Introduction to Bayesian Statistics and an Application and an - PowerPoint PPT Presentation

Introduction to Bayesian Statistics Introduction to Bayesian Statistics and an Application and an Application Timothy M. Bahr Unconfounding the Confounded: Separating Introduction Treatment and Batch Effects in Confounded Definitions Microarray Experiments Bayesian Statistics Microarrays Timothy M. Bahr Confounded Experiments Model Department of Statistics Gibbs Brigham Young University Sampling Application March 16, 2009

Introduction Introduction to Bayesian Statistics and an Who am I? Application Timothy M. Bahr Tim Bahr, Undergrad ... Introduction Definitions Bayesian Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Introduction Introduction to Bayesian Statistics and an Who am I? Application Timothy M. Bahr Tim Bahr, Undergrad ... Introduction Definitions ◮ 22, B.S. in Statistics, Bayesian emphasis: Biostat Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Introduction Introduction to Bayesian Statistics and an Who am I? Application Timothy M. Bahr Tim Bahr, Undergrad ... Introduction Definitions ◮ 22, B.S. in Statistics, Bayesian emphasis: Biostat Statistics Microarrays ◮ My first intro to Statistics Confounded in High School Experiments Model Gibbs Sampling Application

Introduction Introduction to Bayesian Statistics and an Who am I? Application Timothy M. Bahr Tim Bahr, Undergrad ... Introduction Definitions ◮ 22, B.S. in Statistics, Bayesian emphasis: Biostat Statistics Microarrays ◮ My first intro to Statistics Confounded in High School Experiments ◮ Fascination with the Model Gibbs Numerical Patterns in Sampling Science Application

Introduction Introduction to Bayesian Statistics and an Who am I? Application Timothy M. Bahr Tim Bahr, Undergrad ... Introduction Definitions ◮ 22, B.S. in Statistics, Bayesian emphasis: Biostat Statistics Microarrays ◮ My first intro to Statistics Confounded in High School Experiments ◮ Fascination with the Model Gibbs Numerical Patterns in Sampling Science Application ◮ Future Goals

Introduction Introduction to Bayesian Statistics and an Application Who are you? Timothy M. Bahr Bioinformatics Introduction Definitions ◮ Majors? Bayesian Statistics ◮ Math/Stat Background? Microarrays ◮ Microarrays? Confounded Experiments ◮ Research? Model ◮ Why Bioinformatics? Gibbs Sampling ◮ Can I tell you what I think Application about Bioinformatics?

Definitions Introduction to Bayesian Statistics and an Application Timothy M. Bahr Introduction Definitions Bayesian Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Definitions Introduction to Bayesian Statistics and an Application ◮ Bayesian Statistics >>> statistical inferences on Timothy M. Bahr experimental data + prior knowledge. Introduction Definitions Bayesian Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Definitions Introduction to Bayesian Statistics and an Application ◮ Bayesian Statistics >>> statistical inferences on Timothy M. Bahr experimental data + prior knowledge. ◮ Classical (Frequentist) Statistics >>> data from Introduction observations or experiments only. Definitions Bayesian Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Definitions Introduction to Bayesian Statistics and an Application ◮ Bayesian Statistics >>> statistical inferences on Timothy M. Bahr experimental data + prior knowledge. ◮ Classical (Frequentist) Statistics >>> data from Introduction observations or experiments only. Definitions Bayesian ◮ Prior Distribution: The distribution we assume our Statistics parameters come from. Microarrays Confounded Experiments Model Gibbs Sampling Application

Definitions Introduction to Bayesian Statistics and an Application ◮ Bayesian Statistics >>> statistical inferences on Timothy M. Bahr experimental data + prior knowledge. ◮ Classical (Frequentist) Statistics >>> data from Introduction observations or experiments only. Definitions Bayesian ◮ Prior Distribution: The distribution we assume our Statistics parameters come from. Microarrays Confounded ◮ Gibbs Sampling (simplification): An algorithm that Experiments allows us to give interatively infer point estimates for Model “random” parameters. Gibbs Sampling Application

