Bayesian - Study guides, Class notes & Summaries

Applying Bayes (Real-world) correct answers Requires application of Bayes Theorem to every data point First Big Idea correct answers Belief is a matter of degree Second Big Idea correct answers Degree of belief should be treated as probabilities Bayes' Theorem (equation) correct answers P(H given E) x P(H) x P(E given H)/P(E) Probability(Hypothesis) correct answers Measure of prior confidence that the hypothesis is true Probability(Evidence) correct answers Measure of prior confi...

What are the Axioms of Probability correct answers 1. Probability between 0 and 1 2. Adds up to 1 3. Sum of Independent events by adding them What is the Sample Subspace correct answers Set out Outcomes What is an Event correct answers Subset of the sample space What is the Conditional Probability correct answers What is the Sum Rule correct answers P(A) = Sum P(A, B) What is Bayes Rule correct answers What is a Random Variable correct answers Function from sample space to ...

P value correct answers the true probability that the test statistic would be as far from expected as it is IF the null hypothesis is true Induction or falsification? correct answers Falsification - induction is logically invalid - science must proceed by eliminating false ideas Hypothesis testing: confidence interval correct answers - it is not true that there is a 95% chance that the parameter is in the 95% confidence interval - there is a 95% probability that if you collect another s...

BAYESIAN ESSENTIALS WITH R JEAN MICHEL MARIN CHRISTIAN P ROBERT 2ND EDITION

Bayesian Metaphor Correct Answer -Three approaches or metaphors for human cognition - Information processing metaphor - Connectionist Metaphor - Bayesian Metaphor Information processing metaphor Correct Answer -the mind as a serial computer,with memory stores, buffers, executive control, ... Connectionist Metaphor: Correct Answer -the mind as a brain,with parallel distributed processing Bayesian Metaphor Correct Answer -the mind as doing statistical inference Statistics Correct A...

Prior Distribution correct answers

Probability in Bayesian terms (as opposed to classical) correct answers How confident you are that a hypothesis is true Time in Bayesian vs. Classical correct answers Generally you cannot update classical models as time goes on, you can with Bayesian Product Rule correct answers P(A, B) = P(A) * P(B|A) *** Only if A and B are independent Sum Rule correct answers P(A) = P(B) * P(A|B) + P(nB)*P(A|nB) (nB is not B) OR P(A) = Σ P(Bi) * P(A|Bi) Bayes' Rule correct answers P(...

Define thinking correct answers the flexible organisation and manipulation of internal representations helps us to understand the world processes of thinking correct answers physical stimuli - sensory representation - semantic representation - desired goal - plan how are representations formed? correct answers depends rationalism (through a priori knowledge) vs empiricism (through sensory system) constructivists (apriori) vs sensory driven (empiricists) what is perception corre...

in general, the goal of statistics is to correct answers make an inference using observed data,x to make an inference, the data is assumed to have originated from a probability model _________ and our inference is usually expressed in terms of an unobservable parameter ____ of the distribution ___ correct answers f(x|θ) θ f The Frequentist approach to statistics adopts the view that correct answers only the data, x, is random The fundamental principle of Bayesian statistics: everythin...

PROBABILISTIC FINITE ELEMENT MODEL UPDATING USING BAYESIAN STATISTICS APPLICATIONS TO AERONAUTICAL AND MECHANICAL ENGINEERING BY TSHILIDZI MARWALA AND ILYES BOULKAIBET