# Cogntition Hazard Rates - {Proven wrong} : [[Cognitive fMTP]] - Mathematical construct about probability - Continuously tracking the odds the event appeads rn given it has not happened yet - Idea : Use this "hazard rate" to decide when to prepare - RT is proportional to hazard - Optimally prepared if certain ## Distributions Used (PDF) - Constant, exponential, flipped exponential - Hazard rate is this pdf by 1-F - $h(t) = \frac{f(t)}{1-F(t)}$ - ![[Pasted image 20221205133945.webp]] ## Hazard Rates - How does that translate to RT? - Proposed - $RT = c- h(t)$ : linear effect - $RT = c+ \frac{1}{h(t)}$ : inverse relation - dashed : $\frac{1}{hazard}$ - ![[Pasted image 20221205134112.webp]] - ![[Pasted image 20221205133656.webp]] ## Vs ACT-R - Prepare for ‘the right moment’ - ‘degree of preparation’ given by moment-to-moment hz - ‘the right moment’ is estimated based on time (pulses) and memory (DM) - No ‘time’, no explicit memory? - If we are prepared→ benefit, else cost - [[Scaled benefits]] (useful for assignment) - Does not specify why/how; i.e., what preparation is - No active process during the interval - [[Active tracking]] - Once we are prepared, it doesn’t ‘go away’ - A by-product of the Hazard rate - No memory model - Such mathematical models give no mechanism for how the pdf is stored in memory, retrieved, or used… ## Problems - Does not explain preparation - How do particpants ‘learn’ the distribution? - Do participants truly track ‘conditional probabilities’ throughout the foreperiod ## Extending - Does not store PDFs in memory, which sucks - Does not keep track of time as well - Subjective hazard/ anticipation function - Temporal uncertainty - Blur the pdf such that later points are less certain using a [[Gaussian Filter]] that gets wider for later points in time - $f'(t) = \frac{1}{\theta t \sqrt{2 \pi}} \int_{-\infty}^{\infty}f(\tau)e^{-\frac{(r-t)^{2}}{2 \theta^{2}t^{2}}}d \tau$ - Climb to 1 after a while - Hazard is more even though probs are equal in classical. This equates them and makes them less blurred out - ![[Pasted image 20221205140951.webp]] ## Images - ![[Pasted image 20221205133708.webp]]