How to determine if new data lies outside old prediction intervals

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Marcus Glover 2024-6-21

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https://ww2.mathworks.cn/matlabcentral/answers/2130711-how-to-determine-if-new-data-lies-outside-old-prediction-intervals

评论： Marcus Glover 2024-6-21

example_table.mat

I have made a prediction model (using fit and predint) based on data in my table T. I know how to test if the existing data is outside the prediction interval, but I am unsure how to test new datapoints. I do not want to use the new data to make a new fit, I want to use the existing fit model and prediction intervals from the original data.

I am not sure how to generate a continuous function for the upper and lower interval.

Thanks.

load example_table.mat

T=sortrows(T,"Xdata");

x=T.Xdata;

y=T.Ydata;

fitresult = fit(x,y,'exp1');

pred = predint(fitresult,x,0.95);

plot(fitresult,x,y)

hold on

plot(x,pred,'m--')

legend({'Data','Fitted curve', 'Prediction intervals'},...

'FontSize',8,'Location','northwest')

%% See which rows fall outside of interval

outside = (y < pred(:, 1)) | (y > pred(:, 2));

rows_outside_interval = T(outside, :)

rows_outside_interval = 2x4 table

When Data1 Xdata Ydata ____________________ _____ _____ ______ 29-Feb-2024 07:07:54 -1.5 367.5 30.803 26-Feb-2024 21:05:07 18 389.4 9.4924

% Now I add a new row (that would fall outside), and want to test this against the existing

% prediction interval. Stuck here.

ht=height(T);

T(ht+1,:)=T(1,:);

T(ht+1,"Xdata")={300};

T(ht+1,"Ydata")={25};

T(ht+1,:)

ans = 1x4 table

When Data1 Xdata Ydata ____________________ _____ _____ _____ 03-May-2024 14:19:42 27 300 25

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Tony 2024-6-21

One idea is to find the pair of x points in the prediction interval series where the new data x lies in-between, assume the prediction is interpolated linearly in that interval, find the y value of the prediction intervals via linear interpolation for the data x, and then compare with your data y

Marcus Glover 2024-6-21

Thanks, that is a good idea. I'll look at that and I could even fit the prediction line series itself and see which is faster as I may have a lot of new data at times.

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