Bayesian estimator
Okay, let's dive into the exciting world of Bayesian estimators, but make it simple enough for a 5-year-old to understand!
Imagine you have a bag of different colored marbles. You know that some marbles are red and some are blue, but you don't know how many of each there are. You want to figure out how many red and blue marbles are in the bag, so you decide to do some guessing.
First, you take a guess at how many red marbles are in the bag. Let's say you guess there are 10 red marbles. Then, you take a guess at how many blue marbles are in the bag. Let's say you guess there are 5 blue marbles.
Now, you want to figure out if your guesses are any good. You start by looking at some evidence - in this case, you draw a random sample of 5 marbles from the bag and record how many of them are red and how many are blue.
Based on that evidence, you update your guesses. The way you update your guesses is by using a formula that takes into account the evidence you just observed, as well as your prior beliefs (i.e. your initial guesses).
This formula is called Bayes' rule, and it's what makes Bayesian estimators work. Basically, Bayes' rule tells you how to update your beliefs (i.e. your guesses) based on new evidence.
So, you plug in your initial guesses (10 red, 5 blue) and the evidence you observed (5 marbles, 3 red, 2 blue) into Bayes' rule, and out pops new guesses that take into account the evidence you just observed. Let's say the new guesses are 8 red marbles and 4 blue marbles.
Now, you repeat the process - you draw another sample of, say, 5 marbles, record the evidence, and update your guesses using Bayes' rule. You keep doing this over and over again until your guesses are pretty close to the true number of red and blue marbles in the bag.
That's basically how a Bayesian estimator works - it allows you to make guesses about something (like the number of red and blue marbles in a bag) based on some initial beliefs (i.e. your initial guesses) and some evidence (i.e. the marbles you observe). It's a powerful tool that's used in all sorts of fields, from statistics to machine learning to finance.
Imagine you have a bag of different colored marbles. You know that some marbles are red and some are blue, but you don't know how many of each there are. You want to figure out how many red and blue marbles are in the bag, so you decide to do some guessing.
First, you take a guess at how many red marbles are in the bag. Let's say you guess there are 10 red marbles. Then, you take a guess at how many blue marbles are in the bag. Let's say you guess there are 5 blue marbles.
Now, you want to figure out if your guesses are any good. You start by looking at some evidence - in this case, you draw a random sample of 5 marbles from the bag and record how many of them are red and how many are blue.
Based on that evidence, you update your guesses. The way you update your guesses is by using a formula that takes into account the evidence you just observed, as well as your prior beliefs (i.e. your initial guesses).
This formula is called Bayes' rule, and it's what makes Bayesian estimators work. Basically, Bayes' rule tells you how to update your beliefs (i.e. your guesses) based on new evidence.
So, you plug in your initial guesses (10 red, 5 blue) and the evidence you observed (5 marbles, 3 red, 2 blue) into Bayes' rule, and out pops new guesses that take into account the evidence you just observed. Let's say the new guesses are 8 red marbles and 4 blue marbles.
Now, you repeat the process - you draw another sample of, say, 5 marbles, record the evidence, and update your guesses using Bayes' rule. You keep doing this over and over again until your guesses are pretty close to the true number of red and blue marbles in the bag.
That's basically how a Bayesian estimator works - it allows you to make guesses about something (like the number of red and blue marbles in a bag) based on some initial beliefs (i.e. your initial guesses) and some evidence (i.e. the marbles you observe). It's a powerful tool that's used in all sorts of fields, from statistics to machine learning to finance.
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