Week 6 SCM (Bayes) Flashcards
what is bayesian statistics vs. frequentist statistics
- bayesian is a way of understanding data based on the odds of various outcomes
- the frequentist approach looks at the probability of different data under the null hypothesis (pvalues).
what is a latent process?
the name given to an unseen (random) process that generates observed data
what is a latent variable?
a variable that is not observed but rather inferred through a mathematical process
for example a population mean can be a latent variable that is inferred through the sampling of a population and analysis of the sample mean
what is bayesian inference?
the process of making inferences about a latent variable based on observed data, e.g estimating a population mean from the sample mean
how to estimate posterior distribution using bayesian inferences
- if we dont have specific information for the prior we can use a distribution as the prior such as a uniform distribution
- these priors can be uninformative or weakly informative
- its implies that all values are equally likely
what is the MAP (maximum a posterieori) estimate?
- the value in the distribution in which the probability is the highest
what does a 95% credible interval tell us?
- there is a 95% probability that the probability value of an outcome falls between these two values
- it can be used to show that the probability of an outcome is significantly above 0 suggesting that the outcome is likely to happen
how is it common to generate credible intervals?
by sampling from the posterior distribution and then computing quantiles from the samples
whats the bayes factor?
the bayes factor characterises the relative likelyhood of the data under two different hypothesis’s
what is the hypothesis test for the frequentist and bayesian approaches?
Frequentist test= p values
Bayesian= Bayes Factor
What is the estimation of uncertainty for the frequentist and bayesian approaches
Frequentist= maximum likelyhood estimate with confidence intervals
Bayesian= posterior distribution with highest density interval
where is the marginal likelyhood in the bayes formula
the marginal likelyhood is on the denominator of the equation
(the numerator of the equation includes the prior and the likelyhood)
what is the bayes factor formula
BF= P (data | H1) / P (data | H2)
how do you interpret bayes factors
> 150 is very strong significance
20-150 is strong
3-20 is positive
1-3 is not really worth a mention
why is the bayes factor better for assesing evidence for the null hypothesis
- because the bayes factor is comparing evidence for the two hypotheses it allows us to assess whether theres evidence for the two hypotheses
- we cant do this with standard null hypothesis testing because it starts with the assumption that the null is true
what is it called if two vectors have the same orientation but only differ in length?
they are called linearly dependent
when would two vectors be orthogonal?
if theyre inner product equals zero
therefore the scalar between the two vectors must not equal zero
are orthogonal vectors and uncorrelated vectors dependent or independent
all orthogonal and uncorrelated vectors are independent
whats a nonequivalent control group design
uses prexisting groups, one of which serves in the treatment condition and the other in the control condition
whats a posttest only nonequivalent control group design
compares two prexisting groups
one is measured after a treatment and the other is measured at the same time but recieves no treatment
the pretestpostest nonequivalent control group design is much better
whats a pre post design?
when a series of observations is made over time for one group of participants
what is a time series design
like a treatment design except there is an event not a treatment
this event is not controlled by the researcher
