Search results for "Monte Carlo -menetelmät"

Alder pollen in Finland ripens after a short exposure to warm days in early spring, showing biennial variation in the onset of pollen ripening

2017

Abstract We developed a temperature sum model to predict the daily pollen release of alder, based on pollen data collected with pollen traps at seven locations in Finland over the years 2000–2014. We estimated the model parameters by minimizing the sum of squared errors (SSE) of the model, with weights that put more weight on binary recognition of daily presence or absence of pollen. The model results suggest that alder pollen ripens after a couple of warm days in February, while the whole pollen release period typically takes up to 4 weeks. We tested the model residuals against air humidity, precipitation and wind speed, but adding these meteorological features did not improve the model pr…

Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests

2021

We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points x affects another set of points y but not vice versa. We use the model to investigate the effect of large trees to the locations of seedlings. In the model, every point in x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The par…

Coupled conditional backward sampling particle filter

2020

The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous theoretical results have not been able to demonstrate the improvement brought by backward sampling, whereas we provide rates showing that CBPF can remain effective with a fixed number of particles independent of the time horizon. Our result is based on analysis of a new coupling of two CBPFs, the coupled conditional backward sampling particle filter (CCBPF). We show that CCBPF has good stability properties in the sense that with fixed number of particles, …

On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction

2020

Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We consider an approach using a relatively large tolerance for the Markov chain Monte Carlo sampler to ensure its sufficient mixing, and post-processing the output leading to estimators for a range of finer tolerances. We introduce an approximate confidence interval for the related post-corrected estimators, and propose an adaptive approximate Bayesi…

Unbiased Estimators and Multilevel Monte Carlo

2018

Multilevel Monte Carlo (MLMC) and unbiased estimators recently proposed by McLeish (Monte Carlo Methods Appl., 2011) and Rhee and Glynn (Oper. Res., 2015) are closely related. This connection is elaborated by presenting a new general class of unbiased estimators, which admits previous debiasing schemes as special cases. New lower variance estimators are proposed, which are stratified versions of earlier unbiased schemes. Under general conditions, essentially when MLMC admits the canonical square root Monte Carlo error rate, the proposed new schemes are shown to be asymptotically as efficient as MLMC, both in terms of variance and cost. The experiments demonstrate that the variance reduction…

Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions

2021

We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead, our method uses standard time-discretised approximations of diffusions, such as the Euler--Maruyama scheme. Our approach is based on particle marginal Metropolis--Hastings, a particle filter, randomised multilevel Monte Carlo, and importance sampling type correction of approximate Markov chain Monte Carlo. The resulting estimator leads to inference without a bias from the time-discretisation as the number of Markov chain iterations increases. We give conver…

Efficient Bayesian generalized linear models with time-varying coefficients : The walker package in R

2020

The R package walker extends standard Bayesian general linear models to the case where the effects of the explanatory variables can vary in time. This allows, for example, to model the effects of interventions such as changes in tax policy which gradually increases their effect over time. The Markov chain Monte Carlo algorithms powering the Bayesian inference are based on Hamiltonian Monte Carlo provided by Stan software, using a state space representation of the model to marginalise over the regression coefficients for efficient low-dimensional sampling.

Statistical models and inference for spatial point patterns with intensity-dependent marks

2009

CLEASE: a versatile and user-friendly implementation of cluster expansion method

2018

Materials exhibiting a substitutional disorder such as multicomponent alloys and mixed metal oxides/oxyfluorides are of great importance in many scientific and technological sectors. Disordered materials constitute an overwhelmingly large configurational space, which makes it practically impossible to be explored manually using first-principles calculations such as density functional theory due to the high computational costs. Consequently, the use of methods such as cluster expansion (CE) is vital in enhancing our understanding of the disordered materials. CE dramatically reduces the computational cost by mapping the first-principles calculation results on to a Hamiltonian which is much fa…

Monte Carlo simulations of high-energy electron beams : model validation and dose calculations

2017

Komponenttisäteilytykseen valjastetusta Varian Clinac 2100 C/D -lineaarikiihdyttimestä luotiin Monte Carlo -menetelmiä hyödyntävä simulaatiomalli. Malli luotiin aineen ja säteilyn vuorovaikutuksien laskennalliseen mallintamiseen tarkoitettua Geant4 -ohjelmointityökalupakettia käyttäen. Mallin kyky ennustaa mittaustuloksia kiihdyttimen tuottamasta 20 MeV:in elektronisuihkusta todennettiin laskettuja ja mitattuja tuloksia vertailemalla, ja mallin jatkokehityksen kannalta tärkeimmät toimenpiteet määriteltiin. Lisäksi arvioitiin mallin ennustamaa absorpoitunutta annosta vesi- ja piifantomeissa, sekä laskettiin viitearvo absorpoituneen annoksen ja elektronivuon suhteelle. Lasketut annosprofiilit…