Data Modelling

Types of Data

probability Distributions

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CRV

Models

Bernoulli

Poisson

Binomial

Uniform

Gaussian

Discrete

Continuous

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Discrete RV

Sampling

When do we use Probability distributions?

when the Random Variables take continuous data

Taking multiple samples from the population with each an equal sample size

vector y=(y1...yn)

p(y|parm)

Parameter represents the general usage of parameters to control the probability distribution

represents the l

Estimators

Estimators estimating the parameter of a distribution at the population level

Different types of estimators

unbiased estimator (bias=0)

Bias and Variance of an estimator

General method of estimation

Maximum Likelihood estimation arg param max{p(y|param)

solve equivalent problem of minimising the neg log lkelihood

derive in terms of param

dL(y|param)/dparm=0 solve for parm

Estimation

Point estimation

Interval estimation

one METHOD of interval estimation= conf interval

Regression

Interpreting the intercepts

Rss

R^2

LS estimates

Logistic Regression

Classification

Sensitivity

Specificty

Good predictor?

Decesion Tree

Supervised learning

Usupervised learning

Expected value

Variance

independent RV

iid