Grapham: Graphical Models with Adaptive Random Walk Metropolis Algorithms

Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on graphical models for directed acyclic graphs. The implemented algorithms include the seminal Adaptive Metropolis algorithm adjusting the proposal covariance according to the history of the chain and a Metropolis algorithm adjusting the proposal scale based on the observed acceptance probability. Different variants of the algorithms allow one, for example, to use these two algorithms together, employ delayed rejection and adjust several parameters of the algorithms. The implemented Metropolis-within-Gibbs update allows arbitrary sampling blocks. The software is written in C and uses a simple extension language Lua in configuration.Comment: 9 pages, 3 figures; added references, revised language, other minor change

Likelihood informed dimension reduction for inverse problems in remote sensing of atmospheric constituent profiles

We use likelihood informed dimension reduction (LIS) (T. Cui et al. 2014) for inverting vertical profile information of atmospheric methane from ground based Fourier transform infrared (FTIR) measurements at Sodankyl\"a, Northern Finland. The measurements belong to the word wide TCCON network for greenhouse gas measurements and, in addition to providing accurate greenhouse gas measurements, they are important for validating satellite observations. LIS allows construction of an efficient Markov chain Monte Carlo sampling algorithm that explores only a reduced dimensional space but still produces a good approximation of the original full dimensional Bayesian posterior distribution. This in effect makes the statistical estimation problem independent of the discretization of the inverse problem. In addition, we compare LIS to a dimension reduction method based on prior covariance matrix truncation used earlier (S. Tukiainen et al. 2016)

Sleep, health behaviours and weight among ageing employees : A follow-up study

Insomnia symptoms and short sleep duration constitute a notable public-health problem. They impair wellbeing and are risk factors for several diseases, both of which may affect societal functioning. The aim of this study was to examine whether insomnia symptoms are associated with subsequent unhealthy behaviours and weight gain, and whether unhealthy behaviours and weight are associated with subsequent insomnia symptoms. Additionally, the aim was to examine whether sleep duration is associated with weight gain. The data were derived from the Helsinki Health Study cohort baseline and follow-up mail surveys. The baseline data were collected in 2000-2002 among employees of the City of Helsinki aged 40-60 (n=8960, response rate 67%). The follow-up data were collected in 2007 (n=7332, response rate 83%). Insomnia symptoms were measured on frequency about having trouble falling asleep, waking up at night, having trouble staying asleep and waking up tired after one s usual amount of sleep, all during the previous four weeks. The respondents were also asked about their average sleep duration week days. Unhealthy behaviours included heavy and binge drinking, smoking, physical inactivity and unhealthy food habits. Weight was assessed using body mass index (BMI), kilograms and weight gain. Analyses of variance, logistic regression and multinomial regression were used in the statistical analyses. Poor sleep, more specifically insomnia symptoms and short sleep duration, were associated with weight gain, and BMI showed an association with changes in insomnia symptoms. These associations were evident mainly among women. Insomnia symptoms showed a bidirectional association with heavy drinking, and were also associated with subsequent physical inactivity. Additionally, binge drinking showed an association with subsequent insomnia symptoms. This study confirms associations among poor sleep and weight and mainly weak and inconsistent associations among insomnia symptoms and unhealthy behaviours.Unettomuusoireet ja lyhyt unen kesto ovat kansanterveysongelmia. Ne heikentävät hyvinvointia ja ovat monen sairauden riskitekijöitä ja saattavat vaikuttaa koko yhteiskunnan toimintaan. Tämän tutkimuksen tavoitteena oli tutkia, ovatko unettomuusoireet yhteydessä myöhempään terveyskäyttäytymiseen ja painonnousuun ja ovatko terveyskäyttäytyminen ja paino yhteydessä myöhempiin unettomuusoireisiin. Lisäksi tavoitteena oli tutkia, onko unen kesto yhteydessä painonnousuun. Tutkimuksen aineistona käytettiin Helsinki Health Study -kohorttitutkimuksen perus- ja seurantakyselyä. Peruskysely kerättiin vuosina 2000-2002 Helsingin kaupungin 40-60- vuotiaiden työntekijöiden keskuudessa (n=8960, vastausaktiivisuus 67 %). Seurantakysely kerättiin vuonna 2007 (n=7332, vastausaktiivisuus 83 %). Unettomuusoireita mitattiin kysymällä nukahtamisvaikeuksia, vaikeuksia pysyä unessa ja heräilyä yöllä sekä heräämistä väsyneenä tavallisen yöunen jälkeen viimeksi kuluneiden neljän viikon aikana. Lisäksi tiedusteltiin keskimääräistä unen kestoa arkisin. Terveyskäyttäytymisen riskitekijöinä olivat alkoholin suurkulutus, humalahakuinen juominen, tupakointi, vähäinen vapaa-ajan liikunta sekä epäterveelliset ruokatavat. Paino määritettiin painoindeksinä (BMI), kilogrammoina ja painonnousuna seurannan aikana. Tilastollisina menetelminä käytettiin varianssianalyysia, logistista regressioanalyysia ja multinomiaalista regressionanalyysia. Huono uni, tarkemmin sanottuna unettomuusoireet ja lyhyt unen kesto olivat yhteydessä painonnousuun ja BMI oli yhteydessä unettomuusoireiden muutoksiin. Nämä yhteydet todettiin pääsääntöisesti naisilla. Unettomuusoireiden yhteys alkoholin suurkulutukseen oli kaksisuuntainen. Unettomuusoireet olivat yhteydessä myös vähäiseen vapaa-ajan liikuntaan. Lisäksi, humalahakuinen juominen oli yhteydessä myöhempiin unettomuusoireisiin. Tämän tutkimuksen mukaan huonon unen ja painon välillä on yhteyksiä, mutta unettomuusoireiden ja terveyskäyttäytymisen välillä yhteydet ovat enimmäkseen heikkoja ja epäjohdonmukaisia

