{"id":23237,"date":"2021-05-21T15:26:29","date_gmt":"2021-05-21T15:26:29","guid":{"rendered":"https:\/\/www.experfy.com\/blog\/?p=23237"},"modified":"2023-08-19T13:58:07","modified_gmt":"2023-08-19T13:58:07","slug":"frequentist-vs-bayesian-statistics-which-one-is-best","status":"publish","type":"post","link":"https:\/\/www.experfy.com\/blog\/ai-ml\/frequentist-vs-bayesian-statistics-which-one-is-best\/","title":{"rendered":"Frequentist vs Bayesian Statistics: Which One Is Best!"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"23237\" class=\"elementor elementor-23237\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-d05a07a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d05a07a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0120902\" data-id=\"0120902\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c72a518 elementor-widget elementor-widget-text-editor\" data-id=\"c72a518\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>While performing statistical analysis, oftentimes, we face the dilemma about Frequentist Vs\u00a0 Bayesian Strategy for the problem. This choice becomes critical when working with limited-sized datasets. And, if you use one method over the other without having a fundamental understanding of the assumptions and limitations of the two approaches, then you could increase your chance of making a wrong inference.\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0866eac elementor-widget elementor-widget-text-editor\" data-id=\"0866eac\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The philosophical divide between Frequentist Vs Bayesian statistics goes back 250 years. The Bayesian approach dominated 19th-century statistics, while the Frequentist approach gained popularity in the 20th century. The million-dollar question that arises now is \u2013 which philosophy would rule the 21st century?<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1ca5978 elementor-widget elementor-widget-text-editor\" data-id=\"1ca5978\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The Bayesian Vs Frequentist debate reflects upon two different attitudes towards statistical analysis. There\u2019s a saying in statistics, \u201cAll models are wrong, but some are useful\u201d. Both philosophical approaches carry their own merits and demerits. Hence, it becomes essential to understand them and be aware of them in order to adopt one that meets your requirements. In this blog, we\u2019ll provide an intuitive understanding of the differences between the two methodologies.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-f6c4487 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f6c4487\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f3cb58b\" data-id=\"f3cb58b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d2ce1c5 elementor-widget elementor-widget-heading\" data-id=\"d2ce1c5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Bayesian vs. Frequentist problem-solving approach<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-d7f92b3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d7f92b3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9955e4b\" data-id=\"9955e4b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-733313d elementor-widget elementor-widget-text-editor\" data-id=\"733313d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Bayesian statisticians build statistical models by using all the information they have to make the quickest possible progress. However, Frequentist statisticians conclude from sample data with emphasis on the frequency or proportion of the data only, without adding their prior knowledge about the data into the model.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-89c4196 elementor-widget elementor-widget-text-editor\" data-id=\"89c4196\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Let\u2019s understand this with an example. Suppose a Frequentist doctor and a Bayesian doctor diagnose a patient with fever caused by a sudden change in weather. How would each of them reach this diagnosis?<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7037cf6 elementor-widget elementor-widget-text-editor\" data-id=\"7037cf6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>A Frequentist doctor would use a mental diagnostic model to find the problem in the patient by asking about all the symptoms the patient is experiencing, and then would give his diagnosis. However,\u00a0 a Bayesian doctor, along with a mental diagnostic model, would have a history of diagnosing this patient, and would be aware that the weather has changed recently and many people are catching fever due to that. So, the patient could also be susceptible to weather change. Therefore, by asking only a few symptom-related questions, he would diagnose fever in the patient.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-431cc96 elementor-widget elementor-widget-text-editor\" data-id=\"431cc96\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This is how Frequentist and Bayesians take a different approach to problem-solving; one gives inference only based on the data available while the latter adds his own belief in the model to make an inference.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6f04a3c elementor-widget elementor-widget-text-editor\" data-id=\"6f04a3c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>With this explanation, you may believe Bayesian to be better than frequentist as with that approach, you can make an inference quickly. This, however, depends on your prior belief. A strong incorrect prior belief can be very hard to change.\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aa5f945 elementor-widget elementor-widget-text-editor\" data-id=\"aa5f945\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Let us now explain the interpretation of probability in the two different ideologies.