Related Experiment Video
Updated: Dec 18, 2025
06:19
Constructing and Visualizing Models using Mime-based Machine-learning Framework
Published on: July 22, 2025
1.9K
Exchangeable Markov survival processes and weak continuity of predictive distributions
Walter Dempsey1, Peter McCullagh2
1Department of Statistics, Harvard University, Cambridge, MA 02138, wdempsey@fas.harvard.edu.
Electronic Journal of Statistics
|December 18, 2018
Summary
We introduce the harmonic process, a novel family of exchangeable, Markov survival processes. This process provides a natural statistical model for time-to-event data, simplifying analysis and prediction.
Area of Science:
- Stochastic Processes
- Survival Analysis
- Statistical Modeling
Background:
- Exchangeable, Markov survival processes model sequences of event times.
- Understanding these processes is crucial for accurate time-to-event data analysis.
Purpose of the Study:
- To identify and characterize a natural family of exchangeable, Markov survival processes.
- To establish the harmonic process as a key statistical model for time-to-event data.
Main Methods:
- Mathematical derivation of stochastic processes properties.
- Analysis of characteristic index and predictive distributions.
- Sequential generation and probability distribution formulation.
Main Results:
- The harmonic process is identified as the family of exchangeable, Markov survival processes with weakly continuous predictive distributions.
- A simple sequential generation method and expressions for joint probability and multivariate survivor functions are provided.
- A close connection to the Kaplan-Meier estimator is demonstrated.
Conclusions:
- The harmonic process offers a statistically sound and computationally tractable framework for time-to-event data.
- This framework facilitates the analysis of complex survival data structures.
- Further investigation into aspects like block distribution is warranted.
Related Concept Videos
01:14Parametric Survival Analysis: Weibull and Exponential Methods
905
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...
905
01:14Reversible and Irreversible Processes
5.4K
The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
5.4K
01:15Assumptions of Survival Analysis
309
Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.
309
01:32Probability Distributions
11.4K
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...
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
11.4K
01:10Entropy Change in Reversible Processes
3.1K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.1K
01:24BIBO stability of continuous and discrete -time systems
823
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
823