{"id":255,"date":"2017-04-03T21:30:28","date_gmt":"2017-04-03T20:30:28","guid":{"rendered":"https:\/\/marriott-stats.com\/nigels-blog\/?p=255"},"modified":"2021-02-07T18:49:58","modified_gmt":"2021-02-07T18:49:58","slug":"forecasting1-how-do-you-identify-a-good-forecaster","status":"publish","type":"post","link":"https:\/\/marriott-stats.com\/nigels-blog\/forecasting1-how-do-you-identify-a-good-forecaster\/","title":{"rendered":"Forecasting#1 &#8211; How do you identify a good forecaster?"},"content":{"rendered":"<h3><span style=\"color: #339966; font-family: Calibri;\">\u201c<em><strong>I think the people in this country have had enough of experts<\/strong><\/em>\u201d<\/span><\/h3>\n<p><strong><span style=\"color: #000000; font-family: Calibri;\">Michael Gove, Sky News, 3<\/span><sup><span style=\"color: #000000; font-family: Calibri; font-size: small;\">rd<\/span><\/sup><span style=\"color: #000000; font-family: Calibri;\"> June 2016<\/span><\/strong><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">This was one of the most memorable quotes during the EU referendum in 2016 and came in response to a question as to why the forecasts of a whole list of organisations such as the IMF should be ignored.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">It prompted a flurry of rebuttals and articles supporting or damning him and the debate has not gone away.<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">Like so many quotes, it has already become distorted.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">I strongly recommend you listen to <\/span><a href=\"https:\/\/www.youtube.com\/watch?v=GGgiGtJk7MA\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0563c1; font-family: Calibri;\">the full question and answer<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\"> because here is his quote in its entirety.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0<\/span><\/p>\n<p><span style=\"color: #339966;\"><a style=\"color: #339966;\" href=\"https:\/\/fullfact.org\/blog\/2016\/sep\/has-public-really-had-enough-experts\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: Calibri;\">\u201c<em><strong>I think the people in this country have had enough of experts&#8230; from organisations with acronyms saying that they know what is best and getting it consistently wrong.\u201d<\/strong><\/em><\/span><\/a><\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">When I read this full quote I realised I am in complete agreement with Michael Gove.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><\/p>\n<p><!--more--><\/p>\n<p><span style=\"color: #993300;\"><em><span style=\"font-family: Calibri;\">February 2021 &#8211; this article has been edited to add some links to new material, especially those relating to the COVID19 pandemic.<\/span><span style=\"font-family: Calibri;\">\u00a0 <\/span><\/em><\/span><\/p>\n<p>F<span style=\"color: #000000; font-family: Calibri;\">irst of all, he is not condemning all experts.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">He is condemning experts from certain organisations who make regular forecasts and keep getting them wrong.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">It is not just a matter of opinion, it is a matter of fact that the standard of forecasting by so many organisations (especially in economic fields) is lamentable.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Recent <\/span><a href=\"http:\/\/www.telegraph.co.uk\/business\/2017\/02\/21\/bank-england-economic-forecasts-will-always-wrong\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0563c1; font-family: Calibri;\">interviews with key officials at the Bank of England<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\"> has highlighted this issue.<\/span><\/p>\n<h3><span style=\"color: #339966;\"><strong><span style=\"font-family: Calibri;\">Tetlock, Taleb &amp; Silver<\/span><\/strong><\/span><\/h3>\n<p><span style=\"color: #000000; font-family: Calibri;\">This issue was brilliantly explored by Philip Tetlock in his book <\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/Superforecasting\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0563c1; font-family: Calibri;\">&#8220;Superforecasting&#8221;<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\"> and I cannot recommend this book highly enough.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">If you want an in-depth review then I can recommend one written <\/span><a href=\"https:\/\/dominiccummings.wordpress.com\/2016\/11\/24\/a-review-of-tetlocks-superforecasting-2015\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0563c1; font-family: Calibri;\">by Michael Gove\u2019s former Special Advisor<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\"> no less.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Before Tetlock, Nate Silver wrote \u201c<\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/The_Signal_and_the_Noise\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0563c1; font-family: Calibri;\">The Signal &amp; the Noise<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\">\u201d which covered many of the basic principles of good forecasts and I can thoroughly recommend that book as well (I even gave a presentation <a href=\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/Signal-Noise-RSS-Conference-Newcastle-2013.pdf\" target=\"_blank\" rel=\"noopener\">about this book at the 2013 Royal Statistical Society conference in Newcastle<\/a>).