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I have a time series data structure in the form: $$ \stackrel{\mbox{Time $t$}}{% \begin{bmatrix} 0 & 1 & 0 & 0 & 1 & 1 & 1 & \dots & p_{t} & p_{t+1} \end{bmatrix}}\ $$

where each entry is a binary result for some task, I would like to know if it is possible to predict the probability that the next outcome p_t is correct. The assumption regarding the data that is made is that the user performance in the task increases over time and then stabilizes to some value.

Thanks,

Sagar

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You could just fit a model like $p(t) = a+b*(1-exp(-ct))$ to the $(t,p_t)$ pairs, using a least-squares approach for example.

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  • $\begingroup$ Hi could you point toward any resources online? $\endgroup$
    – Sagar Patel
    Commented Jun 12, 2017 at 0:54
  • $\begingroup$ youtube.com/watch?v=3Fd4ukzkxps $\endgroup$
    – Simon Woodward
    Commented Jun 12, 2017 at 1:00
  • $\begingroup$ jkp-ads.com/articles/leastsquares.asp $\endgroup$
    – Simon Woodward
    Commented Jun 12, 2017 at 1:59
  • $\begingroup$ Will this work using binary data? $\endgroup$
    – Sagar Patel
    Commented Jun 12, 2017 at 1:59
  • $\begingroup$ Yes it will. It will look different to the example. Alternatively you could work with the cumulative data and a cumulative model. $\endgroup$
    – Simon Woodward
    Commented Jun 12, 2017 at 2:16

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