Related Experiment Videos
The bootstrap and Markov-chain Monte Carlo.
1Stanford University, Stanford, California 94305, USA. brad@stat.stanford.edu
Journal of Biopharmaceutical Statistics
|October 26, 2011
Summary
Parametric bootstrap sampling offers computational and theoretical advantages for Bayesian inference calculations, complementing Markov-Chain Monte Carlo (MCMC) methods in specific scenarios. This approach provides a viable alternative when applicable, enhancing analytical efficiency.
Area of Science:
- Statistics
- Computational Statistics
Background:
- Bayesian inference is a statistical method for updating probability beliefs with new evidence.
- Markov-Chain Monte Carlo (MCMC) is a common computational technique for Bayesian analysis.
- Parametric bootstrap sampling is a resampling method used to estimate sampling distributions.
Purpose of the Study:
- To explore the application of parametric bootstrap sampling in Bayesian inference.
- To identify the advantages of bootstrap methods over traditional MCMC in certain statistical problems.
Main Methods:
- Utilized parametric bootstrap sampling for Bayesian inference calculations.
- Applied the method to a subset of problems typically addressed by MCMC analysis.
- Illustrated the approach with a simple, illustrative example.
Main Results:
- Demonstrated that parametric bootstrap sampling is feasible for specific Bayesian inference tasks.
- Highlighted computational and theoretical benefits of the bootstrap approach when applicable.
- Showcased the method's utility in a simplified case study.
Conclusions:
- Parametric bootstrap sampling presents a valuable alternative for Bayesian inference in specific contexts.
- The bootstrap method offers advantages over MCMC where applicable.
- Further research could explore broader applications of this technique.
Related Concept Videos
01:24Bootstrapping
The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is small or...
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
01:09Random Variables
A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
01:13Randomized Experiments
The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...
Simple randomization
Simple...
01:14Probability in Statistics
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
01:32Probability Distributions
The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...