scholarly journals On the Hierarchical Bernoulli Mixture Model Using Bayesian Hamiltonian Monte Carlo

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2404
Author(s):  
Wahyuni Suryaningtyas ◽  
Nur Iriawan ◽  
Heri Kuswanto ◽  
Ismaini Zain
Keyword(s):  
Monte Carlo ◽  
Mixture Model ◽  
Hierarchical Structure ◽  
Structure Data ◽  
Information Criteria ◽  
Monte Carlo Algorithm ◽  
Data Driven ◽  
Binary Response ◽  
Bernoulli Distribution ◽  
Hamiltonian Monte Carlo

The model developed considers the uniqueness of a data-driven binary response (indicated by 0 and 1) identified as having a Bernoulli distribution with finite mixture components. In social science applications, Bernoulli’s constructs a hierarchical structure data. This study introduces the Hierarchical Bernoulli mixture model (Hibermimo), a new analytical model that combines the Bernoulli mixture with hierarchical structure data. The proposed approach uses a Hamiltonian Monte Carlo algorithm with a No-U-Turn Sampler (HMC/NUTS). The study has performed a compatible syntax program computation utilizing the HMC/NUTS to analyze the Bayesian Bernoulli mixture aggregate regression model (BBMARM) and Hibermimo. In the model estimation, Hibermimo yielded a result of ~90% compliance with the modeling of each district and a small Widely Applicable Information Criteria (WAIC) value.

Seismic source inversion using Hamiltonian Monte Carlo and a 3-D Earth model in the Japanese Islands

2020 ◽  
Author(s):  
Saulė Simutė ◽  
Lion Krischer ◽  
Christian Boehm ◽  
Martin Vallée ◽  
Andreas Fichtner
Keyword(s):  
Monte Carlo ◽  
Moment Tensor ◽  
Seismic Source ◽  
Monte Carlo Algorithm ◽  
Earth Model ◽  
Model Parameters ◽  
Hamiltonian Monte Carlo ◽  
Double Couple ◽  
Full Moment Tensor ◽  
Japanese Islands

<p>We present a proof-of-concept catalogue of full-waveform seismic source solutions for the Japanese Islands area. Our method is based on the Bayesian inference of source parameters and a tomographically derived heterogeneous Earth model, used to compute Green’s strain tensors. We infer the full moment tensor, location and centroid time of the seismic events in the study area.</p><p>To compute spatial derivatives of Green’s functions, we use a previously derived regional Earth model (Simutė et al., 2016). The model is radially anisotropic, visco-elastic, and fully heterogeneous. It was constructed using full waveforms in the period band of 15–80 s.</p><p>Green’s strains are computed numerically with the spectral-element solver SES3D (Gokhberg & Fichtner, 2016). We exploit reciprocity, and by treating seismic stations as virtual sources we compute and store the wavefield across the domain. This gives us a strain database for all potential source-receiver pairs. We store the wavefield for more than 50 F-net broadband stations (www.fnet.bosai.go.jp). By assuming an impulse response as the source time function, the displacements are then promptly obtained by linear combination of the pre-computed strains scaled by the moment tensor elements.</p><p>With a feasible number of model parameters and the fast forward problem we infer the unknowns in a Bayesian framework. The fully probabilistic approach allows us to obtain uncertainty information as well as inter-parameter trade-offs. The sampling is performed with a variant of the Hamiltonian Monte Carlo algorithm, which we developed previously (Fichtner and Simutė, 2017). We apply an L2 misfit on waveform data, and we work in the period band of 15–80 s.</p><p>We jointly infer three location parameters, timing and moment tensor components. We present two sets of source solutions: 1) full moment tensor solutions, where the trace is free to vary away from zero, and 2) moment tensor solutions with the isotropic part constrained to be zero. In particular, we study events with significant non-double-couple component. Preliminary results of ~Mw 5 shallow to intermediate depth events indicate that proper incorporation of 3-D Earth structure results in solutions becoming more double-couple like. We also find that improving the Global CMT solutions in terms of waveform fit requires a very good 3-D Earth model and is not trivial.</p>

scholarly journals Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

2008 ◽  
Vol 363 (1512) ◽  
pp. 3955-3964 ◽  
Author(s):  
Mark Pagel ◽  
Andrew Meade
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Mixture Model ◽  
Branch Length ◽  
Monte Carlo Algorithm ◽  
Morphological Data ◽  
Reversible Jump ◽  
Rate Variation ◽  
Ancestral State

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon—known as heterotachy—can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our ‘pattern-heterogeneity’ mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of ‘significance’ such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.

scholarly journals Hamiltonian Monte Carlo with Random Effect for Analyzing Cyclist Crash Severity

Signals ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 527-539
Author(s):  
Mahdi Rezapour ◽  
Khaled Ksaibati
Keyword(s):  
Monte Carlo ◽  
Mixture Model ◽  
Random Effect ◽  
Finite Mixture Model ◽  
Finite Mixture ◽  
Model Fit ◽  
Crash Severity ◽  
Optimum Amount ◽  
Mixed Effect ◽  
Hamiltonian Monte Carlo