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-481ca21 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"481ca21\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a578a50\" data-id=\"a578a50\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-81403c1 elementor-widget elementor-widget-heading\" data-id=\"81403c1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Frequentist vs. Bayesian probability<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-aa4d2bb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"aa4d2bb\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-49bf32a\" data-id=\"49bf32a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0fcee75 elementor-widget elementor-widget-text-editor\" data-id=\"0fcee75\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Can you find the probability<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d74061e elementor-widget elementor-widget-text-editor\" data-id=\"d74061e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul>\n<li>of heads if you perform identical tosses of an unbiased coin?<\/li>\n<li>of getting 4 if you identically roll a fair die?<\/li>\n<li>of getting a king if you identically choose a card from a deck?<\/li>\n<\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-331cf7b elementor-widget elementor-widget-text-editor\" data-id=\"331cf7b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>We\u2019ve all solved problems like these several times during our school days. This has led to the notion of probability being hard-wired in us as a point value.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-29a5c0f elementor-widget elementor-widget-text-editor\" data-id=\"29a5c0f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>However, did you notice that the term \u2018identical\u2019 appears in all the above probability statements? This word is the key that challenges the fixed point notion of probability. It means that if you are performing the experiments and keeping all parameters (i.e., external forces acting on all experiments) fixed, then you\u2019ll get a deterministic point estimate of probability if the experiment is done an infinite number of times. This is how a frequentist probability is defined \u2013<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9d31bef elementor-widget elementor-widget-text-editor\" data-id=\"9d31bef\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>However, in the real world, true identical experiments are impossible to perform. Thus, parameters can\u2019t be kept fixed, and for a fixed set of data, you will obtain different probabilities. Hence, probability here would be \u2013<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-51e06d6 elementor-widget elementor-widget-text-editor\" data-id=\"51e06d6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Here, possibilities mean different parameters that are kept under consideration with all of their possible values, and the numerator is the total number of times an event has occurred in all those possibilities. So, the probability in Bayesian doesn\u2019t represent the long-run frequency (or a point value), but it represents the uncertainties and these uncertainties are the initial conditions of parameters that have resulted in the observation. Hence, this probability in the Bayesian world would have multiple values in which all values are relatively likely\/unlikely concerning the parameters. This representation is known as a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Probability_distribution\" target=\"_blank\" rel=\"noreferrer noopener\">probability distribution<\/a>.\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-cce0b3c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cce0b3c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b8e0dcb\" data-id=\"b8e0dcb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fc711ab elementor-widget elementor-widget-heading\" data-id=\"fc711ab\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Frequentist vs. Bayesian in A\/B testing<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-dba3bcd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dba3bcd\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1ff8705\" data-id=\"1ff8705\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-86355ee elementor-widget elementor-widget-text-editor\" data-id=\"86355ee\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>We now know that a Frequentist treats probability as a point estimate while a Bayesian is about representing probabilities as distribution. Let us understand the difference between the two approaches by using an example of <a href=\"http:\/\/www.experfy.com\/blog\/ai-ml\/machine-learning-based-optimization-vs-ab-testing\/\" target=\"_blank\" rel=\"noreferrer noopener\">A\/B testing<\/a>.\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-79d183a elementor-widget elementor-widget-text-editor\" data-id=\"79d183a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Essentially, as the name suggests, the basic idea of an A\/B test is to determine which out of two variations A and B is better in terms of a particular metric. Suppose you are interested in finding which of the two has a higher conversion rate. Let us understand this with an example \u2013\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-01705b4 elementor-widget elementor-widget-text-editor\" data-id=\"01705b4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Say you have recently launched a new blogging website and you want to increase the number of subscribers to it. You have two layouts in your mind, but you are unsure which design is better. To answer that empirically with customer response data instead of your gut feeling, you\u2019ll need to run an A\/B test where some visitors will randomly see website A while others will see website B. After running this experiment for a while, suppose you obtained the following results \u2013<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6f42b49 elementor-widget elementor-widget-text-editor\" data-id=\"6f42b49\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<figure class=\"wp-block-table\">\n<table>\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td><strong>Hits<\/strong><\/td>\n<td><strong>Conversions (No. of subscribers)<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Variation A<\/strong><\/td>\n<td>3000<\/td>\n<td>165<\/td>\n<\/tr>\n<tr>\n<td><strong>Variation B<\/strong><\/td>\n<td>2000<\/td>\n<td>134<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-e71a575 