[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"cms-page:\u002Fblog\u002Fbayesian-statistics-in-media-mix-modelling-a-real-world-analogy":3},{"date":4,"date_gmt":4,"content":5,"sticky":7,"format":8,"categories":9,"collections":11,"coauthors":12,"class_list":14,"acf":23,"head_links":372,"breadcrumbs":373,"reading_minutes":183,"category":381,"head":383},"2024-03-15T11:20:51",{"rendered":6},"\n\u003Cp>\u003Ca rel=\"noreferrer noopener\" href=\"\u002Fblog\u002Fguide-to-media-effectiveness-measurement\u002F\">Bayesian statistics\u003C\u002Fa> is a powerful tool for tackling the complexities inherent in media effectiveness analysis, making it an attractive approach for practitioners in the field. Bayesian statistics particularly shines in \u003Ca rel=\"noreferrer noopener\" href=\"\u002Fblog\u002Fmedia-mix-modelling\u002F\">media mix modelling\u003C\u002Fa> (MMM) for its ability to incorporate prior knowledge and enhance model robustness with limited or missing data. \u003C\u002Fp>\n\n\n\n\u003Cp>Additionally, Bayesian methods facilitate the handling of uncertainty, enabling more reliable inference and decision-making processes.\u003C\u002Fp>\n\n\n\n\u003Cp>The Bayesian framework consists of three main components: the prior, the likelihood and the posterior.\u003C\u002Fp>\n\n\n\n\u003Cp>In the context of MMM, the prior reflects any initial beliefs or assumptions on the model parameters before observing any data. The likelihood quantifies the probability of observing the data given the model’s prior. The posterior integrates the prior and likelihood, yielding “updated” beliefs after considering the observed data.\u003C\u002Fp>\n\n\n\n\u003Cp>It is the posterior that contains all relevant insights for an informed decision-making process.\u003C\u002Fp>\n\n\n\n\u003Cp>As an example, let us consider the task of predicting whether or not to wear a raincoat based on weather conditions. This can be modelled in a similar way to the digital marketer’s crucial challenge of allocating budgets for a campaign across various media channels.\u003C\u002Fp>\n\n\n\n\u003Cfigure class=\"wp-block-table\">\u003Ctable>\u003Ctbody>\u003Ctr>\u003Ctd>\u003Cstrong>Initial Uncertainty (Objective)\u003C\u002Fstrong>\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Raincoat Scenario:\u003C\u002Fstrong> You wake up and your curtains are closed, you can’t hear any rainfall initially. This tells you a little about the chance of rainfall, but not enough to decide whether or not to wear a raincoat.\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Marketing Campaign:\u003C\u002Fstrong> You wish to launch a campaign but don’t have any insights into channel performance to help you decide which channels to advertise on.\u003Cbr>\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>\u003Cstrong>Historical Beliefs (Prior)\u003C\u002Fstrong>\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Raincoat Scenario:\u003C\u002Fstrong> Based on previous years you think there is about a 40% chance of rainfall around this time of year.\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Marketing Campaign:\u003C\u002Fstrong> You recall your knowledge of channel performance for previous campaigns and how budgets were allocated then.\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>\u003Cstrong>Seeing the data (Likelihood)\u003C\u002Fstrong>\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Raincoat Scenario: \u003C\u002Fstrong>Upon looking outside you see the sky is overcast with dark, heavy clouds. The likelihood of needing a raincoat increases considerably, but not to certainty.\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Marketing Campaign:\u003C\u002Fstrong> You update your campaign’s expected success using real-time data from various media channels.\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>\u003Cstrong>Accounting for externalities (Externalities)\u003C\u002Fstrong>\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Raincoat Scenario: \u003C\u002Fstrong>You check a weather app on your phone, which factors in wind speeds and humidity, and see a 60% chance of rainfall in your area.\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Marketing Campaign:\u003C\u002Fstrong> You decide to consider external factors that may impact the performance of your campaign, such as seasonality and consumer behaviour.