I often get asked for a POV on this, so I guess a lot of people are asking the same question.

Recap: What are Priors?

In a Bayesian media mix model, priors are simply what you believe the results might be before you look at the data or do any modelling. Think of them as expressing real-world knowledge — like “it’s very unlikely that my sales go down when I spend more on advertising” — in mathematical language. [5].

My view, in summary: Priors introduce risks of bias which can undermine model integrity — particularly when the priors are derived from last‑touch, platform‑reported metrics or poorly specified experiments. The core issues are that last touch platform reporting is biased to last touch and therefore inaccurate, and experiments are rarely undertaken with the levels of statistical rigour required to make them reliable.

Potential Advantages of Using Priors

Let’s look at the potential advantages of using priors.

1. The biggest argument for Bayesian Priors is that they reduce uncertainty in an MMM environment. Bayesian MMM doesn’t just give you a single point estimate for the impact of each marketing channel. It provides a probability distribution of possible impacts… This allows you to understand the uncertainty associated with the estimates, leading to more informed decision-making [6].
2. Model outputs (e.g. CPA by channel) look “right” and are relatable in the real world: To a large extent, priors fix the model outcomes into sets of values that seem to match the marketing team’s expectations and experience.
3. Priors can help when the data available for modelling is limited: Sometimes there isn’t sufficient spend data to accurate estimate coefficients for media channel performance. Spend may be too low, or the spend in one channel is drowned out by higher spends in other channels at the same time, or the number of weeks with spend may be very low. In these situations, priors can help by preventing coefficients from collapsing toward zero because the data is weak.
4. Priors help when spend variables are highly correlated: Many media campaigns feature multiple channels running at the same time campaigns often take place over 2–8-week periods with media channels being combined to extend reach or delivery efficiency frequency. This means input variables are highly correlated with each other which is a problem for regression models – they can’t isolate the effects of correlated channels. Using priors in a model helps the model find clarity by providing guides to what channels effects should be.

Key Risks and Limitations

1. Priors are beliefs, not data, so they risk injecting bias into your model: A key issue is that Priors are beliefs about media performance. Because they are beliefs about media performance e.g. “our Last Touch Social CPA is always between £10 and £20, so let’s fix that range into our MMM results” – we risk using those findings to inform the model outcomes – clearly this is a form of confirmation bias [7].
2. Priors often rely on inaccurate last‑touch or platform‑reported ROI Data: In practice, most priors come from platform dashboards rather than controlled experiments. The problem with platforms is that they generally provide last touch attribution (sometimes, first etc, but never full funnel i.e. including trend and seasonality an marketing mix variables for example).  This means that from the “get-go” Last Touch reporting is inaccurate – our industry knows that- so why use these results as priors in MMM?  But obviously using Last Touch platform sourced priors is only going to transfer that uncertainty directly into your marketing mix model. This is ironic because most MMMs are commission to provide an alternative view to Last Touch reporting.
3. Priors can pull MMM results toward last‑touch, and away from more statistically reliable findings: One of the big arguments for using priors is that they keep MMM results grounded in reality. But if you are using priors, you are creating an artificial result. If the prior is biased (e.g. towards last touch reporting), the model output will also be biased. Whilst this can make the MMM appear more aligned with platform reporting, but that alignment is artificial and the results are erroneous.
4. Priors can destabilise other coefficients: Let’s go back to high school maths. We know that equations have to balance on both sides – output e.g. Sales on the left, inputs e.g. media spend on the right. If we fix one or more of the input components of our equation on the right, other parts of it will have to move in order to accommodate that prior fix. This means your model will almost certainly inflate some media channels, suppress other, channels especially upper‑funnel media and produce inaccurate results
5. Priors reduce transparency: Stakeholders often struggle to understand how much of a coefficient is “data‑driven” versus “prior‑driven,” which can undermine trust.
6. Priors can mask genuine performance shifts: If a channel’s true effectiveness changes (e.g., due to creative fatigue, privacy changes, or market dynamics), a strong prior can prevent the model from detecting it. Equally performance might improve – dramatically. Let’s say you launch a new social media campaign with a new offer and new creative. Your MMM Social CPA falls from between £10 and £20 to £5. That means your social campaign has become much more effective. But MMM priors would likely exclude that result – or at least suggest it is unrealistic.
7. Priors Do Not Include Adstock or Diminishing Returns: There is a common belief that priors somehow incorporate adstock or saturation assumptions. They do not. Adstock and diminishing returns are structural modelling choices — they define how media works overtime and at different spend levels. They are often subjectively judged but they can and should be extracted from the MMM dataset itself using a grid search loss minimisation technique [8].   This can’t be circumnavigated by experiments as Adstock and diminishing returns are critical parts of advertising evaluation [9]. They can only be determined from  long time-series datasets, not short‑term experiments.
8. Priors can come from experiments, but these are notoriously difficult to get right: Priors can be defensible when grounded in rigorous, repeatable experiments. However, this is a technically demanding area. Getting marketing experiements right requires:
   1. Clean treatment and control regions
   2. No spillover
   3. Stable delivery
   4. Repeatability
   5. Sufficient spend, time and statistical power

