Hi Folks I am trying find how to approach this problem:
I have four input data points - from four data sources of "lets say price of a stock" - each data point has 90 percent chance of being accurate?
How can I combine these data points to get a correct estimate of price with probability higher than 90 percent?
What are the approaches we can have to solve this problem?
I’m assuming that these $90\%$ probabilities of being correct are independent of each other.
The best you can do is to choose a value on which most of the inputs agree. In this case, the probability to get the right value is at least
$$ \binom40\cdot0.9^4+\binom41\cdot0.9^3\cdot0.1+\frac12\cdot\binom42\cdot0.9^2\cdot0.1^2=0.972\;, $$
where the factor $\frac12$ is because you have to choose arbitrarily if the inputs agree in pairs. The probability might even be much higher, depending on how likely it is that wrong inputs agree; you didn’t specify a distribution for the wrong inputs.