\u003C\u002Ftd>\u003C\u002Ftr>\u003Ctr>\u003Ctd>\u003Cstrong>Decision-making insights (Posterior)\u003C\u002Fstrong>\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Raincoat Scenario:\u003C\u002Fstrong> Combining your historical beliefs with today’s observations and the weather forecasts, you estimate there is a 75% chance of needing a raincoat and deciding to wear one.\u003C\u002Ftd>\u003Ctd>\u003Cstrong>Marketing Campaign:\u003C\u002Fstrong> Through incorporating prior knowledge, historical data and externalities, the Bayesian MMM has produced an estimate of your optimal media mix and its associated probabilities. You choose to allocate budgets for the campaign this way.\u003C\u002Ftd>\u003C\u002Ftr>\u003C\u002Ftbody>\u003C\u002Ftable>\u003C\u002Ffigure>\n\n\n\n\u003Cp>To conclude, the increasing popularity of Bayesian statistics within media effectiveness measurement reflects a paradigm shift towards more robust and flexible frameworks. By leveraging Bayesian methods, marketers can better account for uncertainty, incorporate prior knowledge, and refine their insights, leading to more accurate and actionable marketing strategies.\u003C\u002Fp>\n\n\n\n\u003Cfigure class=\"wp-block-image size-full\">\u003Ca rel=\"noreferrer noopener\" href=\"\u002Fmedia-solutions\u002Fmedia-effectiveness\u002F\">\u003Cimg loading=\"lazy\" decoding=\"async\" width=\"3840\" height=\"540\" src=\"https:\u002F\u002Fimages.impression.co.uk\u002F2024\u002F03\u002FMeasurement_Banner_01.jpg?auto=compress%2Cformat&q=90\" alt=\"\" class=\"wp-image-27690\"\u002F>\u003C\u002Fa>\u003C\u002Ffigure>\n",false,"standard",[10],41,[],[13],120,[15,16,17,18,19,20,21,22],"post-27611","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-measurement",{"page_content_modules":24,"hero":179},[25,133],{"acf_fc_layout":26,"reduced":27,"top_overlap":-1,"bottom_underlap":-1,"disable_observer":27,"title":28,"content":6,"authors":29},"blog_post_content",true,"Bayesian Statistics in Media Mix Modelling: A real-world analogy",[30],{"id":31,"path":32,"display_name":33,"job_title":34,"description":35,"avatar_url":36,"acf":37},29,"\u002Fabout\u002Four-team\u002Fharry-brace\u002F","Harry Brace","Director, Head of Solutions","I'm the Director, Head of Solutions at Impression. I spend my time debugging and implementing tracking using Google Tag Manager, managing data warehousing platforms and building Looker Studio reports!","https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress&fit=crop&fm=jpg&h=150&q=80&w=150&bg=CFE6F9",{"full_bio":38,"job_title":34,"specialist_service_links":39,"photo":77},"\u003Cp>Director, Head of Solutions. Joined Impression in November 2017.\u003C\u002Fp>\n\u003Cp>I gained 4 years of experience as a web developer before moving to Impression as a digital account manager in 2017. I moved across to the Analytics department in 2019 and I’ve been strengthening and growing our Analytics offering ever since.\u003C\u002Fp>\n\u003Cp>Day to day, I spend my time debugging and implementing tracking using Google Tag Manager, managing data warehousing platforms and building Looker Studio reports!\u003C\u002Fp>\n\u003Cp>\u003Cstrong>Something that I’m proud of:\u003C\u002Fstrong>\u003Cbr \u002F>\nBuilding the analytics department over the last couple of years with the help of Aaron and now Alex H.\u003C\u002Fp>\n\u003Cp>\u003Cstrong>Outside of work:\u003C\u002Fstrong>\u003Cbr \u002F>\nFind me socialising, skiing or gaming.\u003C\u002Fp>\n",[40,58,68],{"page":41,"link_text":57},{"ID":42,"post_author":43,"post_date":44,"post_date_gmt":44,"post_content":45,"post_title":46,"post_excerpt":45,"post_status":47,"comment_status":48,"ping_status":48,"post_password":45,"post_name":49,"to_ping":45,"pinged":45,"post_modified":50,"post_modified_gmt":50,"post_content_filtered":45,"post_parent":51,"guid":52,"menu_order":51,"post_type":53,"post_mime_type":45,"comment_count":54,"filter":55,"url_path":56},374,"98","2021-01-11 16:25:32","","Analytics","publish","closed","analytics","2026-09-28 11:36:16",0,"\u002F?page_id=374","page","0","raw","\u002Fanalytics\u002F","Web Analytics",{"page":59,"link_text":62},{"ID":60,"post_author":43,"post_date":61,"post_date_gmt":61,"post_content":45,"post_title":62,"post_excerpt":45,"post_status":47,"comment_status":48,"ping_status":48,"post_password":45,"post_name":63,"to_ping":45,"pinged":45,"post_modified":64,"post_modified_gmt":64,"post_content_filtered":45,"post_parent":65,"guid":66,"menu_order":51,"post_type":53,"post_mime_type":45,"comment_count":54,"filter":55,"url_path":67},17916,"2022-06-20 08:56:55","Tag Management","tag-management","2026-09-28 