Probability density function

About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.

An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants

Abstract: Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis-Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.

Optimized computation of the Voigt and complex probabilityfunctions

Abstract: Methods for computing the complex probability function w(z), which is related to the Voigt spectrum line profiles, are developed. The basic method is a rational approximation, minimizing the relative error of the imaginary part on the real axis.

A k‐nearest‐neighbor simulator for daily precipitation and other weather variables

Abstract: A multivariate, nonparametric time series simulation method is provided to generate random sequences of daily weather variables that "honor" the statistical properties of the historical data of the same weather variables at the site. A vector of weather variables (solar radiation, maximum temperature, minimum temperature, average dew point temperature, average wind speed, and precipitation) on a day of interest is resampled from the historical data by conditioning on the vector of the same variables (feature vector) on the preceding day. The resampling is done from the k nearest neighbors in state space of the feature vector using a weight function. This approach is equivalent to a nonparametric approximation of a multivariate, lag 1 Markov process. It does not require prior assumptions as to the form of the joint probability density function of the variables. An application of the resampling scheme with 30 years of daily weather data at Salt Lake City, Utah, is provided. Results are compared with those from the application of a multivariate autoregressive model similar to that of Richardson (1981).

A note on Metropolis-Hastings kernels for general state spaces

Abstract: The Metropolis-Hastings algorithm is a method of constructing a reversible Markov transition kernel with a specified invariant distribution. This note describes necessary and sufficient conditions on the candidate generation kernel and the acceptance probability function for the resulting transition kernel and invariant distribution to satisfy the detailed balance conditions. A simple general formulation is used that covers a range of special cases treated separately in the literature. In addition, results on a useful partial ordering of finite state space reversible transition kernels are extended to general state spaces and used to compare the performance of two approaches to using mixtures in Metropolis-Hastings kernels.