Related papers: Monte Carlo profile confidence intervals
Engineering risk is concerned with the likelihood of failure and the scenarios when it occurs. The sensitivity of failure probability to change in system parameters is relevant to risk-informed decision making. Computing sensitivity is at…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of…
Empirical likelihood enables a nonparametric, likelihood-driven style of inference without restrictive assumptions routinely made in parametric models. We develop a framework for applying empirical likelihood to the analysis of experimental…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
Mathematical models are essential for understanding and making predictions about systems arising in nature and engineering. Yet, mathematical models are a simplification of true phenomena, thus making predictions subject to uncertainty.…
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…
We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions,…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
Monte Carlo methods are used to approximate the means, $\mu$, of random variables $Y$, whose distributions are not known explicitly. The key idea is that the average of a random sample, $Y_1, ..., Y_n$, tends to $\mu$ as $n$ tends to…
The impact of machine learning models on healthcare will depend on the degree of trust that healthcare professionals place in the predictions made by these models. In this paper, we present a method to provide people with clinical expertise…
Extracting maximal information from experimental data requires access to the likelihood function, which however is never directly available for complex experiments like those performed at high energy colliders. Theoretical predictions are…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…
Sequential Monte Carlo methods are a powerful framework for approximating the posterior distribution of a state variable in a sequential manner. They provide an attractive way of analyzing dynamic systems in real-time, taking into account…