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Samenvatting ARMS

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Een goede samenvatting voor arms waar je een 9 mee kan halen!

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  • February 11, 2024
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  • 2023/2024
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ARMS
COLLEGE 1
DIFFERENCES BETWEEN FREQUENTIST AND BAYESIAN

. Frequentist framework:
- Test how well the data fit H0 (NHST)
- P-values, confidence intervals, effect sizes, power analysis.

. Bayesian framework:
- Probability of the hypothesis given the data, taking prior information into account
- Bayes factors, priors, posteriors, credible intervals

Estimate something
. Frequentist= Likelihood function= the joint probability (or probability density) of
observed data viewed as a function of the parameters of a statistical model.
. Bayesian= likelihood function + prior information about u: posterior distribution for u.
- Advantage accumulating knowledge
- Disadvantage results depend on choice of prior (hoe specifieker de prior hoe
specifieker de posterior) (hoe groter de data hoe meer invloed op de posterior).
Posterior distribution mean, mode, SD, 95%credible interval

Lady tasting tea= results and conclusion depend on things not observed and on the sampling
plan, same data can give different results.

Testing hypothesis
. Bayesian: calculate the probability of the hypothesis given the data
 PMP= posterior model probability, the probability of the hypothesis after observing the
data.

2 criteria
1. How sensible is the probability, based on prior knowledge (prior)
2. How well it fits the new evidence (data)

Comparative testing: hypotheses are tested against one another bayes factor (<1 is meer
support voor H0, >1 is meer support voor H1)

Probability=
. Frequentist: is the relative frequency of events
. Bayesian: is the degree or belief

. Frequentist 95% confidence interval= if we were to repeat this experiment many times
and calculate each time 95% of the intervals will include the true parameter value.
. Bayesian 95% credible interval= there is 95% probability that the true value is in the
credible interval

, Linear regression: capture a relationship between two variables. (Scatterplot, x and y
values, positive of negative association)
Yhead
Yi= B0+ B1x1i + ei

Multiple linear regression: 2 predictors values, 1 outcome variable
Yi= B0+ B1x1i + B2x2i + ei

B0 intercept
B1 slope of X1
B2 slope of X2
E residual (residuen zijn gelijk van de geordend boven en onder de lijn, even ver van de
lijn af, punten liggen om de lijn heen ei~N(0;sigmae)

Assumptie multiple regression:
1. Ratio/ interval variables nominal variables can be turned into dummy variables
who has 0 and 1.
2. Dependent variable is continuous
3. Linear relation
4. No outliers

. Frequentist analysis:
 Linear regression tabel:
R2= hoeveel variatie wordt veroorzaakt door het model in de steekproef
R= correlatie tussen de y (afhankelijke variabele) en model
Adjusted R2= hoeveel variantie kan het model verklaren buiten de steekproef (populatie). Is
afhankelijk van hoe groot de steekproef is: Als je een kleine steekproef hebt dan is het
moeilijker om iets te voorspellen in de populatie. En afhankelijk van hoeveelheid variabelen.

 Anova tabel:
Test voor R2 is R2 significant groter dan 0, om Ho te verwerpen
F=
P= p-waarde, significantieniveau

 Coefficients tabel:
Unstandardized= B0/intercept, B1, B2. 1x gaat y zoveel omhoog of omlaag. Je kan de
coëfficiënten niet vergelijken om te kijken welke variabele meer invloed heeft, want ze zijn
op verschillende schalen.
Standard error=
Standardized= welke variabelen heeft de grootste invloed? Hierbij zijn alle variabelen op
dezelfde schaal gezet en dus vergelijkbaar. Kijk naar het hoogste cijfer (zowel – als +)
P= is het significant?

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