<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">To round off the list of my recommendations, many of Nassim Taleb\u2019s books are well worth reading with <\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/Antifragile\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0563c1; font-family: Calibri;\">&#8220;Anti-Fragile&#8221;<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\"> probably the most relevant to the debate around forecasting.<\/span><\/p>\n<h3><span style=\"color: #339966;\"><strong><span style=\"font-family: Calibri;\">Experts &amp; Forecasters<\/span><\/strong><\/span><\/h3>\n<p><span style=\"color: #000000; font-family: Calibri;\">Let\u2019s come back to Michael Gove\u2019s full quote and focus on two aspects:<\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><strong><em><span style=\"font-family: Calibri;\">\u201c\u2026 experts \u2026 saying that they know what is best \u2026\u201d<\/span><\/em><\/strong><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><strong><em><span style=\"font-family: Calibri;\">\u201c\u2026 getting it consistently wrong.\u201d<\/span><span style=\"font-family: Calibri;\">\u00a0<\/span><\/em><\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000; font-family: Calibri;\">What is an expert in the first place?<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Can we define what makes someone an expert?<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">I have written <\/span><u><span style=\"color: #000000; font-family: Calibri;\">a separate post to answer these questions<\/span><\/u><span style=\"color: #000000; font-family: Calibri;\"> as this is a big subject and one that I have a lot of views on based on my own experiences.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">Whilst an expert can be many things, when it comes to forecasting, the credentials of any so called expert are not relevant in my opinion.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">What matters is their track record in forecasting.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">A person with no apparent credentials but whose forecasts are twice as accurate as a person laden with credentials should be given more weight.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">But how do we define forecasting accuracy and can we decide when someone is getting their forecasts \u201cconsistently wrong\u201d?<\/span><\/p>\n<h3><span style=\"color: #339966;\"><strong><span style=\"font-family: Calibri;\">Who is the best election forecaster?<\/span><\/strong><\/span><\/h3>\n<p><span style=\"color: #000000; font-family: Calibri;\">Let\u2019s start with four forecasts made by myself, <\/span><a href=\"https:\/\/www.ncpolitics.uk\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0563c1; font-family: Calibri;\">Matt Singh of NCP politics<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\"> and the opinion polls.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">All of us made forecasts for the 2015, 2017 &amp; 2019 General Elections and the 2016 EU referendum.\u00a0 Of the 3 forecasters, who performed best?\u00a0 <\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3564 alignnone\" src=\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/WhoIsBestForecaster-300x101.png\" alt=\"\" width=\"508\" height=\"171\" srcset=\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/WhoIsBestForecaster-300x101.png 300w, https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/WhoIsBestForecaster-768x260.png 768w, https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/WhoIsBestForecaster-450x152.png 450w, https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/WhoIsBestForecaster.png 793w\" sizes=\"auto, (max-width: 508px) 100vw, 508px\" \/><\/span><\/p>\n<ul>\n<li><span style=\"color: #000000; font-family: Calibri;\">In 2015, Matt was the most accurate and predicted the right outcome, a Conservative majority.\u00a0 I was next closest but <a href=\"https:\/\/marriott-stats.com\/nigels-blog\/uk-general-election-forecast-2015\/\" target=\"_blank\" rel=\"noopener\">my predicted outcome was a Conservative minority government<\/a>.<\/span><\/li>\n<li><span style=\"color: #000000; font-family: Calibri;\">In 2016, I was closest but <a href=\"https:\/\/marriott-stats.com\/nigels-blog\/brexit-why-leave-won\/\" target=\"_blank\" rel=\"noopener\">I was not explicitly predicting a Leave win<\/a>.\u00a0 I was basically saying &#8220;toss a coin&#8221;.<\/span><\/li>\n<li><span style=\"color: #000000; font-family: Calibri;\">In 2017, the polls were closest but <a href=\"https:\/\/marriott-stats.com\/nigels-blog\/uk-general-election-2017-7-review-of-my-predictions\/\" target=\"_blank\" rel=\"noopener\">none of us predicted the right outcom<\/a>e, a Conservative minority government.<\/span><\/li>\n<li><span style=\"color: #000000; font-family: Calibri;\">In 2019, all 3 of us predicted a Conservative majority government but <a href=\"https:\/\/marriott-stats.com\/nigels-blog\/uk-general-election-2019-2-my-forecast-beats-the-exit-poll\/\" target=\"_blank\" rel=\"noopener\">I was closest and even beat Sir John Curtice&#8217;s exit poll!<\/a><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000; font-family: Calibri;\">There is a strong case to be made that when forecasters are evaluated, evaluating their predicted outcomes is more important than their predicted numbers.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">This is probably where I diverge from Tetlock to some degree.