Stochastic Simulations: Ergodicity and Estimators

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Risk and Return Measures

Covers risk and return measures, unbiasedness, and consistency of estimators.

Optimality in Decision Theory: Unbiased Estimation

Explores optimality in decision theory and unbiased estimation, emphasizing sufficiency, completeness, and lower bounds for risk.

Estimation Criteria

Covers criteria for estimating parameters, emphasizing the importance of consistency, bias, variance, and efficiency of estimators.

Statistical Models and Parameter Estimation

Explores statistical models, parameter estimation, and sampling distributions in probability and statistics.

Estimator of Variance

Explores variance estimation, creating personal estimators, correcting bias, and understanding Mean Square Error in statistical analysis.

Density of States and Bayesian Inference in Computational Mathematics

Explores computing density of states and Bayesian inference using importance sampling, showcasing lower variance and parallelizability of the proposed method.

Model Selection Criteria: AIC, BIC, Cp

Explores model selection criteria like AIC, BIC, and Cp in statistics for data science.

Parameter Estimation: Detection & Estimation

Covers the concepts of parameter estimation, including unbiased estimators and Fisher information.

Monte Carlo: Markov Chains

Covers unsupervised learning, dimensionality reduction, SVD, low-rank estimation, PCA, and Monte Carlo Markov Chains.

Path Integral Molecular Dynamics

Explores path integral molecular dynamics simulations, focusing on quantum kinetic energy estimators and convergence with the number of replicas.