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e71a575\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0056ade\" data-id=\"0056ade\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4b91446 elementor-widget elementor-widget-heading\" data-id=\"4b91446\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Frequentist A\/B testing<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-6942264 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6942264\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2ce0c24\" data-id=\"2ce0c24\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bb2afec elementor-widget elementor-widget-text-editor\" data-id=\"bb2afec\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>As we have learned in an earlier section, frequentists work with point estimates. A frequentist estimator will simply\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a276c55 elementor-widget elementor-widget-text-editor\" data-id=\"a276c55\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ol>\n<li>Compute the conversion rate of the two variations.<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bb3206b elementor-widget elementor-widget-text-editor\" data-id=\"bb3206b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<figure class=\"wp-block-table\">\n<table>\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td>Conversion Rate (%)<\/td>\n<\/tr>\n<tr>\n<td>Variation A<\/td>\n<td>5.5<\/td>\n<\/tr>\n<tr>\n<td>Variation B<\/td>\n<td>6.7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cf232e6 elementor-widget elementor-widget-text-editor\" data-id=\"cf232e6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ol start=\"2\">\n<li>Take the difference between the conversion rates<br \/>Variation B &#8211; Variation A : 6.7 &#8211; 5.5 = 1.2%<\/li>\n<li>Compare it to a certain threshold. If the threshold is satisfied, then you have a winner.<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-46fa8c3 elementor-widget elementor-widget-text-editor\" data-id=\"46fa8c3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This is the crux of a frequentist-based A\/B test where only available data is used to make an inference. If you are interested in advanced calculations, you can play with the <a href=\"https:\/\/vwo.com\/tools\/ab-test-siginficance-calculator\" target=\"_blank\" rel=\"noreferrer noopener\">actual calculator<\/a>.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8aee07b elementor-widget elementor-widget-text-editor\" data-id=\"8aee07b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Frequentist approaches are quite useful due to their analytical nature making them computationally inexpensive. However, when data is not sufficient and the analytical assumptions do not hold, they can result in wrong conclusions.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-b3db245 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b3db245\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6c8db61\" data-id=\"6c8db61\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e2cf1f6 elementor-widget elementor-widget-heading\" data-id=\"e2cf1f6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Bayesian A\/B testing<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-38255d9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"38255d9\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-625c341\" data-id=\"625c341\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5a47430 elementor-widget elementor-widget-text-editor\" data-id=\"5a47430\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>As explained in an earlier section, in the real world, identical experiments are impossible to perform. So, as a Bayesian, you will consider a spectrum of possible conversion rates as beliefs, and based on the observed data, you will update your belief of conversion rates in your conceived spectrum. Therefore, the initial question you\u2019ll ask is\u00a0\u00a0\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8f71c79 elementor-widget elementor-widget-text-editor\" data-id=\"8f71c79\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong>Which prior should I start with?<\/strong><strong><br \/><\/strong><strong><br \/><\/strong>Although Bayesian provides the capability to incorporate prior (one\u2019s knowledge) to the model, when it comes to a practical application, most often, the choice of the prior distribution is vague prior where all possibilities are equally likely. For a conversion rate, it could be as below:<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fd9cc27 elementor-widget elementor-widget-text-editor\" data-id=\"fd9cc27\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Often, the choice is a non-informative prior instead of a strong prior as the latter can dominate the posterior (our updated beliefs about the conversion rate after observing the data). If you have a firm prior belief, you don\u2019t need any data to tell you something new. That\u2019s why a non-informative prior is a good choice to start with, and after that, as the experiment progresses. You can update that based on your knowledge. You can then treat your posterior distribution as new prior to the next experiment.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c5662d2 elementor-widget elementor-widget-text-editor\" data-id=\"c5662d2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><strong>Bayesian Learning<\/strong><\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-69f1944 elementor-widget elementor-widget-text-editor\" data-id=\"69f1944\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In the case of A\/B testing on a conversion rate, updating the prior is relatively easy as you can obtain the exact posteriors when specific mathematical functions are chosen as prior. So, if you apply Bayes\u2019 update equation on the obtained observation data from your website, where for both variations, you start with non-informative prior, you will obtain the following posteriors:\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-79fc4a9 elementor-widget elementor-widget-text-editor\" data-id=\"79fc4a9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Once you get the posteriors, you can compute decision metrics to determine which variation is better. Now, if you compute the difference in conversion rates of the two distributions, you\u2019ll get a delta distribution:<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6063555 elementor-widget elementor-widget-text-editor\" data-id=\"6063555\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Notice how beautifully the above plot captures your belief about how much Variation B is better than Variation A. If you are interested in advanced calculations, you can read their <a href=\"https:\/\/help.vwo.com\/hc\/en-us\/articles\/360033471874\" target=\"_blank\" rel=\"noreferrer noopener\">computation approach<\/a> in more detail.