scholarly journals Continualization of Probabilistic Programs With Correction

2020 ◽  
pp. 366-393 ◽  
Author(s):  
Jacob Laurel ◽  
Sasa Misailovic
Keyword(s):  
Parameter Estimation ◽  
Real World ◽  
Stochastic Models ◽  
Original Model ◽  
Continuous Approximation ◽  
Continuous Distributions ◽  
True Parameter ◽  
Inference Algorithms ◽  
Parameter Values ◽  
Probabilistic Programs

AbstractProbabilistic Programming offers a concise way to represent stochastic models and perform automated statistical inference. However, many real-world models have discrete or hybrid discrete-continuous distributions, for which existing tools may suffer non-trivial limitations. Inference and parameter estimation can be exceedingly slow for these models because many inference algorithms compute results faster (or exclusively) when the distributions being inferred are continuous. To address this discrepancy, this paper presents Leios. Leios is the first approach for systematically approximating arbitrary probabilistic programs that have discrete, or hybrid discrete-continuous random variables. The approximate programs have all their variables fully continualized. We show that once we have the fully continuous approximate program, we can perform inference and parameter estimation faster by exploiting the existing support that many languages offer for continuous distributions. Furthermore, we show that the estimates obtained when performing inference and parameter estimation on the continuous approximation are still comparably close to both the true parameter values and the estimates obtained when performing inference on the original model.

Optimal algorithm for distinguishing radio navigation signals by a set of “spaced” correlators

2021 ◽  
Vol 8 ◽  
pp. 11-23
Author(s):  
V.N. Kharisov ◽  
D.A. Eremeev
Keyword(s):  
Parameter Estimation ◽  
Noise Immunity ◽  
Optimal Algorithm ◽  
Average Energy ◽  
Large Signal ◽  
Energy Potential ◽  
True Parameter ◽  
Discrete Parameter ◽  
Classical Algorithm ◽  
Parameter Values

The classical algorithm for signal distinction, signal detecting and estimating signal parameters consists in analyzing discrete parameter values using a correlator. The value of the parameter with the maximum absolute value of the correlator is taken as an estimate. Obviously, this is accompanied by losses in sensitivity and noise immunity, since the specified discrete parameter values do not accurately correspond to the true parameter values of the real signal. In this case, the accuracy of the parameter estimation, even at large signal-to-noise ratios, is limited by the value of the correlators placement interval. Therefore, it is of interest to optimally use the entire set of correlators for parameter estimation and signal detection. The article presents the derivation of algorithm for distinguishing signals by a given parameter by a set of "spaced" correlators. Unlike the classical algorithm, it uses decisive statistics not by one, but by a pair of neighboring correlators, detuned by the correlation interval. In this case, at first, the number of the interval between correlators is estimated according to the maximum of the decisive statistics, and then the value of the parameter is refined within this interval. Additionally, the algorithm allows you to estimate the signal amplitude. The proposed algorithm is compared with the classical one. By means of simulation, the dependences on the energy potential of the average probability of signal distinction for both algorithms are plotted. It is shown that the proposed algorithm has a higher probability of correct distinction than the classical algorithm. It is also shown that the maximum and average energy losses of the distinction algorithm based on a set of "spaced" correlators are less than the losses of the classical algorithm. Thus, the proposed algorithm for distinction signals by a set of "spaced" correlators has greater noise immunity and accuracy of estimating the desired parameter than the classical distinction algorithm.