11:05:27",17552,"\u002F?page_id=17916","\u002Fmedia-solutions\u002Ftag-management\u002F",{"page":69,"link_text":72},{"ID":70,"post_author":43,"post_date":71,"post_date_gmt":71,"post_content":45,"post_title":72,"post_excerpt":45,"post_status":47,"comment_status":48,"ping_status":48,"post_password":45,"post_name":73,"to_ping":45,"pinged":45,"post_modified":74,"post_modified_gmt":74,"post_content_filtered":45,"post_parent":65,"guid":75,"menu_order":51,"post_type":53,"post_mime_type":45,"comment_count":54,"filter":55,"url_path":76},17140,"2022-05-27 14:22:19","Google Marketing Platform","google-marketing-platform","2026-09-25 10:43:13","\u002F?page_id=17140","\u002Fmedia-solutions\u002Fgoogle-marketing-platform\u002F",{"ID":78,"id":78,"title":79,"filename":80,"filesize":81,"url":82,"link":83,"alt":45,"author":84,"description":45,"caption":45,"name":85,"status":86,"uploaded_to":51,"date":87,"modified":87,"menu_order":51,"mime_type":88,"type":89,"subtype":90,"icon":91,"width":92,"height":93,"sizes":94},25135,"Harry-Brace2","Harry-Brace2.png",306919,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&q=90","\u002Fharry-brace2\u002F","12","harry-brace2","inherit","2023-10-03 16:03:03","image\u002Fpng","image","png","\u002Fwp\u002Fwp-includes\u002Fimages\u002Fmedia\u002Fdefault.png",696,600,{"thumbnail":95,"thumbnail-width":96,"thumbnail-height":96,"medium":97,"medium-width":98,"medium-height":99,"medium_large":100,"medium_large-width":101,"medium_large-height":102,"large":103,"large-width":104,"large-height":105,"1536x1536":106,"1536x1536-width":107,"1536x1536-height":108,"2048x2048":109,"2048x2048-width":110,"2048x2048-height":111,"post-thumbnail":112,"post-thumbnail-width":113,"post-thumbnail-height":114,"12_col":115,"12_col-width":116,"12_col-height":117,"default_landscape":118,"default_landscape-width":119,"default_landscape-height":93,"default_portrait":120,"default_portrait-width":93,"default_portrait-height":119,"6_col_and_margin_short":121,"6_col_and_margin_short-width":113,"6_col_and_margin_short-height":117,"11_col_and_margin":122,"11_col_and_margin-width":123,"11_col_and_margin-height":117,"9_col_rectangle":124,"9_col_rectangle-width":125,"9_col_rectangle-height":126,"11_col":127,"11_col-width":128,"11_col-height":117,"staff_image_696_600":129,"staff_image_696_600-width":92,"staff_image_696_600-height":93,"rectangular_thumbnail":130,"rectangular_thumbnail-width":131,"rectangular_thumbnail-height":132},"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=640&q=90&w=640","640","https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=scale&h=172&q=90&w=200",200,172,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=scale&h=662&q=90&w=768",768,662,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=1000&q=90&w=1892","1892","1000","https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=scale&h=1324&q=90&w=1536",1536,1324,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=scale&h=1766&q=90&w=2048",2048,1766,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=1180&q=90&w=1860",1860,1180,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=870&q=90&w=2880",2880,870,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=600&q=90&w=800",800,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=800&q=90&w=600","https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=870&q=90&w=1860","https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=870&q=90&w=3080",3080,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=1400&q=90&w=2150",2150,1400,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=870&q=90&w=2640",2640,"https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=600&q=90&w=696","https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F10\u002FHarry-Brace2.png?auto=compress%2Cformat&fit=crop&h=300&q=90&w=750",750,300,{"acf_fc_layout":134,"reduced":27,"top_overlap":135,"bottom_underlap":135,"disable_observer":-1,"heading":136,"cta_text":137,"cta_link":138,"items":139},"related_module","small","See more posts","See all articles","\u002Fblog\u002F",[140,154,164],{"type_key":16,"title":141,"excerpt":142,"to":143,"postedAt":144,"readingTime":145,"image":146,"authors":147,"category":151},"Beyond ad-level data: Unlocking granular product insights for Meta","\u003Cp>Standard Meta Ads reporting traditionally stops at the ad level, leaving e-commerce brands in the dark about which specific products are actually driving traffic on social platforms. While Dynamic Product Ads (DPAs) are incredibly powerful, they aggregate performance across multiple items, making it difficult to isolate individual product success.  