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Tetlock\u2019s evaluation is based on forecasters\u2019 stated probabilities of certain events happening so someone who said there was a 50% chance of Leave winning (i.e. me) is more accurate than someone who said there was a <a href=\"https:\/\/www.ncpolitics.uk\/uk-eu-referendum\/\" target=\"_blank\" rel=\"noopener\">25% chance of Leave winning <\/a>(i.e. Matt Singh) or <a href=\"https:\/\/projects.fivethirtyeight.com\/2016-election-forecast\/\" target=\"_blank\" rel=\"noopener\">29% chance of Trump winning the presidency <\/a>(Nate Silver in 2016).<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">But an alien who landed on Earth in 2016 without any knowledge of human affairs could have tossed a coin and still had 50% chance of predicting that Leave\/Trump would win.<\/span><\/p>\n<h3><span style=\"color: #339966;\"><strong><span style=\"font-family: Calibri;\">Are forecasters dumb?<\/span><\/strong><\/span><\/h3>\n<p><span style=\"color: #000000; font-family: Calibri;\">My alien analogy brings me onto how I prefer to evaluate forecasters and that is to ask if a forecaster is capable of consistently beating what I call the DUMB forecaster.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Let\u2019s use a forecast of tomorrow\u2019s weather as an example.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">There are two dumb methods available to any weather forecaster:<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000; font-family: Calibri;\">The weather tomorrow will be the same as today.<\/span><\/li>\n<li><span style=\"color: #000000; font-family: Calibri;\">The weather tomorrow will be the average over the last X years for that date.<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000; font-family: Calibri;\">It is not possible to get simpler than these models.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">In many parts of the world, model 1 is a viable model.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">My wife is from Texas and constantly tells me that there is no need for a weather forecaster in the summer in Texas as you can guarantee it will be hot &amp; sunny.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Now she is living in the UK with me, she constantly checks the weather forecasts and in the UK, we would place more emphasis on model 2 as a viable dumb model since all Brits know that the weather today tells us nothing about tomorrow.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">A third dumb model would be to take a straight average of these 2 models which is actually one of the most basic time series models available coming from a class of models known as <\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/Autoregressive%E2%80%93moving-average_model\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0563c1; font-family: Calibri;\">ARMA<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\"> (my post on <a href=\"https:\/\/marriott-stats.com\/nigels-blog\/forecasting2-do-election-pollsters-show-forecasting-skill\/\" target=\"_blank\" rel=\"noopener\">whether UK pollsters have forecasting skill<\/a> uses ARMA as the dumb or baseline forecast).<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">We therefore have 2 or 3 dumb models (sometimes called baseline models) against which all weather forecasters can be evaluated.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Nate Silver demonstrated in his book (concentrating mostly on the US) that weather forecasters are capable of beating the dumb models for up to a week ahead and that there has been consistent improvement in weather forecasting over the last few decades.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">This is in stark contrast to economists who have shown no improvement over time and indeed struggle to show they are better than dumb models.\u00a0 (see this striking chart looking at <a href=\"https:\/\/twitter.com\/mattyglesias\/status\/1358024776359567360\" target=\"_blank\" rel=\"noopener\">long range predictions of interest rates<\/a>!)<\/span><\/p>\n<h3><strong><span style=\"color: #339966; font-family: Calibri;\">Same Again or Major Change?<\/span><\/strong><\/h3>\n<p><span style=\"color: #000000; font-family: Calibri;\">However, I think it is important to make a distinction between two types of forecasts.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">The first can be characterised as \u201csame again\u201d.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">In other words, your forecast of tomorrow\u2019s weather is that it will be broadly the same as today.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">So my wife can rest easy in a Texas summer knowing that tomorrow she can dress in t-shirt and shorts just as she did today.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Notice, that I am not saying that the forecast is that tomorrow will be exactly the same as today.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">A \u201csame again\u201d forecast is one that does not lead to a different OUTCOME tomorrow.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">In this case, the outcome is deciding what to wear and if the forecast does not lead you to change your planned attire for tomorrow then you are reacting to a \u201csame again\u201d forecast.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">The same can be said for economic forecasts.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">If GDP grows by 2% this year and next year the forecast is for growth of 1.5% and this does not lead you to change your investment plans (say) then to all intents and purposes, a same-again forecast has been made.<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">The second type of forecast is one that calls for major change in outcome or behaviour.