In practice, achieving this level of scientific discipline in marketing experiments is difficult. Geographical regions can be more fluid than they look on a map – we live in a mobile world when people can move from one region to another in very short periods of time. [10].

Real‑World Example: Identical Creative, Different Results

There have been cases where a team ran an A/B test using the same creative in both treatment and control. Despite being identical, the experiment produced different lift results for each “creative.”  This highlights how algorithmic targeting, user heterogeneity, and data aggregation conspire to confound the magnitude, and even the sign, of ad A/B test result [11]. If identical creatives can produce different results, it shows how fragile and noisy marketing experiments can be — and why they often lack the stability required to serve as robust priors.

Conclusion:

I conclude with these points:

1. Avoid using Bayesian priors if you want a high integrity MMM.
2. Not using priors may produce more challenging results – but isn’t that what you want? You are building your MMM to get a different perspective on your marketing performance; to identify hidden opporutunities and to improve marketing ROIs. Why gloss over that valuable insight?
3. This may result in a more challenging conversation with the C-suite – but it’s safter to report a challenging result from a high integrity model than any result from a flawed model.
4. If you use priors to shape the answer, then the answer will look better. That doesn’t mean it’s the right answer, in as much as any model can produce the right answer.
5. Priors introduce confirmation bias into your model. If you believe the enemy of good modelling is bias, you must question the use of priors in your MMM project. They may be acceptable to some, but not to others.
6. If you are going to use priors, you must be very careful about where you source them. There are three main sources – Experience, Platforms and Experiments, but all have flaws and all run the risk of introducing bias into your model.

Implications for Marketers – checklist

• If you are going to use priors you must be certain that they are accurate.
• Be aware that in most marketing contexts the risks of priors being inaccurate are high.
• Don’t rely on last touch data for priors.
• If you use experiments, ensure they are properly specified, and even then, use them with care.
• In cases where you have too little data for full MMM, be careful about using Bayesian priors to overcome this problem
• In data light situations, consider reviewing your data, accepting lower granularity or looking at a different attribution modelling technique like regularisation.

References

1. J Martin and P Perez, Frequentists vs Bayesians and Marketing Science, Quantified Nation, July 2024 – https://open.substack.com/pub/quantifiednation/p/qn9-frequentists-vs-bayesians-and
2. Hits and Misses of Meridian – A Thorough Deep Dive, Aryma Labs Feb 2025 https://arymalabs.substack.com/p/hits-and-misses-of-meridian-a-thorough
3. Duncan Stoddard, Is Bayesian MMM worth the faff? DS Analytics Blog, February 2024, https://dsanalytics.co.uk/thoughts/is-bayesian-mmm-worth-the-faff
4. Two key problems that ail Bayesian MMM – Aryma Labs April 2024 https://arymalabs.substack.com/p/two-key-problems-that-ails-bayesian
5. Marty Sanchez, What Are Priors in MMM – And Why They’re Difficult to Get Right (But You Need To) Get Recast Blog June 2025 – https://getrecast.com/what-are-priors-in-mmm-and-why-theyre-difficult-to-get-right-but-you-need-to/
6. Rohit Nair, What is Bayesian MMM & why use it? Medium April 2025 – https://medium.com/@rohitnair.inft/what-is-bayesian-mmm-why-use-it-942d0193e7eb
7. Cognitive bias and data: how human psychology impacts data interpretation – Penn LLPS Features October 2025 https://lpsonline.sas.upenn.edu/features/cognitive-bias-and-data-how-human-psychology-impacts-data-interpretation
8. Nephade, D., A Predictive Modeling Approach to Multi Objective Marketing Mix Optimization: Balancing Performance, Acquisition, and Efficiency – in International Journal on Science and Technology (IJSAT) Volume 16, Issue 1, January-March 2025.
9. Gijsenberg et al., Understanding the Role of Adstock in Advertising Decisions, SSRN, 2011.
10. Tyler Buffington, Eppo, The Bet test – Spotting Problems in Bayesian A/B Test Analysis Dec 2024, https://www.geteppo.com/blog/the-bet-test-problems-in-bayesian-ab-test-analysis
11. Braun and Schwartz, Where A/B Testing Goes Wrong: How Divergent Delivery Affects What Online Experiments Cannot (and Can) Tell You About How Customers Respond to Advertising, Journal of Marketing, American Marketing Association, August 2024. https://journals.sagepub.com/doi/abs/10.1177/00222429241275886