Identification of Biodegradation models under model and data uncertainty

1996 ◽  
Vol 33 (2) ◽  
pp. 91-105 ◽  
Author(s):  
Peter A. Vanrolleghem ◽  
Karel J. Keesman
Keyword(s):  
Parameter Estimation ◽  
Real World ◽  
Data Uncertainty ◽  
Estimation Methods ◽  
Parameter Estimates ◽  
Local Minima ◽  
Real World Data ◽  
Correlation Matrices ◽  
Parameter Estimation Methods ◽  
Parameter Values

In this paper a number of nonlinear parameter estimation methods are evaluated with respect to their ability to identify biodegradation models from “real-world” data. Important aspects are then the sensitivity to local minima, rate of convergence, required prior knowledge and direct or indirect availability of parameter estimates uncertainty. Furthermore, it is important whether a method is robust against invalid assumptions. In addition to the final parameter values, covariance and correlation matrices, confidence intervals and residual sequences are presented to obtain information about the validity of the models and noise assumptions. Finally, recommendations on the method's applicability range are provided.

Approximate, Computationally Efficient Online Learning in Bayesian Spiking Neurons

2014 ◽  
Vol 26 (3) ◽  
pp. 472-496 ◽  
Author(s):  
Levin Kuhlmann ◽  
Michael Hauser-Raspe ◽  
Jonathan H. Manton ◽  
David B. Grayden ◽  
Jonathan Tapson ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Online Learning ◽  
Learning Algorithm ◽  
Computational Cost ◽  
Spiking Neurons ◽  
Estimation Accuracy ◽  
Parameter Estimates ◽  
Computationally Efficient ◽  
True Parameter ◽  
Parameter Values

Bayesian spiking neurons (BSNs) provide a probabilistic interpretation of how neurons perform inference and learning. Online learning in BSNs typically involves parameter estimation based on maximum-likelihood expectation-maximization (ML-EM) which is computationally slow and limits the potential of studying networks of BSNs. An online learning algorithm, fast learning (FL), is presented that is more computationally efficient than the benchmark ML-EM for a fixed number of time steps as the number of inputs to a BSN increases (e.g., 16.5 times faster run times for 20 inputs). Although ML-EM appears to converge 2.0 to 3.6 times faster than FL, the computational cost of ML-EM means that ML-EM takes longer to simulate to convergence than FL. FL also provides reasonable convergence performance that is robust to initialization of parameter estimates that are far from the true parameter values. However, parameter estimation depends on the range of true parameter values. Nevertheless, for a physiologically meaningful range of parameter values, FL gives very good average estimation accuracy, despite its approximate nature. The FL algorithm therefore provides an efficient tool, complementary to ML-EM, for exploring BSN networks in more detail in order to better understand their biological relevance. Moreover, the simplicity of the FL algorithm means it can be easily implemented in neuromorphic VLSI such that one can take advantage of the energy-efficient spike coding of BSNs.

scholarly journals Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

2015 ◽  
Vol 12 (108) ◽  
pp. 20150233 ◽  
Author(s):  
Shuohao Liao ◽  
Tomáš Vejchodský ◽  
Radek Erban
Keyword(s):  
Parameter Estimation ◽  
Stochastic Models ◽  
Regulatory Networks ◽  
Stochastic Modelling ◽  
Qualitative Change ◽  
Biochemical Networks ◽  
Model Parameters ◽  
Cellular Functions ◽  
Indispensable Tool ◽  
Parameter Values

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org .

Reliability of Genotype-Specific Parameter Estimation for Crop Models: Insights from a Markov Chain Monte-Carlo Estimation Approach

2017 ◽  
Vol 60 (5) ◽  
pp. 1699-1712
Author(s):  
Subodh Acharya ◽  
Melanie Correll ◽  
James W. Jones ◽  
Kenneth J. Boote ◽  
Phillip D. Alderman ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Inverse Modeling ◽  
Growth And Yield ◽  
Dry Bean ◽  
True Parameter ◽  
Crop Models ◽  
Parameter Values