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">So a weather forecaster in Texas saying that tomorrow there will be torrential rain and flash floods will clearly cause a change of behaviour from my wife.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Similarly, an economist that forecasts that a vote for Leave will cause a recession is clearly stating that Brexit will lead to major economic impact.<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">In practice of course, the two types of forecast I describe are really the two ends of a full spectrum of forecasts but the simplification I make is a valid one in my opinion.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">After all, Matt Singh\u2019s forecast for the 2015 general election was for \u201cmajor change\u201d from coalition to Conservative majority government whereas I forecast \u201csame again\u201d.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">For the EU referendum, Matt\u2019s forecast was for \u201csame again\u201d since Remain equated to status quo whereas I was on the boundary between \u201csame again\u201d and \u201cmajor change\u201d and unable to decide between the two.<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">Let\u2019s look again at our two dumb forecasting models for weather.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">The first is that tomorrow will be the same as today is a clear \u201csame again\u201d model and by definition will be a good predictor of \u201csame again\u201d events and rubbish at \u201cmajor change\u201d events.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">The second that tomorrow will be the X-year average will good at \u201csame again\u201d and poor at \u201cmajor change\u201d if today is close to the X-year average.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">On the other hand, if today is very different from the X-year average, then it will be poor at \u201csame again\u201d events and good at \u201cmajor change\u201d events.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">The latter point arises from a well-known phenomenon known as \u201c<\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/Regression_toward_the_mean\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0563c1; font-family: Calibri;\">reversion to the mean<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\">\u201d and in my experience is often overlooked by analysts in many industries who seem to prefer \u201csame again\u201d forecasting models.<\/span><\/p>\n<h3><span style=\"color: #008000;\"><strong><span style=\"font-family: Calibri;\">False Positive &amp; False Negative Rates<\/span><\/strong><\/span><\/h3>\n<p><span style=\"color: #000000; font-family: Calibri;\">So when you are evaluating a forecaster, I think there is nothing wrong in producing the following table to summarise their forecasts.<img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-257\" src=\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/GoodForecaster-pic2.png\" alt=\"\" width=\"223\" height=\"147\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">I\u2019ve borrowed two terms from medicine to distinguish between the two types of errors a forecaster can make.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Suppose you are having a test for cancer and the test comes back negative, that can be construed as a \u201csame again\u201d forecast that you do not have cancer.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">A positive test result is a \u201cmajor change\u201d forecast that you do have cancer.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">An incorrect positive test result is called a \u201cfalse positive\u201d and an incorrect negative test result is a \u201cfalse negative\u201d.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">So a forecaster can be evaluated in two ways; their false positive rate which is the % of their \u201cmajor change\u201d forecasts that are wrong and their false negative rate which is the % of their \u201csame again\u201d forecasts that are wrong.<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">Let\u2019s imagine you are comparing two forecasters and trying to decide whether to believe forecaster A or forecaster B.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Forecaster A has a 5% false positive rate and a 40% false negative rate and Forecaster B has a 20% false positive rate and 20% false negative rate.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">A is less likely to \u201ccry wolf\u201d like B does but B is more likely to spot the wolf than A.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Who is better?<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">The boy who cried wolf story is a very apt one for forecasters.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Those who constantly predict doom and gloom will be ignored as the doom fails to materialise but only needs to be correct once to be able to say \u201cI told you so!\u201d<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">On the other hand, the poor track record of doom &amp; gloom merchants makes it hard to trust them and the constant false positives can still have physical and emotional consequences for those that believe and react unnecessarily to the forecasts.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 \u00a0The COVID19 pandemic is in many ways the ultimate test of the boy crying wolf story since we need to predict not only the direct impact of COVID19 deaths and infections but also the direct and indirect impacts of actions and non-actions taken in response.