Topic Outline

1. Bayesian VS. Frequentist Perspective on Interpretation of Probability

• Frequentist: long term frequency of event happening in recurring experiment

• Bayesian: a measure of belief in confidence about an event happening

  • This belief is based on individuals and different observers may come out different beliefs
  • Individuals’ different beliefs do not change what the outcome will come out to be
  • You gather evidences to form and update beliefs
  • Prior Probability: initial belief $P(A)$

  • Posterior Probability: updated belief given evidences $P(A

    X)$

1. Why Simulation Methods and When

   • (1) Simulation versus Asymptotic Assumed Optimization Methods

• the latter uses asymptotic assumptions in population properties) for closed-form solutions while the former uses available observed available samples

• (2) Concept of Simulation

  • you have observed realizations from some target distribution
  • you try to build a pseudo-random number generator that mimics the underlying generation process of the observed realization

• (3) Types of Simulation

  • Resampling: bootstrap, jacknife, permutation

1. Non-parametric Bayesian versus MCMC

Resampling

Parametric Bootstrap

Bayesian Bootstrap

• purpose: estimate distribution for parameter

• Example: (1) observed samples: array([ 3.34135494, 4.03678023, 0.4305536 , 4.11717223]), which is actually from exponential(7) (2) plot density (3) need to simulation distribution of mean

Case Studies

1. Click-through Rate

   Kaggle Click-through Rate Prediction

Reference

(1)[http://www.unc.edu/~carsey/teaching/ICPSR-2011/Sim%20Slides%202%20Handout.pdf]

(2) Simulation-based Estimation