scholarly journals Nested sampling with plateaus

2021 ◽  
Vol 503 (1) ◽  
pp. 1199-1205
Author(s):  
Andrew Fowlie ◽  
Will Handley ◽  
Liangliang Su
Keyword(s):  
Likelihood Function ◽  
Nested Sampling ◽  
Canonical Version

ABSTRACT It was recently emphasized that in the presence of plateaus in the likelihood function nested sampling (NS) produces faulty estimates of the evidence and posterior densities. After informally explaining the cause of the problem, we present a modified version of NS that handles plateaus and can be applied retrospectively to NS runs from popular NS software using anesthetic. In the modified NS, live points in a plateau are evicted one by one without replacement, with ordinary NS compression of the prior volume after each eviction but taking into account the dynamic number of live points. The live points are replenished once all points in the plateau are removed. We demonstrate it on a number of examples. Since the modification is simple, we propose that it becomes the canonical version of Skilling’s NS algorithm.

scholarly journals Mean Shift Cluster Recognition Method Implementation in the Nested Sampling Algorithm

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 185
Author(s):  
Martino Trassinelli ◽  
Pierre Ciccodicola
Keyword(s):  
Parameter Space ◽  
Likelihood Function ◽  
Search Algorithm ◽  
Probability Distributions ◽  
Mean Shift ◽  
Computation Time ◽  
Recognition Method ◽  
Nested Sampling ◽  
Bayesian Evidence ◽  
Cluster Recognition

Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a series of values sets called live points that evolve towards the region of interest, i.e., where the likelihood function is maximal. In presence of several local likelihood maxima, the algorithm converges with difficulty. Some systematic errors can also be introduced by unexplored parameter volume regions. In order to avoid this, different methods are proposed in the literature for an efficient search of new live points, even in presence of local maxima. Here we present a new solution based on the mean shift cluster recognition method implemented in a random walk search algorithm. The clustering recognition is integrated within the Bayesian analysis program NestedFit. It is tested with the analysis of some difficult cases. Compared to the analysis results without cluster recognition, the computation time is considerably reduced. At the same time, the entire parameter space is efficiently explored, which translates into a smaller uncertainty of the extracted value of the Bayesian evidence.

scholarly journals Nested sampling cross-checks using order statistics

2020 ◽  
Vol 497 (4) ◽  
pp. 5256-5263
Author(s):  
Andrew Fowlie ◽  
Will Handley ◽  
Liangliang Su
Keyword(s):  
Data Analysis ◽  
Model Selection ◽  
Cosmological Model ◽  
Gravitational Wave ◽  
Order Statistics ◽  
Particle Physics ◽  
Likelihood Function ◽  
Nested Sampling ◽  
Invaluable Tool ◽  
The Cross

ABSTRACT Nested sampling (NS) is an invaluable tool in data analysis in modern astrophysics, cosmology, gravitational wave astronomy, and particle physics. We identify a previously unused property of NS related to order statistics: the insertion indexes of new live points into the existing live points should be uniformly distributed. This observation enabled us to create a novel cross-check of single NS runs. The tests can detect when an NS run failed to sample new live points from the constrained prior and plateaus in the likelihood function, which break an assumption of NS and thus leads to unreliable results. We applied our cross-check to NS runs on toy functions with known analytic results in 2–50 dimensions, showing that our approach can detect problematic runs on a variety of likelihoods, settings, and dimensions. As an example of a realistic application, we cross-checked NS runs performed in the context of cosmological model selection. Since the cross-check is simple, we recommend that it become a mandatory test for every applicable NS run.

A mutual information‐based likelihood function for particle filter flood extent assimilation

2021 ◽  
Author(s):  
Antara Dasgupta ◽  
Renaud Hostache ◽  
RAAJ Ramasankaran ◽  
Guy J.‐P Schumann ◽  
Stefania Grimaldi ◽  
...  
Keyword(s):  
Mutual Information ◽  
Particle Filter ◽  
Likelihood Function

Bayesian Estimation of DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Likelihood Function ◽  
Academic Research ◽  
Dynamic Stochastic General Equilibrium ◽  
Computational Techniques ◽  
Dsge Models ◽  
Monte Carlo Techniques ◽  
Dynamic Stochastic ◽  
Theoretical Foundations

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations. The book is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

Statistical Justification of Pearson's Criterion for Testing a Complex Hypothesis on the Uniform Distribution

2018 ◽  
pp. 45-53
Author(s):  
T. V. Oblakova
Keyword(s):  
Uniform Distribution ◽  
Degrees Of Freedom ◽  
Likelihood Function ◽  
Random Number Generator ◽  
Maximum Likelihood Estimates ◽  
Chi Square ◽  
Main Hypothesis ◽  
Pearson Criterion ◽  
Complex Hypothesis ◽  
Uniform Law

