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what is the difference between epistemic and aleatory uncertainty. Give and example for each. Give an example when one can turn into another.
Aleatory uncertainty (or statistical uncertainty) is the physical variability or natural randomness present in the system or environment. Cannot be reduced.
An example is an arrow fired the exact same way every time will not hit the same spot every time.
Epistemic is due to lack of knowledge, data, or deficient models. This can be reduced by creating better models and getting more data.
An example is limited data (such as earthquakes or structural failures).
An example is when concrete is poured into a foundation, it turns from epistemic (at design) to aleatory, once it hardens.
what is a likelihood function?
The likelihood function contains information about the model parameters contained in the data; it quantifies what is known BEFORE observing data.
What is the posterior distribution?
The posterior distribution is formed from the likelihood function and prior distribution; it represents the total knowledge about the parameters AFTER additional data is observed
What is the difference between Bayesian and Classical approaches to inferential statistics?
The classical or frequentist approach views probability as a long-run frequency.
The bayesian approach uses a subjective probability to express belief in a statement about unknown quantities.
What is a prior distribution?
Quantifies uncertainty in the the values of the unknown model parameters, BEFORE data is observed
Describe the steps in a bayesia analyis or updating.
- 1) formulate the probability model for the data
- 2) Decide on the prior distribution which quantifies the uncertainty in the values of the unknown model parameters before updating
- 3)Observe data and construct a likelihood function based on the data and probability model. This function quantifies what is known about the model parameters before observing data
- 4)Combine the likelihood with the prior distribution to determine the posterior distribution; at this step the uncertainty in the values of the unknown parameters are quantified AFTER the data is observed
- 5) can now use posterior distribution to calculate quantities of interest
What is the difference between risk and reliability?
- Risk = probability x consequence
- Reliability is 1 - probability of failure
Why is "degree or belief" or bayesian a more popular belief than classical or frequentist
because we cannot observe many instances of structural failure
What does mutually exclusive and collectively exhaustive mean?
Mutually exclusive is the events cannot occur simultaneously. Collectively exhausted means that the probability for all events adds up to 1; all possibilities are covered.
In Bayesian inference, what is a conjugate prior?
A conjugate prior is an algebraically convenient expression that ensures that posterior distribution and the same as the prior distribution -> conjugate pairs. Avoids the integration for the normalizing constant; posterior is closed-formed equation
What is the difference between correlation and statistical dependence?
Correlation describes the linear relationship between a set of variables. Varies from 1 to -1.
Statistical dependence is when the outcome of one variable depends on outcome of another. Ex when one occurs, it affects the probability of the other occurring.
What is the predictive distribution?
It is the theorem of total probability. The distribution of yet to be observed observations that are conditional on observed data.
What is vulnerability?
Measure of direct impact or consequence
What is robustness?
Measure of indirect consequence
What is resiliance?
Measure of cost and time for recovery
What is a realization
An observed value.
Why do we use bounds?
Because of the difficulty in evaluating Ik, or the joint CDF
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