Vulnerable traffic users, such as bikers and pedestrians, account for a significant number of fatalities on the roadways. Extensive research has been conducted in the literature review to identify factors to those crashes. Studying factors to those crashes is especially important in the Western state in the US, due to one of the highest fatality rates in the nation and its unique geographic conditions. The first step in identifying factors to the severity of cyclist crashes is to find the underlying factors to that type of crash, while accounting for the heterogeneity in the dataset. Various techniques such as mixed parameter or mixed effect models have been employed in the literature to account for the heterogeneity of the dataset. In the mixed effect model, often the random effect parameter has been assigned subjectively, and based on some attributes and engineering intuitions. Those assignments are expected to account for the heterogeneity in the dataset and enhancement of the model fit. However, a question might arise whether those factors could account for an optimum amount of the heterogeneity in the dataset. A more reasonable way might be to let the algorithm such as the finite mixture model (FMM) to identify those clusters based on parameters of the Gaussian model, means and covariance matrices of the dataset, and allocate each observation to the related clusters. Thus, in this study, to capture optimum amount of heterogeneity, first we implemented the finite mixture model in the context of maximum likelihood, due the label switching issue of the method in the context of the Bayesian method. After assignment of the parameters to the observation, the main method of Hamiltonian Monte Carlo (HMC) with random effect was implemented. The results highlighted a significant improvement in the model fit, in terms of Widely Applicable Information Criterion (WAIC). The results of this study highlighted factors such as older biker age, increased number of lanes, nighttime travelling, increased posted speed limit and driving while under emotional conditions are some factors contributing to an increased severity of bikers’ crash severity. Extensive discussion has been made regarding the methodological algorithms and model parameters estimations.

Transdimensional seismic inversion using the reversible jump Hamiltonian Monte Carlo algorithm

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. R119-R134 ◽  
Author(s):  
Mrinal K. Sen ◽  
Reetam Biswas
Keyword(s):  
Monte Carlo ◽  
A Priori ◽  
Seismic Inversion ◽  
Monte Carlo Algorithm ◽  
Model Parameters ◽  
Reversible Jump ◽  
Step Method ◽  
Acceptance Probability ◽  
Hamiltonian Monte Carlo ◽  
Impedance Inversion

Prestack or angle stack gathers are inverted to estimate pseudologs at every surface location for building reservoir models. Recently, several methods have been proposed to increase the resolution of the inverted models. All of these methods, however, require that the total number of model parameters be fixed a priori. We have investigated an alternate approach in which we allow the data themselves to choose model parameterization. In other words, in addition to the layer properties, the number of layers is also treated as a variable in our formulation. Such transdimensional inverse problems are generally solved by using the reversible jump Markov chain Monte Carlo (RJMCMC) approach, which is a tool for model exploration and uncertainty quantification. This method, however, has very low acceptance. We have developed a two-step method by combining RJMCMC with a fixed-dimensional MCMC called Hamiltonian Monte Carlo, which makes use of gradient information to take large steps. Acceptance probability for such a transition is also derived. We call this new method “reversible jump Hamiltonian Monte Carlo (RJHMC).” We have applied this technique to poststack acoustic impedance inversion and to prestack (angle stack) AVA inversion for estimating acoustic and shear impedance profiles. We have determined that the marginal posteriors estimated by RJMCMC and RJHMC are in good agreement. Our results demonstrate that RJHMC converges faster than RJMCMC, and it therefore can be a practical tool for inverting seismic data when the gradient can be computed efficiently.

scholarly journals Quantum-Inspired Magnetic Hamiltonian Monte Carlo

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258277
Author(s):  
Wilson Tsakane Mongwe ◽  
Rendani Mbuvha ◽  
Tshilidzi Marwala
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Learning Community ◽  
Broad Class ◽  
Hamiltonian Dynamics ◽  
Mass Matrix ◽  
Monte Carlo Algorithm ◽  
Posterior Distributions ◽  
Hamiltonian Monte Carlo ◽  
Random Mass

Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo algorithm that is able to generate distant proposals via the use of Hamiltonian dynamics, which are able to incorporate first-order gradient information about the target posterior. This has driven its rise in popularity in the machine learning community in recent times. It has been shown that making use of the energy-time uncertainty relation from quantum mechanics, one can devise an extension to HMC by allowing the mass matrix to be random with a probability distribution instead of a fixed mass. Furthermore, Magnetic Hamiltonian Monte Carlo (MHMC) has been recently proposed as an extension to HMC and adds a magnetic field to HMC which results in non-canonical dynamics associated with the movement of a particle under a magnetic field. In this work, we utilise the non-canonical dynamics of MHMC while allowing the mass matrix to be random to create the Quantum-Inspired Magnetic Hamiltonian Monte Carlo (QIMHMC) algorithm, which is shown to converge to the correct steady state distribution. Empirical results on a broad class of target posterior distributions show that the proposed method produces better sampling performance than HMC, MHMC and HMC with a random mass matrix.

Hamiltonian Monte Carlo algorithm for the characterization of hydraulic conductivity from the heat tracing data

2016 ◽  
Vol 97 ◽  
pp. 120-129 ◽  
Author(s):  
A. Djibrilla Saley ◽  
A. Jardani ◽  
A. Soueid Ahmed ◽  
R. Antoine ◽  
J.P. Dupont
Keyword(s):  
Monte Carlo ◽  
Hydraulic Conductivity ◽  
Monte Carlo Algorithm ◽  
Hamiltonian Monte Carlo
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