<\/span><\/p>\n<h3><span style=\"color: #339966;\"><strong><span style=\"font-family: Calibri;\">Turkeys, Wolves &amp; Coins<\/span><\/strong><\/span><\/h3>\n<p><span style=\"color: #000000; font-family: Calibri;\">Taleb prefers to use Turkeys instead of Wolves.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">A flock of turkeys will come to believe that the farmer who feeds and looks after them so well is a wonderful person until Thanksgiving &amp; Christmas arrives and their illusions are shattered.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">The point about the Turkey story is that the turkeys have no data at all that will allow them to assign a probability to their existence coming to an abrupt end and therefore are incapable of being able to forecast their imminent demise.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">This is one of the reasons why Taleb believes that forecasts are not important in the first place.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">What matters is your resilience and\/or ability to thrive in spite of forecasting errors.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">This theme is what his book \u201cAnti-Fragile\u201d covers in great depth and provides a very thought-provoking philosophy to consider.<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">In fact, Taleb\u2019s book is much more about risk management than forecasting.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Rather than trying to predict events, one instead manages one\u2019s organisation in order to resist or benefit from risks.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Risk management is a dirty word in Taleb\u2019s world given his own experiences but I am using it as the counter point of forecasting.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">For me, <a href=\"https:\/\/marriott-stats.com\/forecasting\/\" target=\"_blank\" rel=\"noopener\">forecasting and risk management are two sides of the same coin <\/a>and depending on what clients are trying to achieve, the first part of any consultation I do is to decide which side of the coin is more important to the client.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">From that, I can decide what the best modelling approach is.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">By now, I hope I have convinced you that any organisation making a forecast should be evaluated on their forecasting track record rather than their status or credentials.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">In an ideal world, organisations making forecasts should be publishing their track record so that their false positive and false negative rates can be evaluated.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">In particular, the track record should include evidence of the forecast being made ahead of time so that we know that we have a true forecast rather than a hindcast.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">In my opinion, It was thoughts along these lines that prompted Michael Gove\u2019s now famous comment and they are the reasons why I endorse his comments.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0<\/span><\/p>\n<h3><strong><span style=\"color: #339966; font-family: Calibri;\">Forecasts come in 3 flavours<\/span><\/strong><\/h3>\n<p><span style=\"color: #000000; font-family: Calibri;\">I have been assuming that you understand what a forecast is but I want to finish off by defining this in more detail and to illustrate ways forecasters can get it wrong.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">I have already talked about the distinction between numerical forecasts (where we express our predictions as a single number or numerical range) and outcome forecasts (where we express our predictions as a probability of a specific outcome or outcomes occurring).<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">I have also introduced the concept of a dumb forecast as a benchmark for evaluating forecasts.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Together, these highlight a useful distinction in forecasting, namely technical &amp; fundamental forecasting.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">A <strong>TECHNICAL<\/strong> forecast is one that is based on observed trends and patterns in the quantity I am trying to forecast.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">For example, I could look at the chart of UK GDP growth and try to discern a pattern that can be extrapolated into the future.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">So I might observe that the moving average for GDP growth is currently +0.5% and the moving standard deviation is +0.2% and use those figures to predict that GDP growth in 2017 Q1 will be +0.5% (numerical forecast) or that there is a 2 in 3 chance of it being within +\/-0.2% of this figure (numerical range forecast).<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Alternatively I might predict that there is only a 2% chance of negative or no growth which would be an outcome forecast.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-258 alignnone\" src=\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/GoodForecaster-pic3-300x196.jpg\" alt=\"\" width=\"645\" height=\"422\" srcset=\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/GoodForecaster-pic3-300x196.jpg 300w, https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/GoodForecaster-pic3-768x502.jpg 768w, https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/GoodForecaster-pic3-1024x670.jpg 1024w, https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/GoodForecaster-pic3-450x294.jpg 450w, https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2017\/04\/GoodForecaster-pic3.jpg 1222w\" sizes=\"auto, (max-width: 645px) 100vw, 645px\" \/><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">More complicated pattern extraction methods could be used instead and might result in a different technical forecast.