Density estimation with Gaussian processes for gravitational wave posteriors

ABSTRACT The properties of black hole and neutron-star binaries are extracted from gravitational waves (GW) signals using Bayesian inference. This involves evaluating a multidimensional posterior probability function with stochastic sampling. The marginal probability distributions of the samples are sometimes interpolated with methods such as kernel density estimators. Since most post-processing analysis within the field is based on these parameter estimation products, interpolation accuracy of the marginals is essential. In this work, we propose a new method combining histograms and Gaussian processes (GPs) as an alternative technique to fit arbitrary combinations of samples from the source parameters. This method comes with several advantages such as flexible interpolation of non-Gaussian correlations, Bayesian estimate of uncertainty, and efficient resampling with Hamiltonian Monte Carlo.

Unpaid Caregiving and Labor Force Participation among Chinese Middle-Aged Adults

Unpaid family caregivers must consider the economic trade-off between caregiving and paid employment. Prior literature has suggested that labor force participation (LFP) declines with caregiving intensity, but no study has evaluated this relationship by accounting for the presence of both kinks and discontinuities. Here we used respondents of the China Health and Retirement Longitudinal Study baseline survey who were nonfarming, of working age (aged 45–60) and had a young grandchild and/or a parent/parent-in-law. For women and men separately, a caregiving threshold-adjusted probit model was used to assess the association between LFP and weekly unpaid caregiving hours. Instrumental variables were used to rule out the endogeneity of caregiving hours. Of the 3718 respondents in the analysis, LFP for men was significantly and inversely associated with caregiving that involved neither discontinuities nor kinks. For women, a kink was identified at the caregiving threshold of eight hrs/w such that before eight hours, each caregiving hour was associated with an increase of 0.0257 in the marginal probability of LFP, but each hour thereafter was associated with a reduction of 0.0014 in the marginal probability of LFP. These results have implications for interventions that simultaneously advance policies of health, social care and labor force.

Unpaid Caregiving and Labour Force Participation among Chinese Middle-aged Adults

Unpaid family caregivers must consider the economic trade-off between caregiving and paid employment. Prior literature has suggested labour force participation (LFP) to decline with caregiving intensity, but no study has evaluated this relationship by accounting for the presence of both kinks and discontinuities. Here we used respondents of the China Health and Retirement Longitudinal Study baseline survey who were non-farming, of working-age (aged 45-60) and had a young grandchild and/or a parent/parent-in-law. For women and men separately, a caregiving threshold-adjusted probit model was used to assess the association between LFP and weekly unpaid caregiving hours. Instrumental variables were used to rule out the endogeneity of caregiving hours. Of the 3,718 respondents in the analysis, for men, LFP was significantly and inversely associated with caregiving that involved neither discontinuities nor kinks. For women, a kink was identified at the caregiving threshold of 8 hours per week such that before 8 hours, each caregiving hour was associated with an increase of 0.0257 in the marginal probability of LFP, but each hour thereafter was associated with a reduction of 0.0014 in the marginal probability of LFP. These results have implications for interventions that simultaneously advance policies of health, social care and labour force.

Revealing a temporal symmetry/asymmetry dichotomy in a Markovian setting, and a parameterization based on fractional low-order joint moments

<p>We show that "an arrow of time", which is reflected by the joint distributions of successive variables in a stochastic process, may exist (or not) solely on grounds of marginal probability distributions, without affecting stationarity or involving the structural dependencies within the process. The temporal symmetry/asymmetry dichotomy thus revealed, is exemplified for the simplest case of stably-distributed Markovian recursions, where the lack of Gaussianity, even when the increments of the process are independent and identically distributed (i.i.d.) with symmetric marginal, is generating a break of temporal symmetry. We devise a statistical tool to evidence this striking result, based on fractional low-order joint moments, whose existence is guaranteed even for the case of "fat-tailed" strictly-stable distributions, and is thereby suited for parameterizing structural dependencies within such a process.</p>

Parameterization of multifractal cascade models based on their breakdown coefficients

<p>Breakdown coefficients of multifractal cascades have been shown, in various contexts, to be ergodic in their (marginal) probability distribution functions, however the necessary connection between the cascading process (or a tracer thereof, such as rainfall) and the breakdown coefficients of the measure generated by the cascade, was missing. This work presents a method of parameterization of certain types of multiplicative cascades, using the breakdown coefficients of the measures they generate. The method is based on asymptotic properties of the probability distributions of the breakdown coefficients in “dressed” cascades, as compared with the respective distributions of the cascading weights. An application to rainfall intensity time series is presented.</p>

Statistical compression of protein sequences and inference of marginal probability landscapes over competing alignments using finite state models and Dirichlet priors

The information criterion of minimum message length (MML) provides a powerful statistical framework for inductive reasoning from observed data. We apply MML to the problem of protein sequence comparison using finite state models with Dirichlet distributions. The resulting framework allows us to supersede the ad hoc cost functions commonly used in the field, by systematically addressing the problem of arbitrariness in alignment parameters, and the disconnect between substitution scores and gap costs. Furthermore, our framework enables the generation of marginal probability landscapes over all possible alignment hypotheses, with potential to facilitate the users to simultaneously rationalize and assess competing alignment relationships between protein sequences, beyond simply reporting a single (best) alignment. We demonstrate the performance of our program on benchmarks containing distantly related protein sequences.Availability and implementationThe open-source program supporting this work is available from: http://lcb.infotech.monash.edu.au/seqmmligner.Supplementary informationSupplementary data are available at Bioinformatics online.

Bayesian Analysis of Skills Importance in World Champions Men’s Volleyball across Ages

In volleyball, due to the sequential structure of the game, each outcome results from events that follow consistent consecutive patterns: pass–set–attack–outcome, serve–outcome and block–dig–set–counter attack–outcome. There are three possible outcomes: point won, point lost, and rally continuation. With the aim of quantifying the importance of volleyball skills, data of world champions of the male International Volleyball Federation tournaments for three age categories (Youth, Juniors and Men) were used to construct a transition matrix between subsequent moves and skills within the game. A Dirichlet-Multinomial Bayesian model was used to estimate the transition probabilities between the subsequent moves along with the marginal probability of success of each skill in the complex. The prior distribution of each transition probabilities between moves/skills was elicited to incorporate experts' opinion. For the final evaluation of the skills a simple Monte Carlo scheme was applied to obtain a random sample from the posterior distribution. The findings of the study indicate that the relative importance of volleyball skills is robust across world champions of different age categories. Slight variations are observed on specific skills. A new index (Quantile Mid-range Ratio) is proposed for highlighting skills that are valuable for team’s gameplay.