While pollsters have the result of the UK's EU referendum as too close to call, the bookies have Remain comfortably ahead. Prof David Bell will be monitoring the odds through the remaining campaign with results updated here. Updated chart - 16 June 2016.

Update, April 26

The latest data from the betting odds show a significant reduction in the probability of a Leave vote in the last week. It started with the Treasury’s gloomy view of Britain’s prospects outside the EU, which brought the slight increase in the leave probability from the beginning of April to a halt.

The downturn accelerated after Barack Obama argued that the UK would be at the back of the queue for a trade deal with the US. Even though he moderated this statement subsequently, the implied probability of leaving the EU fell from 0.34 to 0.31 last week – the sharpest fall in the bookies' odds so far. It is not possible to show whether Boris Johnson’s intervention further accelerated the decline, but it is interesting that his decision to join the Leave campaign has also coincided with a period of lengthening odds on that outcome.

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The BREXIT referendum will be held on June 23. The latest opinion polls put the “remain” and “leave” campaigns neck and neck. But the reputation of opinion polls has plummeted following their abject failure to predict the winner of last year’s general election. This has been linked by the Sturgis Review to inadequate sampling procedures leading to biased estimates of party support.

Prediction markets, which are often based on betting odds, are an increasingly popular alternative to opinion polling for predicting election outcomes. This popularity is based on their relative success in forecasting election outcomes.

Betting data is collected continuously and on a consistent basis. Opinion polling tends to be irregular and noisy because of the different sampling methods used by the various companies that are involved.

The prediction markets approach successfully forecast the outcome of the Scottish referendum. Whereas the opinion polls suggested the outcome was uncertain, the betting odds suggested that the probability of a majority vote for independence was always quite small.

So what are the odds for the BREXIT referendum? The most recent data suggest that the probability of a “remain” vote is around 70%, with the chance of a “leave” vote being correspondingly around 30%. These data are based on the website www.oddschecker.com, which lists more than 20 companies which have offered odds on the BREXIT referendum at different times. Most are currently active, given the increasing level of interest in the outcome.  The most active company is Matchbook, which frequently offers multiple small variations in its odds during a single day. The odds from the different companies are transformed into estimates of the average daily probability for each outcome. The figure shows the evolution of these odds since the beginning of February. It also shows the timing of some key events which might have been expected to influence the odds. Of course some of these may have been expected and therefore already discounted by punters.

Some may have been genuine surprises, in which case an immediate impact could be expected. Arguably Iain Duncan Smith’s resignation was a surprise, but had little impact on the odds, suggesting that those placing bets did not feel that this event would have a significant effect on the referendum outcome. Similarly, Boris’s decision to throw his weight behind the leave campaign had little impact on the odds.

What is clear is that there has been a gradual whittling away of the advantage enjoyed by the remain campaign since the beginning of March. When the referendum was called, the probability of leaving was around 29%. It fell to 27% in early March, but has been rising since, before levelling off in the last few days of March. The most recent data, for April 6, suggests that this probability has risen above 32%. Even so, there is still a clear feeling among those with a monetary interest in the outcome that the UK will remain part of the European Union.