Some of you will probably hear of this two terms and wonder what’s the difference. Both of them are a statistical approach/ inference method. Personally, I am a Bayesian and use more of Bayesian Methods to do my stuffs.

Firstly, the frequentist approach is a much simple model and does not consider prior knowledge. This is a very stark difference that we should note, before looking at a bette definition.

To illustrate it, I’ll borrow an example that I saw online. So I lost my phone somewhere at home and I can use the “find my phone” app to locate it. Once I activate the app, the phone will start to beep. So which area should I search?

Now, the Frequentist reasoning considers probability derived from long run frequency distributions and the underlying parameters are constant during the process. Going back to the example, I’ll have the ability to identify the area where the beep is coming from. And upon hearing the beep, I infer the area that I must search.

Next, the Bayesian reasoning considers probability to be constantly updated from the realisation of new information. Parameters are unknown and described probabilistically. Going back to the example again, apart from the ability to identify the area where the beep is coming from, I also have prior knowledge of where I had misplaced my phone at before. With the aid of the beep and prior knowledge of my clumsiness, I will be able to identify which area to search now. Here, you should intuitively realise that, we have better chance of finding the phone faster. 🙂

This blog post does an excellent job to realise the intuition behind frequentist and bayesian reasoning.

In A’levels Statistics, the closest contact students have with Bayesian Statistics will be Conditional Probability, whereby we understand that the probability of an event changes given new information.

Bayesian Statistics has a branch called Bayesian Estimations which, in the context of what we had discussed, considers probability by constantly being updated with current information. Examples will be the interest rate trends, hedging. This is used widely in real world today. Of course, to do this branch of statistics, one has to be really well acquitted with statistic distributions.

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