W8 - Control Strategies II Flashcards
What is Bayesian Statistics?
What is a p-value?
- Bayesian statistics: making inferences on uncertain data - what is the optimal strategy based on the fact we are making decisions based on what we believe to be true
- it allows us to come up with realistic results, to assess the energy efficiency of human movements
the probability of the observed outcome and all more extreme outcomes if the null hypothesis is true
Describe the Bayesian approach ( Kruschke & Liddell, 2018):
- More intuitive approach, based on the way people naturally think
- Harder to do, easier to understand
–> Happens with constant updating of measures/boundaries based on overall data. (updating beliefs)
What is Bayesian Inference?
- prior: begin with some knowledge –> prior distribution
- data: update knowledge as data available –> new info
- posterior: reduce uncertainty in our knowledge –> post data
The more data collected the more certain your knowledge becomes
In what way is data updated in a Bayesian approach?
Draw the maximum likelihood estimation (Wolpert, 2007)
- Prior beliefs (hypothesis)
- Posterior beliefs - somewhere in-between prior and data, involving prior x evidence(likelihood)
- Evidence(likelihood) - data collected on the matter in order to come up with a posterior belief.
But, If we know nothing we could make all outcomes equal
Explain the Bayesian decision theory:
- Bayesian Decision Theory: aim to select optimal actions based on inferences (Wolpert, 2007)
- selecting the decision/ action based on current beliefs, minimising the expected loss given our beliefs.
What is meant by decision time (Wolpert, 2007)
- Decision time: choosing the best action calculating the expected loss for a given action = avg loss across all possible states & the degree of belief in the state –> Make decisions based on overall trial function
Describe the tennis example of Bayesian statistics (Wolpert, 2007)
Red zone(data) is where we predict the ball to land based on visual tracking, so we would aim to get to the centre of the zone.
Prior data(green zone):
- Based on general tennis knowledge
- Or specific opponents
We may conclude that it will land somewhere closer to the line
Centre of combined zone (yellow zone) replicates how tennis players actually react and hit the ball
How do people combine prior data and current information exposed to them to generate an outcome
How was the Bayesian approach applied to the button pressing study (Wolpert, 2007)
- no sensory input available, but we do know muscle lengths and velocities feeling
- subjects tried to find their hand location
by generating the sensory input that is most likely representative of what you are feeling = how people actually move
What study was used to show sensory system noise?
(Harris & Wolpert, 1998)
- as well as noise in the sensory system(saccades eye movement), there is also noise at the command level (arm movement)
- If noise is signal dependent large signal has more noise, suggesting a smooth lower signal would be better
- Affects confidence and certainty in our movement
- for a given amp and duration of movement, the final positional variance will depend on the actual neural commands and velocity profile
What were the consequences shown from movement strategy choice (Wolpert, 2007)?
2 different movement strategies that can produce the same outcome when successful
- Going along ball path you can still catch the ball if off time
- Going across you would miss the ball if not timed correctly
(Hiley & Yeadon, 2012) also showed that maximum success in gymnasts was the strategy with smallest RMS difference in the shoulder and hips
What is the maximum likelihood estimation (MLE)?
- assesses how probable is it that we observe a
particular data set. - likelihood is the probability given by the data
- we are close to optimal when we combine visual and auditory information to estimate the position of a stimulus
What example was used in the study by (Wolpert, 2007) for MLE?
- pea shooter (spit out virtual peas at the rate of 10 per second to hit a target) pointing to a cursor on a straight line which appears briefly
- Dot appearing along a line, then disappearing quickly.
–> usually guess the middle of the area you think you saw it - if there is prior info e.g.: dot usually appears in the centre of scree, this will influence subjects thoughts
- noise can cause some probability deviations, but Bayesian estimate optimally trades off bias for variance.
What is the Kalman filter?
What does MAP stand for?
The Kalman filter is a recursive filter that maintains an estimate of the current state and updates this based on both the sensory feedback and motor commands. The Kalman filter is in fact a Bayesian estimator for time varying systems.
Maximum a posteriori estimator
For example, which is preferable when pointing to
a target twice: a 2 cm error followed by a 2 cm error or a 1 cm followed by a 3 cm error?
- If the loss function is error^2 then the first scenario has total loss of 2^2 + 2^2 = 8, and the second has total loss 1^2 + 3^2 = 10, so first scenario is better.
- If the loss function is absolute error then the first scenario has total loss of 2 + 2 = 4 and the second has total loss
1 + 3 = 4 and both scenarios are equally good. - If the loss function is the square root of
error, then the first scenario has total loss of root(2) + root(2) = 2.8 and the second has total loss root(1) + root(3) = 2.7, so the second scenario is better. - depending on loss function error is distributed differently.