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This paper defines the marketing attribution problem and looks at the ways marketers can generate an accurate view of their return on marketing and media investment.

There are lots of views, approaches and tools available to assist marketers with marketing and media attribution but unfortunately, most are limited in one way or another and some are actually dangerously misleading.

This paper aims to sort the wheat from the chaff when it comes to attribution – especially in paid media environments.

First, let’s define the problem attribution modelling seeks to solve.

Marketers are investing large sums of money for their companies and and for many larger brands, that money is often shareholder funds. Marketers therefore have a responsibility to ensure that their budgets are being invested optimally.

The marketing ecosystem is much more complex than it appears; different channels work in different ways across the marketing funnel. And, in addition, the channels that present sales are not necessarily the channels that drive sales. Moreover, what appears to be a cause often isn’t; before marketers can make judgements about their own investments they must strip out the effect of extraneous factors like competitors, pricing, climate, the economy, seasonally and any other variables that may have an impact on how their own sales are, or are not generated. Failure to consider all these effects will ultimately lead to flawed analysis.

Inaccurate analysis will lead to poorly informed media investment decisions at best and ineffective – potentially loss making – media investment decisions at worst. With media budgets running into millions, those mistakes can be expensive.

So it’s critical that the best approaches are used. Anything less carries risk. Let’s take a look at some of the main forms of attribution here:

1 – Last touch media attribution

Last touch attribution is the most readily available but potentially most misleading form of marketing attribution. Last touch measures the last journey point that consumers touched before they reached your business or brand. Usually this is a google search, but it could also be a banner view or click or a visit to an aggregator. Either way, it’s the last action the performed before they visited your site visit or call centre. All these touch points can be measured – Google produces a full suite of last touch metrics via Google Analytics and GA360. Direct site visits can be measured by your own web stats package or GA. Phone calls can be measured and attributed to a source through the use of unique phone numbers.

Because these last touch channels are so readily measurable and can be linked so closely with sales it’s tempting to make them the sole focus of your attribution analysis. But there’s a problem here – focusing your attribution measurement on last touches doesn’t give any insight into the previous interactions in the customer journey i.e. what consumers were doing just before that last touch – in other words, what really drove them to you. This could mean you fail to spot the important stages in the customer journey before you see that last touch.

Let’s look at an example: a consumer follows a typical need-research-shortlisting-choice-purchase customer journey. A number of influences will be at play in the early stages of this process – a display, AV or outdoor ad may encourage our consumer to say “I must do something about that <problem>. The prospect may wait a few days and then another AV ad re-prompts a visit to solving the problem. The consumer then moves to the “information search” stage of the buying process – they may use Google, they may visit a retailer, they may visit a brand directly – in the case of financial services, they may visit an aggregator. Still no final decision though. And then they receive a bill from their current supplier. At that point they perform a brand search and review competitors. From this brand search our prospect shortlists three potential suppliers and then another AV ad prompts them to undertake another brand search and make a final purchase.

We can see this is a complex journey with many touch points. The last touch is a tiny part of the journey. It’s the last one you see, but it is by no means the only one.

This means that rather than focusing on the last touch you have to find out how where credit is due in the customer journey.

2 – ‘Artificial’ attribution models

One of the most popular ways of attributing across the journey is to use a predefined attribution model to break prospect journeys into a number of stages. The best example of these is six variants often used in digital marketing – last touch, first touch, even weight across all touch points etc. These models aim to split the responsibility (and revenue) for driving the prospect to your business across several pre-last touch points.

Unfortunately, there is often very little factual basis in these models. The postulated pre-last touch pattern is little more than an unproven hypothesis of what might have happened in the journey. As such, artificial models offer little or no scientific value to discerning marketers.