Definitions Introduction to Bayesian Statistics and an Application Timothy M. Bahr Introduction Definitions Bayesian Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Definitions Introduction to Bayesian Statistics and an Application ◮ Biostatistics: The application of statistics to a wide Timothy M. Bahr range of topics in biology. Introduction Definitions Bayesian Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Definitions Introduction to Bayesian Statistics and an Application ◮ Biostatistics: The application of statistics to a wide Timothy M. Bahr range of topics in biology. Introduction ◮ Gene Expression Microarray: A high-throughput Definitions technology in molecular biology used to detect gene Bayesian expression levels in a cellular sample. Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Definitions Introduction to Bayesian Statistics and an Application ◮ Biostatistics: The application of statistics to a wide Timothy M. Bahr range of topics in biology. Introduction ◮ Gene Expression Microarray: A high-throughput Definitions technology in molecular biology used to detect gene Bayesian expression levels in a cellular sample. Statistics Microarrays ◮ Confounded Experiment: when two or more variables Confounded vary together so that it is impossible to separate Experiments their unique effects. Model Gibbs Sampling Application

Bayesian Inference Introduction to Bayesian Probabilistic inference that computes the distribution of the Statistics and an model parameters and gives prediction for previously unseen Application input values probabilistically. Timothy M. Bahr Introduction Freqentist Definitions Bayesian Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Bayesian Inference Introduction to Bayesian Probabilistic inference that computes the distribution of the Statistics and an model parameters and gives prediction for previously unseen Application input values probabilistically. Timothy M. Bahr Introduction Freqentist Definitions Bayesian Statistics ◮ θ , parameters, are fixed Microarrays and unknown Confounded Experiments Model Gibbs Sampling Application

Bayesian Inference Introduction to Bayesian Probabilistic inference that computes the distribution of the Statistics and an model parameters and gives prediction for previously unseen Application input values probabilistically. Timothy M. Bahr Introduction Freqentist Bayesian Definitions Bayesian Statistics ◮ θ , parameters, are fixed Microarrays and unknown Confounded ◮ X , random variables Experiments Model (data), are random Gibbs Sampling Application

Bayesian Inference Introduction to Bayesian Probabilistic inference that computes the distribution of the Statistics and an model parameters and gives prediction for previously unseen Application input values probabilistically. Timothy M. Bahr Introduction Freqentist Bayesian Definitions Bayesian Statistics ◮ θ , parameters, are fixed ◮ θ , parameters, are random Microarrays and unknown and unknown Confounded ◮ X , random variables Experiments Model (data), are random Gibbs Sampling Application

Bayesian Inference Introduction to Bayesian Probabilistic inference that computes the distribution of the Statistics and an model parameters and gives prediction for previously unseen Application input values probabilistically. Timothy M. Bahr Introduction Freqentist Bayesian Definitions Bayesian Statistics ◮ θ , parameters, are fixed ◮ θ , parameters, are random Microarrays and unknown and unknown Confounded ◮ X , random variables ◮ X , random variables Experiments Model (data), are random (data), are random Gibbs Sampling “If you want to work on really interesting problems [Bayesian Application Inference] is where those problems lie” -Don Rubin, Ph.D., Dept. Chair, Harvard Statistics

Bayesian Inference Introduction to Bayesian Statistics and an Application Timothy M. The idea of a prior Bahr Introduction Definitions Bayesian Statistics Microarrays Confounded Experiments Model Gibbs Sampling Application

Bayesian Inference Introduction to Bayesian Statistics and an Application Timothy M. The idea of a prior Bahr Introduction ◮ Frequentists assume a parameter is fixed: Definitions ◮ For example X ∼ N ( µ, σ 2 ) Bayesian Statistics ◮ µ is a fixed unknown value Microarrays Confounded Experiments Model Gibbs Sampling Application