GJP_revisited/Inverse_BrierScoreCalc.m

function [ Poc_final ] = Inverse_BrierScoreCalc( BrierScore, Occured )
% Given an set outcome and a set brier score, what was the probability that
% the individual responded? We get it by basically doing the inverse of the
% BrierScoreCalc function


BS = BrierScore;
b = Occured;
d = 1 - Occured;

a_root = 1 ;
b_root = ((-2*b) - 2 + (2*d)) /2;
c_root = (b^2 + 1 - (2*d) + d^2 -BS) /2;

results = roots([a_root b_root c_root]);

Poc = results(results>=0 & results<=1);
Poc_final = Poc(1);

% ProbNotOccurs = 1 - ProbOccurs; 
% Outcome_Y = Occured;
% Outcome_N = 1-Outcome_Y;
% 
% Poc = (Outcome_Y^2 - Outcome_N^2 - BrierScore + 1 - (2*Outcome_N)) / ((2*Outcome_Y) - 2 - (2*Outcome_N));

% BS = (ProbOccurs - Occured)^2 + (ProbNotOccurs - (1-Occured) )^2;



end