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">But in the end, whether complex or simple, technical forecasts are still dumb forecasts as they assume that the trend or pattern identified will be repeated in the future.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">If you are reading a forecast in the news or a report, the clue that it is a technical forecast will be that the only data presented is the quantity being forecast and the pattern or trend will be described.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">A <strong>FUNDAMENTAL<\/strong> forecast is one where a model is used to correlate the quantity we are trying to forecast e.g. GDP, with some other variable e.g. number of job adverts in the UK.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">The forecast will then be based on known values of that other variable and with that knowledge we apply our model to derive an estimate of what the quantity will be in the future.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">So a 10% increase in job adverts might equate to 1% growth in GDP and if we see such growth in the number of adverts, we can make a forecast of GDP.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Again if you are reading a report or news article, the clue that you are reading about a fundamental forecast will be if you see references to two or more variables and a description of the correlation between them.<\/span><\/p>\n<p><span style=\"color: #000000; font-family: Calibri;\">Our 3rd flavour is a forecast based on <strong>SCENARIOS<\/strong>.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">In this type of forecast, a range of scenarios for a variable is put forward e.g. CO2 emissions over the next 20 years, the model is applied to every scenario generating a range of future climates and then from the data generated a forecast is made (point forecast, range or outcome probability).<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Such forecasts should include probabilities of each scenario coming to pass e.g. scenario A might be deemed likely, scenario B unlikely, etc so that one ends up with a weighted average of scenarios.\u00a0\u00a0<\/span><\/p>\n<h3><span style=\"color: #339966;\"><strong><span style=\"font-family: Calibri;\">Detecting bad forecasters<\/span><\/strong><\/span><\/h3>\n<p><span style=\"color: #000000; font-family: Calibri;\">So if you are reading about a recent forecast and you don\u2019t have any information as to the track record of the person making the forecast, how can you sort the wheat from the chaff?<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">The full list of clues is endless and I intend to use my blog to highlight these in future but here are some that I have seen over the years.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000; font-family: Calibri;\"><strong>Cherry picking your history<\/strong> \u2013 In the GDP chart, I think you can see that GDP growth used to be much more volatile in the past until around 1990.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Since then, growth has been more consistent.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Too often, forecasters will cut off their history at some date and only use the data since that date.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Taleb is especially critical of this thought process and believes the financial crisis of 2008 was partly brought on by this kind of thinking.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">That doesn\u2019t mean that all history has to be used equally, you can give less weight to some periods of time than others but it is wrong to give zero weight to some data if the data is available. <\/span><\/li>\n<li><span style=\"color: #000000; font-family: Calibri;\"><strong>Failure of imagination with scenarios<\/strong> \u2013 A similar error can occur with scenario based forecasts.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">If the forecast is based on a limited range of scenarios or even rules out certain scenarios, it is guilty of cherry picking as with point 1.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Again it is reasonable to give more weight to certain scenarios than others provided the reasoning is explained but no scenario should be ruled out as impossible.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Lack of imagination is a common problem with scenario forecasts as I found to my cost with <a href=\"https:\/\/marriott-stats.com\/nigels-blog\/by-election-model-2-review-of-copeland-stoke-central-predictions\/\" target=\"_blank\" rel=\"noopener\">my forecast of the Stoke Central by-election<\/a>!<\/span><\/li>\n<li><span style=\"color: #000000; font-family: Calibri;\"><strong>Fundamental forecasts based on a scenario<\/strong> \u2013 a problem with fundamental models is that in order to make a forecast of the future, you need to forecast the input variable as well.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">So in my GDP example earlier, to make a forecast of GDP in a year\u2019s time, I have to predict how many jobs will be advertised next year.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">This just adds uncertainty to the forecast so what some people do instead is imagine a specific scenario in a year\u2019s time with job adverts and then use the model to make the GDP forecast.