3 – Direct URL or phone number tracking

This approach – sometimes called “linear” tracking – was originally developed by traditional direct marketers. They used coupon codes and later unique phone numbers to track the origin of sales back to different ads and media channels. As the internet grew, this approach was trialled by digital marketers using unique page URLs. However, whilst unique phone numbers were a reliable way of capturing the last touch, the web URL approach was not. Consumers tend to search brands and products they’ve seen advertised, or distinctive phrases that have lodged in their memory – “compare the meerkat / market” for example. But consumers don’t search www.abtaholidays.com / tube. And, in any event, direct tracking does not move us beyond the last touch attribution problem.

4 – Universal Journey Tracking

Universal tracking can only be implemented in digital environments. It involves setting a tracking tag or cookie at each touch point – a banner ad view, an email opening or a site visit. If each tag is time-stamped it is possible to plot the chronology of the different times and channels in which views or visits were made and the tag was activated. This allows analysts to plot the journey before, up to and including the last click. Setting up this type of campaign can enable a reasonable amount of journey reporting through DV360, GA360 or simple GA. but the problem here is that this type of tracking is restricted to digital only environments. It can’t be deployed in offline media – and it’s often offline media that drives the upper funnel by providing high reach and scale-up opportunities. So, for many brands the challenge is to understand the relationships between upper, mid and low funnel activities.

5 – Attribution through patterns, trends and correlation

What are the options if you want to move beyond last touch or linear tracking to get an understanding of how your marketing and media drives clicks, leads, calls, sales and market share?

There are two options here – econometrics or simple trend and correlation analysis. We will cover econometrics in point 6 – first, let’s look at more simple correlation analysis.

When marketers run a campaign they usually have an objective to change a variable. Let’s call it sales. In the statistical space, the sale becomes the “dependent variable” – that means it’s the variable we are trying to change by applying different “forces” to it. We might apply TV, OOH, press, radio or digital advertising to drive reach, brand uplift and visits.

By collecting daily or weekly levels of investment over time in each media channel, alongside the dependent variable, it will be possible to observe whether any one or combination of media channels are correlated with changes in our dependent variable.

So we might observe for example, that direct web traffic increases are highly correlated with a new TV campaign.

Some TV “spot matching” tools like Adalyser and TVSquared fall into this category. These tools match two trend datasets – TV impacts over time and web or call traffic over the same period – often on a minute by minute basis.

These trend approaches based on time-series data give us a much clearer picture than “last touch” metrics. “Last touch” would simply observe an increase, but it wouldn’t necessarily explain why it was happening – especially if the driver variable/s are outside the digital ecosystem. But trend analysis has an Achilles heel – any changes observed must be separated from what might have happened if no advertising had run at all. This “baseline” question is a key issue in trend analysis and only econometrics can solve it correctly.

6 – Econometrics / Market and Media Mix Modelling

The trend analysis outlined in point 5 above takes us to a more sophisticated level of multi-channel attribution. But it doesn’t consider the external factors that shape the effectiveness of our own advertising – things like underlying seasonality, competitor spend, price promotions, incentives, consumer confidence, weather and even house prices and other wider economic measures like RPI and unemployment. It’s only when you consider your own marketing investments within the context of all the factors that you have the full and clear picture of your marketing effectiveness.

And that’s where econometrics comes in. Econometrics considers all these factors and attaches a value to them – positive, negative or neutral. It will also help you understand what the unique impact of these factors is and it will also allow to identify factors that work together.

But most importantly, econometrics allows you to understand how your brand, promotions, media and pricing sit in the context of the way your category works and in particular the impact of competitors.

Econometrics also gets marketers and media planners over the “last touch” problem because it allows you to quantify the effects of all channel metrics on sales. It will reveal the effect of all upper funnel channels sales channels – so for example – econometrics will tell you how many sales TV generates but it will also tell you how the sales generated by TV distribute across all lower funnel channels like search, direct traffic, phone and retail.

So in any time period econometrics can attribute your total sales back from the channel where they appeared to the channel that generated them – whether online or offline – with consideration for all factors driving sales and therefore with a high degree of accuracy.

Conclusion

Because of the sums being invested and the value of the results at stake, marketing and media attribution are core responsibility areas for marketing directors, CMOs and agency media practitioners. But it’s a field where last touch linear metrics offer a tempting but misleading view of how marketing and media investments really work. More sophisticated approaches require a wide number of datasets and take time to enable, but they give you a much more accurate view of how your investments are working. The time and patience required to deploy advanced techniques will pay off and enable you to fully understand how these investments work and optimise them to produce the best possible results.