\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-df818cb elementor-widget elementor-widget-text-editor\" data-id=\"df818cb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Even though Bayesian provides a convenient and more intuitive framework for learning and decision making for A\/B testing, its adoption is still not mainstream in the industry due to the following reasons:<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5842809 elementor-widget elementor-widget-text-editor\" data-id=\"5842809\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ol>\n<li>If specific priors are not chosen, then determining the resultant posterior is computationally expensive.\u00a0<\/li>\n<li>A Bayesian can never be 100% sure about anything while humans have a preference for binary outcomes in order to make decisions.<\/li>\n<li>Modelling approaches can be mathematically involved.<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-510bdf8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"510bdf8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e96f9a0\" data-id=\"e96f9a0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-21b9318 elementor-widget elementor-widget-heading\" data-id=\"21b9318\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-c25de79 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c25de79\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ed25779\" data-id=\"ed25779\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b0c4595 elementor-widget elementor-widget-text-editor\" data-id=\"b0c4595\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In this chapter, we have covered some of the fundamental differences between Bayesian and Frequentist philosophies. However, there is still a lot more that distinguishes the two ideologies, so if this topic interests you, you can read more at: <a href=\"https:\/\/cxl.com\/blog\/bayesian-frequentist-ab-testing\/\" target=\"_blank\" rel=\"noreferrer noopener\">bayesian vs frequentist ab testing<\/a>.\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-19272bc elementor-widget elementor-widget-text-editor\" data-id=\"19272bc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>After reading this article, if you have a preference for a statistical model, that\u2019s great! If you don\u2019t, that\u2019s even better as you don\u2019t have to choose any side. Many experimentation platforms use some flavor of a traditional statistical model (Bayesian or Frequentist) with some heuristics.\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-653170a elementor-widget elementor-widget-text-editor\" data-id=\"653170a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>More than the methodology, what matters is how well you can understand the results and make a decision on them. This understanding can be useful for building a data-driven approach for assessing the risk that an organization is willing to take, and what the predicted improvement in business outcomes could be.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-94af540 elementor-widget elementor-widget-text-editor\" data-id=\"94af540\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>However, if you ever find yourself in a heated discussion concerning the pros and cons of the two approaches, then this article can be helpful for you to get the hang of that debate.\u00a0<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>While performing statistical analysis, oftentimes, we face the dilemma about Frequentist Vs\u00a0 Bayesian Strategy for the problem. This choice becomes critical when working with limited-sized datasets. And, if you use one method over the other without having a fundamental understanding of the assumptions and limitations of the two approaches, then you could increase your chance<\/p>\n","protected":false},"author":1153,"featured_media":23239,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"content-type":"","footnotes":""},"categories":[183],"tags":[111,1587,1589,1588],"ppma_author":[3666],"class_list":["post-23237","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai-ml","tag-ai-amp-machine-learning","tag-bayesian-models","tag-bayesian-statistics","tag-frequentist"],"authors":[{"term_id":3666,"user_id":1153,"is_guest":0,"slug":"anshul-gupta","display_name":"Anshul Gupta","avatar_url":"https:\/\/www.experfy.com\/blog\/wp-content\/uploads\/2021\/05\/anshul_gupta-150x150.jpeg","user_url":"https:\/\/datascienceinsider.wordpress.com","last_name":"Gupta","first_name":"Anshul","job_title":"","description":"Anshul Gupta\u2019s expertise lies in building interpretable machine learning solutions. He works in the Data Science team at VWO where he handles the mathematical function of their Bayesian optimization platform."}],"_links":{"self":[{"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/posts\/23237","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/users\/1153"}],"replies":[{"embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/comments?post=23237"}],"version-history":[{"count":11,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/posts\/23237\/revisions"}],"predecessor-version":[{"id":30793,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/posts\/23237\/revisions\/30793"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/media\/23239"}],"wp:attachment":[{"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/media?parent=23237"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/categories?post=23237"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/tags?post=23237"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/ppma_author?post=23237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}