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Except that this is not a forecast!<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">It is a single scenario only.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">This is a surprisingly common error and sometimes hard to catch.\u00a0 Sir Patrick Vallance, the UK Chief Scientific Officer, found this out in September 2020 <a href=\"https:\/\/www.telegraph.co.uk\/news\/2020\/09\/21\/implausible-scientists-hit-warning-50000-covid-cases-day\/\" target=\"_blank\" rel=\"noopener\">when presenting a scenario that the government wanted to avoid<\/a> (outcome was they avoided it within their stated timescale but ended in that scenario 6 weeks later).<\/span><\/li>\n<li><span style=\"color: #000000; font-family: Calibri;\"><strong>Post-hoc explanation of history<\/strong> \u2013 when making technical forecasts, all one should be doing is extrapolating the pattern or trend.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Being human we often want to explain why we see the history that we do.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">As noted in point 1, UK GDP growth was steadier after 1990 so it is natural to ask why.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Three things that come to mind are the collapse of communism, the start of the single market in the EU and Britain being kicked out of the ERM.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Unless you can build proper statistical models of these effects, such apparent explanations can be no more than co-incidence of timing and have to be treated as hypotheses.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Unfortunately, articles do get written which use such coincidences as a way of explaining why something will or will not happen in the future.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">A recent example was explored in this BBC article on <\/span><a href=\"http:\/\/www.bbc.co.uk\/news\/magazine-39366596\"><span style=\"color: #0563c1; font-family: Calibri;\">whether baby boxes will help reduce infant mortality<\/span><\/a><span style=\"color: #000000; font-family: Calibri;\">.<\/span><\/li>\n<\/ol>\n<p><span style=\"color: #000000; font-family: Calibri;\">So there you have it, my guide on how to identify a good forecaster.<\/span><span style=\"color: #000000; font-family: Calibri;\">\u00a0 <\/span><span style=\"color: #000000; font-family: Calibri;\">Please do look out for future posts where I illustrate the good, bad and ugly of forecasting.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong><span style=\"color: #993300;\">&#8212; Subscribe to my newsletter to receive more articles like this one! &#8212;-<\/span><\/strong><\/p>\n<p>If you would like to receive notifications from me of news, articles and offers relating to weather, please <strong><a href=\"https:\/\/marriott-stats.com\/nigels-blog\/subscribe-to-our-newsletter\/\" target=\"_blank\" rel=\"noopener\">click here to go to my Newsletter Subscription page<\/a><\/strong> and tick the Forecasting category and other categories that may be of interest to you.\u00a0 You will be able to unsubscribe at anytime.<\/p>\n<p><span style=\"color: #993300;\"><strong>&#8212; Want to read more articles about Forecasting? &#8212;<\/strong><\/span><\/p>\n<p>Please click on the <a href=\"https:\/\/marriott-stats.com\/nigels-blog\/category\/forecasting\/\" target=\"_blank\" rel=\"noopener\">Forecasting tab at the top of the screen<\/a> to a see a list of my forecasting posts in reverse chronological.\u00a0 Alternatively, click on <a href=\"https:\/\/marriott-stats.com\/nigels-blog\/stats-training-materials-forecasting-risk-modelling\/\" target=\"_blank\" rel=\"noopener\">this link to see a list<\/a> of my most relevant posts sorted by theme.\u00a0 The latter link forms part of my training course &#8220;<a href=\"https:\/\/marriott-stats.com\/identifying-trends-in-data-making-forecasts\/\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #008000;\"><em>Identifying Trends &amp; Making Forecasts<\/em><\/span><\/strong><\/a>&#8220;.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u201cI think the people in this country have had enough of experts\u201d Michael Gove, Sky News, 3rd June 2016 This was one of the most memorable quotes during the EU referendum in 2016 and came in response to a question as to why the forecasts of a whole list of organisations such as the IMF [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":257,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[9,6],"tags":[24,39,18,25,14],"class_list":{"0":"post-255","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-featured-blog","8":"category-forecasting","9":"tag-eu-referendum","10":"tag-experts","11":"tag-forecasting","12":"tag-forecasting-model","13":"tag-forecasts","14":"entry","15":"override"},"_links":{"self":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts\/255","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/comments?post=255"}],"version-history":[{"count":11,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts\/255\/revisions"}],"predecessor-version":[{"id":3565,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/posts\/255\/revisions\/3565"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/media\/257"}],"wp:attachment":[{"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/media?parent=255"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/categories?post=255"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/marriott-stats.com\/nigels-blog\/wp-json\/wp\/v2\/tags?post=255"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}