Estimating and anticipating a dynamic probabilistic bias in visual motion direction
Laurent Perrinet, Chloé Pasturel and Anna Montagnini
Visual motion Fest - Invibe Team – INT / Marseille February 1 & 2, 2018
Outline
-
A dynamic probabilistic bias in visual motion direction
- Raw psychophysical results
- The Bayesian Changepoint Detector
- Results using the BCP
A dynamic probabilistic bias in visual motion direction
A dynamic probabilistic bias in visual motion direction
A dynamic probabilistic bias in visual motion direction
A dynamic probabilistic bias in visual motion direction
A dynamic probabilistic bias in visual motion direction
Outline
- A dynamic probabilistic bias in visual motion direction
-
Raw psychophysical results
- The Bayesian Changepoint Detector
- Results using the BCP
Raw psychophysical results
Raw psychophysical results
Raw psychophysical results
Raw psychophysical results
Raw psychophysical results
Raw psychophysical results
Outline
- A dynamic probabilistic bias in visual motion direction
- Raw psychophysical results
-
The Bayesian Changepoint Detector
- Results using the BCP
The Bayesian Changepoint Detector
The Bayesian Changepoint Detector
The Bayesian Changepoint Detector
Bayesian Changepoint Detector
- Initialize
- $P(r_0)= S(r)$ or $P(r_0=0)=1$ and
- $ν^{(0)}_1 = ν_{prior}$ and $χ^{(0)}_1 = χ_{prior}$
- Observe New Datum $x_t$
- Evaluate Predictive Probability $π_{1:t} = P(x |ν^{(r)}_t,χ^{(r)}_t)$
- Calculate Growth Probabilities $P(r_t=r_{t-1}+1, x_{1:t}) = P(r_{t-1}, x_{1:t-1}) π^{(r)}_t (1−H(r^{(r)}_{t-1}))$
- Calculate Changepoint Probabilities $P(r_t=0, x_{1:t})= \sum_{r_{t-1}} P(r_{t-1}, x_{1:t-1}) π^{(r)}_t H(r^{(r)}_{t-1})$
- Calculate Evidence $P(x_{1:t}) = \sum_{r_{t-1}} P (r_t, x_{1:t})$
- Determine Run Length Distribution $P (r_t | x_{1:t}) = P (r_t, x_{1:t})/P (x_{1:t}) $
- Update Sufficient Statistics :
- $ν^{(0)}_{t+1} = ν_{prior}$, $χ^{(0)}_{t+1} = χ_{prior}$
- $ν^{(r+1)}_{t+1} = ν^{(r)}_{t} +1$, $χ^{(r+1)}_{t+1} = χ^{(r)}_{t} + u(x_t)$
- Perform Prediction $P (x_{t+1} | x_{1:t}) = P (x_{t+1}|x_{1:t} , r_t) P (r_t|x_{1:t})$
- go to (2)
The Bayesian Changepoint Detector
The Bayesian Changepoint Detector
Outline
- A dynamic probabilistic bias in visual motion direction
- Raw psychophysical results
- The Bayesian Changepoint Detector
-
Results using the BCP
Results using the BCP
Results using the BCP
Results using the BCP
Results using the BCP
Results using the BCP
Results using the BCP
Estimating and anticipating a dynamic probabilistic bias in visual motion direction
Laurent Perrinet, Chloé Pasturel and Anna Montagnini