05:15 Outro

With the result now clear, there’s no point in further forecasts.

I hope that the forecasts I’ve provided have been useful. If you’ve made a lot of money on the basis of these forecasts, you might want to consider donating to the Jo Cox fund.

I’d like to thank Maeva Bouda, an intern here at the University of East Anglia, for helping me with data entry through the night.

On a personal note, I should say that I am tremendously disappointed by this result.

In particular, I'm disappointed that the referendum has been won by a campaign both mendacious and nasty. I think the decision to Leave will greatly damage the country, and I think some of that is already clear from the reactions of the markets.

05:04 Eighth and final forecast update

This is my final forecast. The only forecast quantity that matters is the vote share for Remain.

Predicted vote share for Remain: 47.8 percent.

(90% prediction interval: 47.3 to 48.2 percent)

Predicted vote share for Leave: 52.2 percent.

(90% prediction interval: 51.8 to 52.7 percent)

04:41 Competitors weigh in

ITV called the result for Leave at 04:36; BBC have just followed at 4:41am.

04:30 Seventh forecast update

Predicted probability of Britain Remaining: 0

(189 of 382 areas reporting.)

Predicted vote share for Remain: 47.8 percent.

(90% prediction interval: 47.2 to 48.3 percent)

Once again, Remain drift upwards, but only by 0.2 percentage points.

04:00 Sixth forecast update

Predicted probability of Britain Remaining: 0

(152 of 382 areas reporting)

Predicted vote share for Remain: 47.6 percent.

(90% prediction interval: 47 to 48.2 percent)

Remain vote share is edging up slightly, but only slightly. It's awkward for the Betfair over/under market on Remain < 47.5%.

03:30 What the markets say

Implied probability of Brexit on Betfair is now 0.66.

Pound is down from 1.50 to the dollar before 10pm, to 1.40 now. That's an insane movement.

03:00 Fifth forecast update

My predictions continue to be much more pessimistic for Remain than the betting markets, though they seem to be in between estimates from Michael Thrasher and JP Morgan.

Predicted probability of Britain Remaining: 0

(81 of 382 areas reporting.)

Predicted vote share for Remain: 47.1 percent.

(90% prediction interval: 46.1 to 48.1 percent)

02:08 Fourth forecast update

This is a big update, and I'm conscious that I may have made a terrible mistake somewhere in estimating differential turnout, but here goes:

Predicted probability of Britain Remaining: 0.03

(33 of 382 areas reporting.)

Predicted vote share for Remain: 47.5 percent.

(90% prediction interval: 45.5 to 49.6 percent)

01:46 Third forecast update

Predicted probability of Britain Remaining: 0.32

(15 of 382 areas reporting.)

Predicted vote share for Remain: 48.9 percent.

(90% prediction interval: 44.5 to 53.3 percent)

01:17 Second forecast update

Predicted probability of Britain Remaining: 0.55

(10 of 382 areas reporting.)

Predicted vote share for Remain: 50.2 percent.

(90% prediction interval: 45.1 to 54.9 percent)

Best not to read too much in the probability when that predicted vote share is so close to 50:50.

01:06 In between forecasts

We’re at a bit of a lull in the results. There are a couple of results not yet included in the forecast, but we’ll hold off a little while before the next update.

So far the results have been better than expected for Leave. However, it’s not yet clear whether this is because Leave is doing better everywhere, or because Leave is doing better in areas which (with the exception of Newcastle) Leave was already expected to do well.

00:19 First forecast update

Predicted probability of Britain Remaining: 0.48

(5 of 382 areas reporting.)

Predicted vote share for Remain: 49.8 percent.

(90% prediction interval: 42.7 to 56.8 percent)

23:39 Gibraltar

Remain win 96% of the vote in Gibraltar — but we’ll hold off updating our forecast.

23:33 What do the betting markets say?

Some stats from Betfair:

Implied probability of Remain vote: 88.7%

Implied probability of Remain vote > 52.5%: 69%

Implied probability of Remain vote > 54.5%: 48%

23:09 Our baseline

Our baseline is the following:

Predicted probability of Britain Remaining: 0.52

Predicted vote share for Remain: 50.5 percent.

(90% prediction interval: 41.4 to 59.9 percent)

Which is near enough a tie, give or take Monte Carlo error and a bit of fun with variable turnout. You might think that’s been overtaken by events (or recent polls), but we’ll be trying to keep these predictions based as much as possible on the results.

22:51 Our forecast model

We’ll be basing these forecasts on a model of how each area will vote. This model is based on some preparatory work done by Chris (discussed here and here, though some of these have been subsequently adjusted slightly), which gives us estimates of how each area would vote in a tied referendum. Using these estimates, we can adjust our estimates of how well each side is doing as the results come in. We needn’t wait for a large number of results before we can come out with some informed guesses about the outcome.

(Technical details: this is a linear regression with a single intercept and a single predictor, namely the local authority estimates. There are informative priors on both intercept and predictor variables. You can find a writeup of a similar model I did for the Scottish independence referendum here).

22:42 What we hope to give you throughout the night

Over the course of tonight, we’ll be providing rolling forecasts of the probability that Britain will stay in the European Union, and our best guess as to the share of the vote won by the Remain option.

We’ll also be providing a 90% forecast interval of the share of the vote won by Remain. That interval will start of large, and get narrower as the evening progresses. You’ll want to bear that in mind throughout.