The paper is studying the justification of the Pearson criterion for checking the hypothesis on the uniform distribution of the general totality. If the distribution parameters are unknown, then estimates of the theoretical frequencies are used [1, 2, 3]. In this case the quantile of the chi-square distribution with the number of degrees of freedom, reduced by the number of parameters evaluated, is used to determine the upper threshold of the main hypothesis acceptance [7]. However, in the case of a uniform law, the application of Pearson's criterion does not extend to complex hypotheses, since the likelihood function does not allow differentiation with respect to parameters, which is used in the proof of the theorem mentioned [7, 10, 11].A statistical experiment is proposed in order to study the distribution of Pearson statistics for samples from a uniform law. The essence of the experiment is that at first a statistically significant number of one-type samples from a given uniform distribution is modeled, then for each sample Pearson statistics are calculated, and then the law of distribution of the totality of these statistics is studied. Modeling and processing of samples were performed in the Mathcad 15 package using the built-in random number generator and array processing facilities.In all the experiments carried out, the hypothesis that the Pearson statistics conform to the chi-square law was unambiguously accepted (confidence level 0.95). It is also statistically proved that the number of degrees of freedom in the case of a complex hypothesis need not be corrected. That is, the maximum likelihood estimates of the uniform law parameters implicitly used in calculating Pearson statistics do not affect the number of degrees of freedom, which is thus determined by the number of grouping intervals only.

Bayesian Inference in Human Time Perception

2017 ◽  
Author(s):  
Darren Rhodes
Keyword(s):  
Time Perception ◽  
Likelihood Function ◽  
Human Perception ◽  
Future Research ◽  
Temporal Properties ◽  
History Of Research ◽  
Psychophysical Testing ◽  
History Of ◽  
Fundamental Dimension ◽  
Perception Of Time

Time is a fundamental dimension of human perception, cognition and action, as the perception and cognition of temporal information is essential for everyday activities and survival. Innumerable studies have investigated the perception of time over the last 100 years, but the neural and computational bases for the processing of time remains unknown. First, we present a brief history of research and the methods used in time perception and then discuss the psychophysical approach to time, extant models of time perception, and advancing inconsistencies between each account that this review aims to bridge the gap between. Recent work has advocated a Bayesian approach to time perception. This framework has been applied to both duration and perceived timing, where prior expectations about when a stimulus might occur in the future (prior distribution) are combined with current sensory evidence (likelihood function) in order to generate the perception of temporal properties (posterior distribution). In general, these models predict that the brain uses temporal expectations to bias perception in a way that stimuli are ‘regularized’ i.e. stimuli look more like what has been seen before. Evidence for this framework has been found using human psychophysical testing (experimental methods to quantify behaviour in the perceptual system). Finally, an outlook for how these models can advance future research in temporal perception is discussed.

scholarly journals Zero-inflated-censored Weibull and gamma regression models to estimate wild boar population dispersal distance

2021 ◽  
Author(s):  
Eduardo de Freitas Costa ◽  
Silvana Schneider ◽  
Giulia Bagatini Carlotto ◽  
Tainá Cabalheiro ◽  
Mauro Ribeiro de Oliveira Júnior
Keyword(s):  
Wild Boar ◽  
Regression Models ◽  
Likelihood Function ◽  
Complex Structure ◽  
Dispersal Distance ◽  
Wild Boar Population ◽  
Gamma Distributions ◽  
Excess Of Zeros ◽  
Censored Observations ◽  
Positive Effect

AbstractThe dynamics of the wild boar population has become a pressing issue not only for ecological purposes, but also for agricultural and livestock production. The data related to the wild boar dispersal distance can have a complex structure, including excess of zeros and right-censored observations, thus being challenging for modeling. In this sense, we propose two different zero-inflated-right-censored regression models, assuming Weibull and gamma distributions. First, we present the construction of the likelihood function, and then, we apply both models to simulated datasets, demonstrating that both regression models behave well. The simulation results point to the consistency and asymptotic unbiasedness of the developed methods. Afterwards, we adjusted both models to a simulated dataset of wild boar dispersal, including excess of zeros, right-censored observations, and two covariates: age and sex. We showed that the models were useful to extract inferences about the wild boar dispersal, correctly describing the data mimicking a situation where males disperse more than females, and age has a positive effect on the dispersal of the wild boars. These results are useful to overcome some limitations regarding inferences in zero-inflated-right-censored datasets, especially concerning the wild boar’s population. Users will be provided with an R function to run the proposed models.

scholarly journals Discussion on Competition for Spatial Statistics for Large Datasets

2021 ◽  
Author(s):  
Roman Flury ◽  
Reinhard Furrer
Keyword(s):  
Spatial Statistics ◽  
Covariance Function ◽  
Likelihood Function ◽  
Large Datasets ◽  
Missing Observations ◽  
Covariance Model ◽  
Compactly Supported ◽  
Covariance Tapering ◽  
Simple Kriging ◽  
Estimated Parameters

AbstractWe discuss the experiences and results of the AppStatUZH team’s participation in the comprehensive and unbiased comparison of different spatial approximations conducted in the Competition for Spatial Statistics for Large Datasets. In each of the different sub-competitions, we estimated parameters of the covariance model based on a likelihood function and predicted missing observations with simple kriging. We approximated the covariance model either with covariance tapering or a compactly supported Wendland covariance function.

scholarly journals Nested Sampling Approach to Set-membership Estimation

2020 ◽  
Vol 53 (2) ◽  
pp. 7228-7233
Author(s):  
Radoslav Paulen ◽  
Lucian Gomoescu ◽  
Benoît Chachuat
Keyword(s):  
Nested Sampling ◽  
Set Membership ◽  
Sampling Approach
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