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Before we get into the techniques themselves you will see that one recurring theme is the impact of ‘extraneous variables’ – that is the impact of factors beyond or outside the media campaign itself. The six main extraneous variables are:

1. Competitor spend – almost all companies and brands have competitors. Competitor spends can have an impact on your campaign, usually by taking business away from you. You will need to quantify this effect before you can make statements about your campaign’s effectiveness.
2. Distribution – if you have uneven distribution of a product or service or if you have a shortage of a given product, this will impact on the results you report.
3. Economy – two economic variables are known to have an effect on marketing and media performance are interest rates and consumer confidence  – both of which can have a positive or negative effect on consumer spending. When confidence is high consumers spend more and campaigns perform better. You will need to understand how this affects your own campaign performance.
4. Seasonality – most markets have inherent seasonality which can have a powerful effect on sales patterns. If you are evaluating activity in seasonal peaks or troughs, you must account for the seasonality effect.
5. Pricing – price remains an important influence on consumer behaviour. If you have a 50% off sale, you will generate higher traffic and sales response than in a period of normal pricing. If your competitors are using pricing aggressively, this will also have an impact on your media ROI. You will need to take account of this.
6. Weather – many product sales are influenced by weather. Good weather can increase sales, bad weather can decrease ales, or vice versa. Again you will need to take account of this in any meaningful analysis of media ROI.

Why are extraneous variables important?

Extraneous variables can have a major influence on the results your campaigns generate. At best they can render any top-line results erroneous. At worse, the impact of extraneous variables could lead you down the route of making suboptimal media investment decisions which could damage your ROI.

Here is a short summary of the main media advertising evaluation techniques available and a note on whether or not extraneous variables are considered:

1. Linear data reporting
   • Involves the use of response codes, phone number tracking, SMS number tracking, drop downs or tick box menus to ask consumers how they found you
   • Tends to report only the last touch or last click i.e. the last thing the consumer remembers seeing before they connected with you
   • This tends to favour lower funnel channels like PPC and DM
   • Findings tend to reflect what the consumer thinks motivated them to interact
   • Works very well if you are only running one channel and one campaign, but can produce dangerously misleading results in a multi-channel environment
   • Limited to observed data only
   • Does not account for extraneous variables eg competitor spend, economy, pricing, seasonality or weather
2. Descriptive data reporting 
   • Basic counting of descriptive results e.g. web traffic during a TV campaign
   • Plots traffic before, during and after campaigns
   • Should be possible to measure and plot uplifts in campaign period (e.g. YoY)
   • Incremental traffic can be plotted against TV spend to calculate incremental CPC
   • Limited to observed data only
   • Does not account for extraneous variables eg competitor spend, economy, pricing, seasonality or weather
3. Uplift Analysis
   • Similar to 2 above but looks at the effects of media spend within a sales funnel or database
   • So, did sales conversion rates increase or bounce rates fall?
   • Did enquiries from current customers increase?
   • Did churn rates fall?
   • Does not account for extraneous variables eg competitor spend, economy, pricing, seasonality or weather
4. Correlation and Regression
   • Looks for basic statistical relationships in-campaign between media spend and a response variable eg web traffic
   • Allows advertisers to measure relationship between spend and response e.g. for every £1000 spend 2,000 clicks appear to be delivered
   • Limited to observed data only
   • Does not account for extraneous variables eg competitor spend, economy, pricing, seasonality or weather
5. Multiple Regression
   • Uses statistical modelling to estimate (I use the word “estimate” in a  statistical sense) the effect of multiple independent variables (e.g. adspend by channel) on a dependent or target variable e.g. web traffic new users
   • Can be structured to account for extraneous variables eg competitor spend, economy, pricing, seasonality or weather
6. Non-Linear multiple regression (AKA econometrics or Media Mix Models)
   • More advanced version of 5 above which incorporates the estimation of non-linear effects
   • Examples of non-linear effects include AdStock (the rate at which advertising spend effect decays over time) and diminishing returns (the rate at which adspend becomes less efficient as spend is increased).
   • Requires time series data covering multiple years to incorporate seasonal patterns in data
   • Requires at least 100 observations of data (e.g. weeks)
   • Will account for extraneous factors such as seasonality, competition, pricing or weather

All approaches are data dependent which means that if you are not collecting response or sales data you will need to.

Costs for implementation can vary but should always be viewed in the context of the potential savings that can be made from subsequent optimisation. For example, if an econometric media mix model costs £25k, but can optimise a £2.5m budget to save £500k, then the £25k is money very well spent.

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