Related Experiment Video
Updated: May 8, 2026
04:35
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
The multivariate beta process and an extension of the Polya tree model
Lorenzo Trippa1, Peter Müller, Wesley Johnson
1Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, Massachusetts 02115, U.S.A. , ltrippa@jimmy.harvard.edu.
Biometrika
|August 20, 2013
Summary
We introduce a novel multivariate beta process for modeling dependent probabilities with beta marginal distributions. This new stochastic process enables flexible nonparametric inference for survival distributions and extends parametric regression models.
Area of Science:
- Statistics
- Probability Theory
- Survival Analysis
Background:
- Modeling dependent random probabilities is crucial in various statistical applications.
- Existing methods may lack flexibility in handling unknown distributions indexed by covariates.
Purpose of the Study:
- Introduce a novel stochastic process, the multivariate beta process.
- Develop a probability model for unknown distributions using this process.
- Implement nonparametric inference for survival distributions.
Main Methods:
- Define the multivariate beta process for dependent random probabilities with beta marginals.
- Utilize a Polya tree prior for marginal distributions.
- Center the nonparametric model around parametric regression models.
Main Results:
- The multivariate beta process provides a flexible framework for probability modeling.
- The proposed prior facilitates easy centering around parametric regression models.
- The model enables nonparametric inference for survival distributions.
Conclusions:
- The multivariate beta process is a valuable tool for statistical modeling.
- This approach extends the support of prior distributions for parametric regression.
- The methodology offers enhanced flexibility in survival analysis and related fields.
Related Concept Videos
01:30Binomial Expansion Using Pascal's Triangle
Expanding a binomial expression such as (a + b)n results in a predictable sequence of terms that can be systematically derived using Pascal’s Triangle. This triangular array of numbers plays a central role in understanding and computing the coefficients of binomial expansions.Pascal’s Triangle is constructed such that each row corresponds to the coefficients of a binomial raised to a power. The topmost row, known as the zeroth row, corresponds to (a + b)0, and each successive row gives the...
01:19Survival Tree
Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
Building a Survival Tree
Constructing a survival tree begins...
Building a Survival Tree
Constructing a survival tree begins...
01:14Parametric Survival Analysis: Weibull and Exponential Methods
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
01:25Multiple Regression
Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
01:22Multi-input and Multi-variable systems
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
In the absence of...
01:30The Binomial Theorem
The Binomial Theorem is a foundational principle in algebra used to expand expressions raised to a power. It provides a structured approach for expanding binomials of the form (a+b)n, where a and b are variables or constants representing algebraic expressions, and n is a non-negative integer.The general form of the Binomial Theorem is:Each term in the expansion involves a binomial coefficient, which is calculated using factorials:The exponent of a in each term decreases from n to 0, while the...