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### A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function [article]

Pedro A. Ortega, Jordi Grau-Moya, Tim Genewein, David Balduzzi, Daniel A. Braun
2012 arXiv   pre-print
Here we skip the representation step and directly model the distribution over extrema. To this end, we devise a non-parametric conjugate prior based on a kernel regressor.  ...  We illustrate the effectiveness of our model by optimizing a noisy, high-dimensional, non-convex objective function.  ...  This in turn, enabled us to state a conjugate prior distribution over the optimal test point.  ...

### Page 4875 of Mathematical Reviews Vol. 58, Issue 6 [page]

1979 Mathematical Reviews
a posteriori probability functions maximize this criterion.  ...  The role of maximum-entropy methods to generate system complexity measures is viewed as having principal value in generating the prior or canonical distribution of system defects for a given state of knowledge  ...

### Bayesian Entropic Inverse Theory Approach to Implied Option Pricing with Noisy Data [article]

Igor Halperin
2002 arXiv   pre-print
A popular approach to nonparametric option pricing is the Minimum Cross Entropy (MCE) method based on minimization of the relative Kullback-Leibler entropy of the price density distribution and a given  ...  The method can be used for a non-parametric pricing of American/Bermudan options with a possible weak path dependence.  ...  In what follows we analyze both δ-function (30) and conjugate (36) choices for the prior. Jeffrey's prior is recovered by the particular choice α = 3 2 , β = 0 (37) in the conjugate prior (36).  ...

### Nonparametric Bayesian label prediction on a graph

Jarno Hartog, Harry van Zanten
2018 Computational Statistics & Data Analysis
PRIOR ON ℓ To put a prior on ℓ we first use the probit link Φ (i.e. the cdf of the standard normal distribution) to write ℓ = Φ( f ) for some function f : V → R and then put a prior on f .  ...  The gamma distribution is conjugate for the inverse variance (precision) of a univariate normal distribution. So, if X | θ ∼ N (µ, 1/θ) and θ ∼ Γ(α, β) then θ | X ∼ Γ(α + 1 2 , β + 1 2 (X − µ) 2 ).  ...  However, we do not know the correct truncation level beforehand. As we have a conjugate prior for c, we treat it as an unknown parameter of the model that we estimate in the posterior.  ...

### An Overview of Bayesian Methods for Neural Spike Train Analysis

Zhe Chen
2013 Computational Intelligence and Neuroscience
On the application side, the topics include spike sorting, tuning curve estimation, neural encoding and decoding, deconvolution of spike trains from calcium imaging signals, and inference of neuronal functional  ...  With the advancement of multielectrode recording and imaging technologies, it has become increasingly demanding to develop statistical tools for analyzing large neuronal ensemble spike activity.  ...  Acknowledgments The author was supported by an Early Career Award from the Mathematical Biosciences Institute, Ohio State University.  ...

### Nonparametric estimation of diffusions: a differential equations approach

O. Papaspiliopoulos, Y. Pokern, G. O. Roberts, A. M. Stuart
2012 Biometrika
We adopt a probabilistic approach to regularize the problem by the adoption of a prior distribution for the unknown functional.  ...  We establish that a Bayesian-Gaussian conjugate analysis for the drift of one-dimensional nonlinear diffusions is feasible using high-frequency data, by expressing the loglikelihood as a quadratic function  ...  We adopt a probabilistic approach to regularize the problem by the adoption of a prior distribution for the unknown functional.  ...

### GaussianProcesses.jl: A Nonparametric Bayes Package for the Julia Language

Jamie Fairbrother, Christopher Nemeth, Maxime Rischard, Johanni Brea, Thomas Pinder
2022 Journal of Statistical Software
In this paper, we present a tutorial of the GaussianProcesses.jl package that has been developed for the Julia programming language.  ...  Gaussian processes are a class of flexible nonparametric Bayesian tools that are widely used across the sciences, and in industry, to model complex data sources.  ...  TP is supported by the Data Science for the Natural Environment project (EPSRC grant number EP/R01860X/1).  ...

### Digital Image Reconstruction: Deblurring and Denoising

R.C. Puetter, T.R. Gosnell, Amos Yahil
2005 Annual Review of Astronomy and Astrophysics
impose a variable degree of restriction across the image.  ...  Digital image reconstruction is a robust means by which the underlying images hidden in blurry and noisy data can be revealed.  ...  ACKNOWLEDGMENT The authors thank George Romano of the Aerospace Corporation for help in preparing the collage of scans from IRAS used in Figure 6 .  ...

### Stochastic Variational Inference [article]

Matt Hoffman, David M. Blei, Chong Wang, John Paisley
2013 arXiv   pre-print
We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions.  ...  We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models, latent Dirichlet allocation and the hierarchical Dirichlet process topic model  ...  In Section 2, we assumed that we can calculate p(β|x, z), the conditional distribution of the global hidden variables β given the local hidden variables z and observed variables x.  ...

### Wavelet-Based Nonparametric Bayes Methods [chapter]

Brani Vidakovic
1998 Practical Nonparametric and Semiparametric Bayesian Statistics
For a discussion and examples see Walter (1994) . These arguments identify wavelet bases as suitable tools for effective statistical modeling.  ...  Wavelets are the building blocks of wavelet transformations the same way that the functions e inx are the building blocks of the ordinary Fourier transformation.  ...  The authors propose a linear, empirical Bayes estimatorf of f that enjoys Gauss-Markov type of optimality. Several non-linear versions of the esrimator are proposed, as well.  ...

### Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising

S. Lefkimmiatis, P. Maragos, G. Papandreou
2009 IEEE Transactions on Image Processing
Our main contributions include: 1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the noisy  ...  We build on previous work, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities (rates) in adjacent scales are modeled as mixtures of conjugate  ...  ACKNOWLEDGMENT The authors would like to thank B. Zhang for providing the images used for comparisons in Table IV .  ...

### GaussianProcesses.jl: A Nonparametric Bayes package for the Julia Language [article]

Jamie Fairbrother, Christopher Nemeth, Maxime Rischard, Johanni Brea, Thomas Pinder
2019 arXiv   pre-print
In this paper, we present a tutorial of the GaussianProcesses.jl package that has been developed for the Julia programming language.  ...  Gaussian processes are a class of flexible nonparametric Bayesian tools that are widely used across the sciences, and in industry, to model complex data sources.  ...  Prior distributions are assigned to the parameters of the mean and kernel parameters through the set priors! function. The log-noise parameter σ is set to a non-informative prior p(σ) ∝ 1.  ...

### Finding Convincing Arguments Using Scalable Bayesian Preference Learning [article]

Edwin Simpson, Iryna Gurevych
2018 arXiv   pre-print
We introduce a scalable Bayesian preference learning method for identifying convincing arguments in the absence of gold-standard rat- ings or rankings.  ...  We demonstrate how the Bayesian approach enables more effective active learning, thereby reducing the amount of data required to identify convincing arguments for new users and domains.  ...  It reflects only the authors views and the EU is not liable for any use that may be made of the information contained therein.  ...