Abstract. Parameter estimation is a critical step in successful application of dynamic crop models to simulate crop growth and yield under various climatic and management scenarios. Although inverse modeling parameterization techniques significantly improve the predictive capabilities of models, whether these approaches can recover the true parameter values of a specific genotype or cultivar is seldom investigated. In this study, we applied a Markov Chain Monte-Carlo (MCMC) method to the DSSAT dry bean model to estimate (recover) the genotype-specific parameters (GSPs) of 150 synthetic recombinant inbred lines (RILs) of dry bean. The synthetic parents of the population were assigned contrasting GSP values obtained from a database, and each of these GSPs was associated with several quantitative trait loci. A standard inverse modeling approach that simultaneously estimated all GSPs generated a set of values that could reproduce the original synthetic observations, but many of the estimated GSP values significantly differed from the original values. However, when parameter estimation was carried out sequentially in a stepwise manner, according to the genetically controlled plant development process, most of the estimated parameters had values similar to the original values. Developmental parameters were more accurately estimated than those related to dry mass accumulation. This new approach appears to reduce the problem of equifinality in parameter estimation, and it is especially relevant if attempts are made to relate parameter values to individual genes. Keywords: Crop models, Equifinality, Genotype-specific parameters, Markov chain Monte-Carlo, Parameterization.

Heterotrophic Kinetic Parameter Estimation for Enhanced Biological Phosphorus Removal Processes Operated in Conventional and Membrane-Assisted Modes

2006 ◽  
Vol 41 (1) ◽  
pp. 72-83 ◽  
Author(s):  
Zhe Zhang ◽  
Eric R. Hall
Keyword(s):  
Parameter Estimation ◽  
Phosphorus Removal ◽  
Growth Yield ◽  
Pilot Scale ◽  
Enhanced Biological Phosphorus Removal ◽  
Biological Phosphorus Removal ◽  
Nitrogen And Phosphorus ◽  
Parameter Values ◽  
The Impact ◽  
Biological Phosphorus

Abstract Parameter estimation and wastewater characterization are crucial for modelling of the membrane enhanced biological phosphorus removal (MEBPR) process. Prior to determining the values of a subset of kinetic and stoichiometric parameters used in ASM No. 2 (ASM2), the carbon, nitrogen and phosphorus fractions of influent wastewater at the University of British Columbia (UBC) pilot plant were characterized. It was found that the UBC wastewater contained fractions of volatile acids (SA), readily fermentable biodegradable COD (SF) and slowly biodegradable COD (XS) that fell within the ASM2 default value ranges. The contents of soluble inert COD (SI) and particulate inert COD (XI) were somewhat higher than ASM2 default values. Mixed liquor samples from pilot-scale MEBPR and conventional enhanced biological phosphorus removal (CEBPR) processes operated under parallel conditions, were then analyzed experimentally to assess the impact of operation in a membrane-assisted mode on the growth yield (YH), decay coefficient (bH) and maximum specific growth rate of heterotrophic biomass (µH). The resulting values for YH, bH and µH were slightly lower for the MEBPR train than for the CEBPR train, but the differences were not statistically significant. It is suggested that MEBPR simulation using ASM2 could be accomplished satisfactorily using parameter values determined for a conventional biological phosphorus removal process, if MEBPR parameter values are not available.

scholarly journals An Integrated Framework for the Inference of Viral Population History From Reconstructed Genealogies

Genetics ◽  
2000 ◽  
Vol 155 (3) ◽  
pp. 1429-1437
Author(s):  
Oliver G Pybus ◽  
Andrew Rambaut ◽  
Paul H Harvey
Keyword(s):  
Maximum Likelihood ◽  
Sequence Data ◽  
Demographic History ◽  
Population History ◽  
Maximum Likelihood Estimates ◽  
Viral Population ◽  
True Parameter ◽  
Subtype B ◽  
Exponential Growth Model ◽  
Parameter Values

Abstract We describe a unified set of methods for the inference of demographic history using genealogies reconstructed from gene sequence data. We introduce the skyline plot, a graphical, nonparametric estimate of demographic history. We discuss both maximum-likelihood parameter estimation and demographic hypothesis testing. Simulations are carried out to investigate the statistical properties of maximum-likelihood estimates of demographic parameters. The simulations reveal that (i) the performance of exponential growth model estimates is determined by a simple function of the true parameter values and (ii) under some conditions, estimates from reconstructed trees perform as well as estimates from perfect trees. We apply our methods to HIV-1 sequence data and find strong evidence that subtypes A and B have different demographic histories. We also provide the first (albeit tentative) genetic evidence for a recent decrease in the growth rate of subtype B.