To bridge this data gap, the […]\u003C\u002Fp>\n","\u002Fblog\u002Funlocking-granular-product-insights-for-meta\u002F","2026-06-24T14:13:48",4,"https:\u002F\u002Fimages.impression.co.uk\u002F2026\u002F06\u002Fallison-saeng-B7VlWt3pRM0-unsplash.jpg?auto=compress%2Cformat&fit=crop&h=640&q=90&w=640",[148],{"name":149,"image":150},"Zoe Le","https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F08\u002FZoe-Le-NEW.png?auto=compress&fit=crop&fm=jpg&h=150&q=80&w=150&bg=CFE6F9",{"to":152,"name":153},"\u002Fblog\u002Fcategory\u002Fmeasurement\u002F","Measurement",{"type_key":16,"title":155,"excerpt":156,"to":157,"postedAt":158,"readingTime":159,"image":160,"authors":161,"category":163},"Which Marketing Mix Modelling platform should you use?","\u003Cp>If you’ve decided to build a Marketing Mix Model (MMM), an important first step is to choose what platform you want to use. There are quite a few options, ranging from simple to complex, with different benefits to each You’ve probably come across these libraries already: Google’s Meridian, Meta’s Robyn, PyMC Marketing and a handful […]\u003C\u002Fp>\n","\u002Fblog\u002Fwhich-marketing-mix-modelling-platform-should-you-use\u002F","2026-06-10T11:28:01",6,"https:\u002F\u002Fimages.impression.co.uk\u002F2026\u002F06\u002Fvaleria-nikitina-ie2R2t9fC9Q-unsplash.jpg?auto=compress%2Cformat&fit=crop&h=640&q=90&w=640",[162],{"name":33,"image":36},{"to":152,"name":153},{"type_key":16,"title":165,"excerpt":166,"to":167,"postedAt":168,"readingTime":169,"image":170,"authors":171,"category":178},"Beyond the click: Can you use MMM to prove the value of LLMs?","\u003Cp>LLMs (Large Language Models) have quickly become a significant influence on a customer’s journey, and all signs point to this influence only increasing. Even before we consider how to influence visibility across AI search, the first question we have to ask ourselves is: How do we measure the impact LLMs have on top-line results? The […]\u003C\u002Fp>\n","\u002Fblog\u002Fcan-mmm-prove-the-value-of-lmms\u002F","2026-04-28T11:48:18",8,"https:\u002F\u002Fimages.impression.co.uk\u002F2026\u002F04\u002Faerps-com-bUUrG6CMHiA-unsplash.jpg?auto=compress%2Cformat&fit=crop&h=640&q=90&w=640",[172,175],{"name":173,"image":174},"Alex Howat","https:\u002F\u002Fimages.impression.co.uk\u002F2021\u002F06\u002FkMgPqCLz-Alex-Howat.png?auto=compress&fit=crop&fm=jpg&h=150&q=80&w=150&bg=CFE6F9",{"name":176,"image":177},"Petar Jovetic","https:\u002F\u002Fimages.impression.co.uk\u002F2023\u002F08\u002FPete-Jovetic-NEW.png?auto=compress&fit=crop&fm=jpg&h=150&q=80&w=150&bg=CFE6F9",{"to":152,"name":153},{"type":180,"style":181,"heading":28,"date":4,"updatedAt":182,"reading_minutes":183,"image":184,"imageAlt":28,"categories":185,"collections":371},"blog-post","light","2024-03-22T10:21:02",3,"https:\u002F\u002Fimages.impression.co.uk\u002F2024\u002F03\u002Fjakub-zerdzicki-ip7GFn5JqX8-unsplash.jpg?auto=compress%2Cformat&fit=crop&h=1180&q=90&rect=0%2C78%2C2400%2C1522&w=1860",[186],{"id":10,"count":187,"description":188,"link":152,"name":153,"slug":189,"taxonomy":190,"parent":51,"meta":191,"acf":192,"head_links":193,"resource_count":194,"yoast_title":195,"yoast_meta":196,"yoast_json_ld":241,"_links":339,"path":152},131,"Here at Impression, ongoing research and training is a huge part of how we keep our \u003Ca href=\"\u002Fmedia-solutions\u002F\">Media Solutions\u003C\u002Fa> team up-to-date with the latest happenings in the world of web & app analytics, martech, \u003Ca href=\"\u002Fmedia-solutions\u002Fdata-science\u002F\">data science\u003C\u002Fa> and \u003Ca href=\"\u002Fmedia-solutions\u002Fmedia-effectiveness\u002F\">media effectiveness\u003C\u002Fa>. We regularly share our thoughts on the latest digital news right here on our blog, so you can keep up to date too.\r\n\r\nFind out more about our \u003Ca href=\"\u002Fanalytics\u002F\">Analytics Agency\u003C\u002Fa> services, or browse our latest tips, advice and opinions below.","measurement","category",[],{"sub_title_override":45,"title_override":45},[],23,"Online Measurement, Analytics & Effectiveness Blog | Impression",[197,199,202,205,208,211,214,216,218,220,223,226,229,232,235,238],{"property":198,"content":195},"title",{"property":200,"content":201},"description","Keeping up to date with the latest measurement and analytics trends and strategies can be difficult. 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