Summary ARMS
Week 1
Two statistical frameworks
- Frequentist framework: based on H0 (NHST), p-values, confidence intervals, effect sizes,
power analysis
- Bayesian framework: increased criticism against NHST: mistakes, incorrect interpretations of
test results, p-hacking, over-emphasis on significance, underpowered studies, publication
bias.
Empirical research uses collected data to learn from. Interpretation in this data is captured in a
likelihood function.
Estimation:
- Frequentist approach: all relevant information for inference is contained in the likelihood
function.
- Bayesian approach: in addition to the likelihood function to capture the information in the
data, we may also have prior information about µ.
o Central idea/mechanism: prior knowledge is updated with information in the data
and together provides posterior distributions for µ.
o Advantage: accumulating knowledge
o Disadvantage: results depend on the choice of prior
- Posterior is the revised or updated probability of an event occurring after taking into
consideration new information. The posterior probability is calculated by updating the prior
probability using Bayes' theorem. (google)
- The posterior distribution of the parameters of interest provides all desired estimates:
o Posterior mean or mode
o Posterior SD
o Posterior 95% credible interval: providing the bound of the part of the posterior in
which 95% of the posterior mass is
- Pr(HJ I data): Probability that hypothesis Hj is supported by the data
- Pr(data I H0): P-value = probability of observing same or more extreme data given …
- PMP = prosterior model probability -> the (bayesian) probability of the hypothesis after
observing the data
- Bayes factor: BF10 = P(data H1) / P(data H0)
- Bayes Factor of 10 meant that the support for one hypothesis is 10 times stronger than the
other
Both frameworks use probability theory, but:
- Frequentists: probability is relative frequency (more formal) (either it rains or it doesn't
- Bayesians: probability is degree of belief (more intuitive)
Frequentists 95% CI: if we were to repeat this experiment many times and calculate CI each time,
95% of the intervals will include the true parameter value (and 5% does not)
Bayesian 95%: there is 95% probability tant the true value is in the credible interval.
Week 1
Two statistical frameworks
- Frequentist framework: based on H0 (NHST), p-values, confidence intervals, effect sizes,
power analysis
- Bayesian framework: increased criticism against NHST: mistakes, incorrect interpretations of
test results, p-hacking, over-emphasis on significance, underpowered studies, publication
bias.
Empirical research uses collected data to learn from. Interpretation in this data is captured in a
likelihood function.
Estimation:
- Frequentist approach: all relevant information for inference is contained in the likelihood
function.
- Bayesian approach: in addition to the likelihood function to capture the information in the
data, we may also have prior information about µ.
o Central idea/mechanism: prior knowledge is updated with information in the data
and together provides posterior distributions for µ.
o Advantage: accumulating knowledge
o Disadvantage: results depend on the choice of prior
- Posterior is the revised or updated probability of an event occurring after taking into
consideration new information. The posterior probability is calculated by updating the prior
probability using Bayes' theorem. (google)
- The posterior distribution of the parameters of interest provides all desired estimates:
o Posterior mean or mode
o Posterior SD
o Posterior 95% credible interval: providing the bound of the part of the posterior in
which 95% of the posterior mass is
- Pr(HJ I data): Probability that hypothesis Hj is supported by the data
- Pr(data I H0): P-value = probability of observing same or more extreme data given …
- PMP = prosterior model probability -> the (bayesian) probability of the hypothesis after
observing the data
- Bayes factor: BF10 = P(data H1) / P(data H0)
- Bayes Factor of 10 meant that the support for one hypothesis is 10 times stronger than the
other
Both frameworks use probability theory, but:
- Frequentists: probability is relative frequency (more formal) (either it rains or it doesn't
- Bayesians: probability is degree of belief (more intuitive)
Frequentists 95% CI: if we were to repeat this experiment many times and calculate CI each time,
95% of the intervals will include the true parameter value (and 5% does not)
Bayesian 95%: there is 95% probability tant the true value is in the credible interval.