Spatial scale effects on model parameter estimation and predictive uncertainty in ungauged basins

2012 ◽  
Vol 44 (3) ◽  
pp. 441-453 ◽  
Author(s):  
Denis A. Hughes ◽  
Evison Kapangaziwiri ◽  
Jane Tanner
Keyword(s):  
Parameter Estimation ◽  
Spatial Scale ◽  
Scale Effects ◽  
Physical Property ◽  
Hydrological Modelling ◽  
Ungauged Basins ◽  
Estimation Equations ◽  
Property Data ◽  
Physical Property Data ◽  
Parameter Values

The most appropriate scale to use for hydrological modelling depends on the model structure, the purpose of the results and the resolution of available data used to quantify parameter values and provide the climatic forcing. There is little consensus amongst the community of model users on the appropriate model complexity and number of model parameters that are needed for satisfactory simulations. These issues are not independent of modelling scale, the methods used to quantify parameter values, nor the purpose of use of the simulations. This paper reports on an investigation of spatial scale effects on the application of an approach to quantify the parameter values (with uncertainty) of a rainfall-runoff model with a relatively large number of parameters. The quantification approach uses estimation equations based on physical property data and is applicable to gauged and ungauged basins. Within South Africa the physical property data are available at a finer spatial resolution than is typically used for hydrological modelling. The results suggest that reducing the model spatial scale offers some advantages. Potential disadvantages are related to the need for some subjective interpretation of the available physical property data, as well as inconsistencies in some of the parameter estimation equations.

scholarly journals A Note on Ordering Probability Distributions by Skewness

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 286
Author(s):  
V. García ◽  
M. Martel-Escobar ◽  
F. Vázquez-Polo
Keyword(s):  
Data Analysis ◽  
Probability Distributions ◽  
Continuous Distributions ◽  
Parameter Values

This paper describes a complementary tool for fitting probabilistic distributions in data analysis. First, we examine the well known bivariate index of skewness and the aggregate skewness function, and then introduce orderings of the skewness of probability distributions. Using an example, we highlight the advantages of this approach and then present results for these orderings in common uniparametric families of continuous distributions, showing that the orderings are well suited to the intuitive conception of skewness and, moreover, that the skewness can be controlled via the parameter values.

scholarly journals Calibration of Conceptual Rainfall-Runoff Models Using Global Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Chao Zhang ◽  
Ru-bin Wang ◽  
Qing-xiang Meng
Keyword(s):  
Global Optimization ◽  
Parameter Optimization ◽  
Hydrological Model ◽  
Optimization Method ◽  
Difficult Problem ◽  
Rainfall Runoff ◽  
True Parameter ◽  
Shuffled Complex Evolution ◽  
Structure Lead ◽  
Parameter Values

Parameter optimization for the conceptual rainfall-runoff (CRR) model has always been the difficult problem in hydrology since watershed hydrological model is high-dimensional and nonlinear with multimodal and nonconvex response surface and its parameters are obviously related and complementary. In the research presented here, the shuffled complex evolution (SCE-UA) global optimization method was used to calibrate the Xinanjiang (XAJ) model. We defined the ideal data and applied the method to observed data. Our results show that, in the case of ideal data, the data length did not affect the parameter optimization for the hydrological model. If the objective function was selected appropriately, the proposed method found the true parameter values. In the case of observed data, we applied the technique to different lengths of data (1, 2, and 3 years) and compared the results with ideal data. We found that errors in the data and model structure lead to significant uncertainties in the parameter optimization.

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