometimes experiences bubbles that artificially inflate prices because of a runaway feedback loop: Investors see prices going up and want to jump on a hot market, so they buy, which drives prices up even further and convinces more investors to do the same\u2014even when there\u2019s no rational reason for prices to be spiking in the first place.&nbsp;<\/p>\n\n\n\n<p>(Shortform note: The authors of <a href=\"https:\/\/www.shortform.com\/app\/book\/noise\" target=\"_blank\" rel=\"noreferrer noopener\"><em>Noise<\/em><\/a> explain that these kinds of <a href=\"https:\/\/www.shortform.com\/blog\/feedback-loop-meaning\/\">feedback loops<\/a> result from a psychological phenomenon known as an <em>information cascade<\/em> in which <a href=\"https:\/\/www.shortform.com\/app\/book\/noise#where-noise-comes-from\" target=\"_blank\" rel=\"noreferrer noopener\">real or perceived popularity influences how people interpret information<\/a>. Moreover, the authors argue that information cascades often amount to little more than luck\u2014whichever idea receives initial support (which typically correlates with which idea is presented first) tends to be the idea that wins out regardless of its merits.)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is Bayesian Theory? How does it help forecasters make better predictions? Named after Thomas Bayes, Bayesian Theory is one of the best ways to determine the probability of an event in the future. In his book The Signal and the Noise, Nate Silver shares two lessons you can use to correctly apply Bayesian Theory to any situation. Let&#8217;s take a look at Bayesian Theory in detail.<\/p>\n","protected":false},"author":14,"featured_media":72200,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[160,25,30],"tags":[1032],"class_list":["post-103073","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-science","category-statistics","category-work","tag-the-signal-and-the-noise","","tg-column-two"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.3 (Yoast SEO v24.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How Bayesian Theory Helps Us Predict the Future - Shortform Books<\/title>\n<meta name=\"description\" content=\"It&#039;s embarrassing when a prediction you made is inaccurate. 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