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# Our final predictions: 95% credible interval

One big thing we’ve tried to stress on this blog is the role of uncertainty in making predictions. This post is about the uncertainty around our final seat count predictions. With our Monte Carlo simulations, we simulate 100,000 elections and the predictions are the average number of seats each party will win. But as we’ve shown before, there is a distribution of outcomes. The shape of this distribution depends on the covariance structure between seats. We don’t know what this is, so we run two models representing two extreme cases: an independent seats model and a maximum covariance model. Here is the distribution when we assume independence between seats:

What we’d like to do now is provide the 95% credible interval for the predictions. What the hell is a 95% credible interval? Most of you would have heard of a 95% confidence interval which is based off repeated sampling. We don’t have that here. A credible interval is much simpler to interpret. We had 100,000 simulations – a 95% credible interval tells us the range of outcomes which cover 95% of the simulations. The 95% credible interval for the independence model:

a. ALP: 43-53 seats

b. Coalition: 94-104 seats

So in 95% of our simulations, the ALP will win between 43-53 seats and the Coalition will win between 94-104 seats. Really should have put money on the result a few weeks back!

The distribution under the maximum covariance model is a bit more funky looking. It’s not a classical bell shape, with the extremes having the highest probability. The reason for this was discussed in a previous blog post. Unsurprisingly, the variance of this distribution is greater than under the independence model.

The 95% credible interval for the maximum covariance model

a. ALP: 32-64 seats

b. Coalition: 84-114 seats

With this maximum covariance model, the credible intervals are wider.

Note that there is zero probability of a Labor victory under both models.

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# Probability Distributions

In the last post, we showed some early probability distributions that model the number of seats each party would win, and the associated probabilities. Probability distributions are perhaps not polite dinner party conversation topics (K and I have made this mistake many a time) but they are hugely important. Its a neat way to represent the degree of uncertainty about the outcome of certain events. The only thing we know for sure re how many seats the ALP will win:

1. They will definitely win between 0 and 150 seats.
2. The probability of them winning exactly 0 seats, 1 seat, 2 seats etc must be between 0 and 1.
3. If we add up all the probabilities for winning each seat, it would add up to 1.

I thought it might be relevant to point a few things out about the probability distribution we showed in the previous blog.

1. We’ve obviously put two probability distributions into the same chart. In future, we’ll likely separate them out in case there is any overlap which makes it hard to see stuff.
2. The shape of the distributions look bell shaped (ie. normally distributed). This is called a Poisson-Binomial distribution, and is well-approximated by a normal distribution in some cases.

Only bell we could find

We hope to dive into more analysis of the politics in future blog posts instead of making you go through our version of stats 101!