Large deviation estimates for a conditional probability distribution. Applications to random interaction Gibbs measures

1989 ◽  
Vol 80 (3) ◽  
pp. 407-432 ◽  
Author(s):  
F. Comets
Keyword(s):  
Probability Distribution ◽  
Conditional Probability ◽  
Large Deviation ◽  
Gibbs Measures ◽  
Conditional Probability Distribution ◽  
Random Interaction

scholarly journals Precision Annealing Monte Carlo Methods for Statistical Data Assimilation: Metropolis-Hastings Procedures

2019 ◽  
Author(s):  
Adrian S. Wong ◽  
Kangbo Hao ◽  
Zheng Fang ◽  
Henry D. I. Abarbanel
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Data Assimilation ◽  
Conditional Probability ◽  
Information Transfer ◽  
Statistical Data ◽  
Laplace Method ◽  
Conditional Probability Distribution ◽  
Expected Values ◽  
Transfer Of Information

Abstract. Statistical Data Assimilation (SDA) is the transfer of information from field or laboratory observations to a user selected model of the dynamical system producing those observations. The data is noisy and the model has errors; the information transfer addresses properties of the conditional probability distribution of the states of the model conditioned on the observations. The quantities of interest in SDA are the conditional expected values of functions of the model state, and these require the approximate evaluation of high dimensional integrals. We introduce a conditional probability distribution and use the Laplace method with annealing to identify the maxima of the conditional probability distribution. The annealing method slowly increases the precision term of the model as it enters the Laplace method. In this paper, we extend the idea of precision annealing (PA) to Monte Carlo calculations of conditional expected values using Metropolis-Hastings methods.

Pseudo Independent Models

2011 ◽  
pp. 935-940
Author(s):  
Yang Xiang
Keyword(s):  
Probability Distribution ◽  
Computer System ◽  
Conditional Probability ◽  
Graphical Models ◽  
Intelligent Systems ◽  
Probabilistic Reasoning ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Conditional Probability Distribution ◽  
Binary Variables

Graphical models such as Bayesian networks (BNs) (Pearl, 1988) and decomposable Markov networks (DMNs) (Xiang, Wong & Cercone, 1997) have been applied widely to probabilistic reasoning in intelligent systems. Figure1 illustrates a BN and a DMN on a trivial uncertain domain: A virus can damage computer files, and so can a power glitch. A power glitch also causes a VCR to reset. The BN in (a) has four nodes, corresponding to four binary variables taking values from {true, false}. The graph structure encodes a set of dependence and independence assumptions (e.g., that f is directly dependent on v, and p but is independent of r, once the value of p is known). Each node is associated with a conditional probability distribution conditioned on its parent nodes (e.g., P(f | v, p)). The joint probability distribution is the product P(v, p, f, r) = P(f | v, p) P(r | p) P(v) P(p). The DMN in (b) has two groups of nodes that are maximally pair-wise connected, called cliques. Each clique is associated with a probability distribution (e.g., clique {v, p, f} is assigned P(v, p, f)). The joint probability distribution is P(v, p, f, r) = P(v, p, f) P(r, p) / P(p), where P(p) can be derived from one of the clique distributions. The networks, for instance, can be used to reason about whether there are viruses in the computer system, after observations on f and r are made.

Prediction of the contributions to the Reynolds stress from bursting events in open-channel flows

1977 ◽  
Vol 80 (1) ◽  
pp. 99-128 ◽  
Author(s):  
Hiroji Nakagawa ◽  
Iehisa Nezu
Keyword(s):  
Probability Distribution ◽  
Conditional Probability ◽  
Reynolds Stress ◽  
High Speed ◽  
Processing System ◽  
Digital Data ◽  
Conditional Probability Distribution ◽  
Sequence Of Events ◽  
Dual Sensor ◽  
Bursting Events

In this paper we intend to predict the magnitude of the contribution to the Reynolds stress of bursting events: ‘ejections’, ‘sweeps’, ‘inward interactions’ and ‘outward interactions’. We shall do this by making use of the conditional probability distribution of the Reynolds stress −uv, which can be derived by applying the cumulant-discard method to the Gram-Charlier probability distribution of the two variablesuandv. The Reynolds-stress fluctuations in openchannel flows over smooth and rough beds are measured by dual-sensor hot-film anemometers, whose signals are conditionally sampled and sorted into the four quadrants of theu, vplane by using a high-speed digital data processing system.We shall verify that even the third-order conditional probability distribution of the Reynolds stress shows fairly good agreement with the experimental results and that the sequence of events in the bursting process, i.e. ejections, sweeps and interactions, is directly related to the turbulent energy budget in the form of turbulent diffusion. Also, we shall show that the roughness effect is marked in the area from the wall to the middle of the equilibrium region, and that sweeps appear to be more important than ejections as the roughness increases and as the distance from the wall decreases.

The limiting conditional probability distribution in a stochastic model of T cell repertoire maintenance

2010 ◽  
Vol 224 (2) ◽  
pp. 74-86 ◽  
Author(s):  
Emily R. Stirk ◽  
Grant Lythe ◽  
Hugo A. van den Berg ◽  
Gareth A.D. Hurst ◽  
Carmen Molina-París
Keyword(s):  
T Cell ◽  
Probability Distribution ◽  
Stochastic Model ◽  
Conditional Probability ◽  
T Cell Repertoire ◽  
Cell Repertoire ◽  
Conditional Probability Distribution

scholarly journals Covariate-based stochastic parameterization of baroclinic ocean eddies

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Nick Verheul ◽  
Jan Viebahn ◽  
Daan Crommelin
Keyword(s):  
Probability Distribution ◽  
Conditional Probability ◽  
Ocean Circulation ◽  
Reference Model ◽  
Coarse Graining ◽  
Stochastic Approach ◽  
Distribution Functions ◽  
Conditional Probability Distribution ◽  
Probability Distribution Functions ◽  
Temporal Correlations

AbstractIn this study we investigate a covariate-based stochastic approach to parameterize unresolved turbulent processes within a standard model of the idealised, wind-driven ocean circulation. We focus on vertical instead of horizontal coarse-graining, such that we avoid the subtle difficulties of horizontal coarsegraining. The corresponding eddy forcing is uniquely defined and has a clear physical interpretation related to baroclinic instability.We propose to emulate the baroclinic eddy forcing by sampling from the conditional probability distribution functions of the eddy forcing obtained from the baroclinic reference model data. These conditional probability distribution functions are approximated here by sampling uniformly from discrete reference values. We analyze in detail the different performances of the stochastic parameterization dependent on whether the eddy forcing is conditioned on a suitable flow-dependent covariate or on a timelagged covariate or on both. The results demonstrate that our non-Gaussian, non-linear methodology is able to accurately reproduce the first four statistical moments and spatial/temporal correlations of the stream function, energetics, and enstrophy of the reference baroclinic model.

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