Discrete Multivariate Distributions Revision and Simulation

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Presentation transcript:

Discrete Multivariate Distributions Revision and Simulation 18/01/2019 ST2352 Week 2

Simulation Excel file 18/01/2019 ST2352 Week 2

Bivariate Dist (Marg) Dist X Cov(X,Y) Dist (X+Y) Var(X+Y) E[min(X,Y)] Derive by probability Explain by simulation Marginalise: Prob: sum across one dim Sim: ignore one col 18/01/2019 ST2352 Week 2

Summaries of sample 18/01/2019 ST2352 Week 2

Multivariate Stochastic System Multiple Columns/Random Variables Interest often lies in a few cols/RVs Marginalise ST2351. Tut2.Q2 Sit 6 exams. Pr pass each is 0.8 indep others Pr(Fail at least 2)= 18/01/2019 ST2352 Week 2

Conditional Distribution Simulating from Cond distribution Simulate system And restrict attention to subset (of random size) Alt Focus on aspect of joint sim (rescale rel freq) | 18/01/2019 ST2352 Week 2

Conditional Distribution Simulating from Cond distribution Compute by prob Explain by simulation Dist [X|Y=0] E [X |Y=0] Var[X|Y=0] E [X2 |Y=0] | Prove. Explain via simulation 18/01/2019 ST2352 Week 2

Conditioning in Stoch Systems Modelling uncertainties in system Exploiting partial info on a system X and Z often multivariate in real applications 18/01/2019 ST2352 Week 2

Stoch System: Exams Passed Pr(Pass exam A, B, C, D): A 0.6 B 0.7 C 0.8 D 0.9 Seek dist of N = no. exams past Simulation and Marginalising Probability 18/01/2019 ST2352 Week 2

Prob method 1: Enumeration 18/01/2019 ST2352 Week 2

Prob method 2: Recursion via Conditional Dist 18/01/2019 ST2352 Week 2

Prob method 2: Recursion via Conditional Dist 18/01/2019 ST2352 Week 2