A Bayesian Approach to Modelling Biological Pattern Formation with Limited Data

Pattern formation in biological tissues plays an important role in the development of living organisms. Since the classical work of Alan Turing, a pre-eminent way of modelling has been through reaction-diffusion mechanisms. More recently, alternative models have been proposed, that link dynamics of diffusing molecular signals with tissue mechanics. In order to distinguish among different models, they should be compared to experimental observations. However, in many experimental situations only the limiting, stationary regime of the pattern formation process is observable, without knowledge of the transient behaviour or the initial state. The unstable nature of the underlying dynamics in all alternative models seriously complicates model and parameter identification, since small changes in the initial condition lead to distinct stationary patterns. To overcome this problem the initial state of the model can be randomised. In the latter case, fixed values of the model parameters correspond to a family of patterns rather than a fixed stationary solution, and standard approaches to compare pattern data directly with model outputs, e.g., in the least squares sense, are not suitable. Instead, statistical characteristics of the patterns should be compared, which is difficult given the typically limited amount of available data in practical applications. To deal with this problem, we extend a recently developed statistical approach for parameter identification using pattern data, the so-called Correlation Integral Likelihood (CIL) method. We suggest modifications that allow increasing the accuracy of the identification process without resizing the data set. The proposed approach is tested using different classes of pattern formation models. For all considered equations, parallel GPU-based implementations of the numerical solvers with efficient time stepping schemes are provided.Comment: More compact version of the text and figures, results unchange

On the flexibility of the design of Multiple Try Metropolis schemes

The Multiple Try Metropolis (MTM) method is a generalization of the classical Metropolis-Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities and show different numerical results

On the stability and ergodicity of adaptive scaling Metropolis algorithms

The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. The both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of the algorithms, the adapted scaling parameter is not constrained within a predefined compact interval. The first algorithm is based on scale adaptation only, while the second one incorporates also covariance adaptation. A strong law of large numbers is shown to hold assuming that the target density is smooth enough and has either compact support or super-exponentially decaying tails.Comment: 24 pages, 1 figure; major revisio

Simulation and data processing of GOMOS measurements

In this paper the data simulation and data inversion studies for stellar occultation measurements are discussed. The specific application is the Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument which has been proposed for the first European Platform, Polar Orbiting Earth Mission (POEM-1)

Evidence for 9 planets in the HD 10180 system

We re-analyse the HARPS radial velocities of HD 10180 and calculate the probabilities of models with differing numbers of periodic signals in the data. We test the significance of the seven signals, corresponding to seven exoplanets orbiting the star, in the Bayesian framework and perform comparisons of models with up to nine periodicities. We use posterior samplings and Bayesian model probabilities in our analyses together with suitable prior probability densities and prior model probabilities to extract all the significant signals from the data and to receive reliable uncertainties for the orbital parameters of the six, possibly seven, known exoplanets in the system. According to our results, there is evidence for up to nine planets orbiting HD 10180, which would make this this star a record holder in having more planets in its orbits than there are in the Solar system. We revise the uncertainties of the previously reported six planets in the system, verify the existence of the seventh signal, and announce the detection of two additional statistically significant signals in the data. If of planetary origin, these two additional signals would correspond to planets with minimum masses of 5.1$^{+3.1}_{-3.2}$ and 1.9$^{+1.6}_{-1.8}$ M$_{\oplus}$ on orbits with 67.55$^{+0.68}_{-0.88}$ and 9.655$^{+0.022}_{-0.072}$ days periods (denoted using the 99% credibility intervals), respectively.Comment: 12 pages, 7 figures, accepted for publication in the Astronomy and Astrophysic