- Introduction - Estimating model parameters from data
- Classical statistics
- Introduction - Classical Statistics
- Normal distribution
- Estimating the mean of a Normal distribution when the distribution's standard deviation is known
- Estimating the mean of a Normal distribution when the distribution's standard deviation is unknown
- Estimating the standard deviation of a Normal distribution when the distribution's mean is known
- Estimating the standard deviation of a Normal distribution when the distribution's mean in unknown
- Derivations
- Classical statistics estimation of the Normal distribution mean when the standard deviation is known
- Classical statistics estimation of the Normal distribution mean when the standard deviation is not known
- Classical statistics estimation of the Normal distribution standard deviation when the mean is known
- Classical statistics estimation of the Normal distribution standard deviation when the mean is unknown
- Binomial process
- Poisson process
- Introduction - Poisson Process
- Poisson distribution method of estimating a rate - not recommended
- Normal approximation to the Poisson distribution method of estimating a rate lambda
- Cumulative confidence construction estimate for the Poisson intensity
- Estimating the mean of an Exponential distribution using Classical statistics
- Comparison of classical estimates of Poisson lambda and beta
- Estimating the parameters of a least squares regression
- Two sample problems
- Bayesian statistics
- Introduction - Bayesian Statistics
- Bayesian inference concepts
- Prior distributions
- Introduction - Prior Distributions
- Uninformed priors
- Conjugate priors
- Subjective priors
- Improper priors
- Informed prior
- Determining a prior distribution for a single parameter estimate
- Determining prior distributions for correlated parameters
- Determining prior distributions for uncorrelated parameters
- Hyperparameters
- Likelihood functions
- Calculation methods
- Examples
- -Normal distribution
- Bayesian estimate of the mean of a Normal distribution with known standard deviation
- Bayesian estimate of the mean of a Normal distribution with unknown standard deviation
- Bayesian estimate of the standard deviation of a Normal distribution with known mean
- Bayesian estimate of the standard deviation of a Normal distribution with unknown mean
- Normal approximation to the Beta posterior distribution
- Bayesian analysis example: Gender of a random sample of people
- Bayesian analysis example: Identifying a weighted coin
- Bayesian analysis example: Tigers in the jungle
- Bayesian analysis example: The Monty Hall problem
- Bayesian analysis example: Using cow pats to estimate infected animals in a herd
- Hyperparameter example: Micro-fractures on turbine blades
- Bayesian analysis with threshold data
- -Normal distribution
- The Jacobian transformation
- Bootstrap
- Introduction - The Bootstrap
- The Jackknife
- The non-parametric Bootstrap
- The parametric Bootstrap
- Bootstrap Examples
- Bootstrap estimate of prevalence
- Non-parametric Bootstrap example
- Parametric Bootstrap example
- Example: Parametric Bootstrap estimate of mean number of calls per hour at a telephone exchange
- Example: Parametric Bootstrap estimate of the mean of a Normal distribution with known standard deviation
- Multiple variables Bootstrap Example 1: Estimate of regression parameters
- Multiple variables non-parametric Bootstrap Example 2: Difference between two population means
- Linear regression Bootstrap
- The Bootstrap likelihood function for Bayesian inference
- Estimating parameters for multiple variables
- Comparison of Classical and Bayesian methods
- Introduction - Comparison of Classical and Bayesian Methods
- Comparison of classical and Bayesian estimates of intensity lambda in a Poisson process
- Comparison of classical and Bayesian estimates of mean 'time' beta in a Poisson process
- Comparison of classical and Bayesian estimates of Normal distribution parameters
- Comparison of classical and Bayesian estimates of probability p in a binomial process
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