Likelihood-free inference for simulator-based statistical models has recently attracted an interest, both in the machine learning and statistics. The primary focus of has been to approximate the posterior distribution of model parameters, either by various types of Monte Carlo sampling algorithms or deep neural network -based surrogate models. Frequentist inference for simulator-based models has been given much less attention to date, despite that it would be particularly amenable to applications, where implicit asymptotic approximation of the likelihood is expected to be accurate and can leverage computationally efficient strategies. Here we derive a set of results to enable estimation, hypothesis testing and construction of confidence intervals for model parameters using asymptotic properties of the Jensen–Shannon divergence. Such asymptotic approximation offers a rapid alternative to more computation-intensive approaches and can be attractive for diverse applications of simulator-based models.

The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in the drift, where the pairwise interaction among loci is modelled by an inter-locus selection. In this paper, an ancestral process, which is dual to the coupled Wright-Fisher diffusion, is derived. The dual process corresponds to the block counting process of coupled ancestral selection graphs, one for each locus. Jumps of the dual process arise from coalescence, mutation, single-branching, which occur at one locus at the time, and double-branching, which occur simultaneously at two loci. The coalescence and mutation rates have the typical structure of the transition rates of the Kingman coalescent process. The single-branching rate not only contains the one-locus selection parameters in a form that generalises the rates of an ancestral selection graph, but it also contains the two-locus selection parameters to include the effect of the pairwise interaction on the single loci. The double-branching rate reflects the particular structure of pairwise selection interactions of the coupled Wright-Fisher diffusion. Moreover, in the special case of two loci, two alleles, with selection and parent independent mutation, the stationary density for the coupled Wright-Fisher diffusion and the transition rates of the dual process are obtained in an explicit form.

In this paper an exact rejection algorithm for simulating paths of the coupled Wright- Fisher diffusion is introduced. The coupled Wright-Fisher diffusion is a family of multivariate Wright-Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of networks of interacting genes. The proposed rejection algorithm uses independent neutral Wright-Fisher diffusions as candidate proposals, which are only needed at a finite number of points. Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright-Fisher bridges, for which an exact sampling strategy is also provided. Finally, the algorithm's complexity is derived and its performance demonstrated in a simulation study.

Ranked events are pivotal in many important AI-applications such as Question Answering and recommendations systems. This paper studies ranked events in the setting of harness racing. For each horse there exists a probability distribution over its possible rankings. In the paper, it is shown that a set of expected positions (and more generally, higher moments) for the horses induces this probability distribution. The main contribution of the paper is a method, which extracts this induced probability distribution from a set of expected positions. An algorithm is proposed where the extraction of the induced distribution is given by the estimated expectations. MATLAB code is provided for the methodology. This approach gives freedom to model the horses in many different ways without the restrictions imposed by for instance logistic regression. To illustrate this point, we employ a neural network and ordinary ridge regression. The method is applied to predicting the distribution of the finishing positions for horses in harness racing. It outperforms both multinomial logistic regression and the market odds. The ease of use combined with fine results from the suggested approach constitutes a relevant addition to the increasingly important field of ranked events.

We study the asymptotic behaviour of the expected exit time from an interval for the ARMA process, when the noise level approaches 0.

Dark Matter particles are commonly assumed to be weakly interacting massive particles (WIMPs) with a mass in the GeV to TeV range. However, recent interest has shifted toward lighter WIMPs, which are more difficult to probe experimentally. A detection of sub-GeV WIMPs will require the use of small gap materials in sensors. Using recent estimates of the WIMP mass, we identify the relevant target space toward small gap materials (100 to 10 meV). Dirac Materials, a class of small- or zero-gap materials, emerge as natural candidates for sensors for Dark Matter detection. We propose the use of informatics tools to rapidly assay materials band structures to search for small gap semiconductors and semimetals, rather than focusing on a few preselected compounds. As a specific example of the proposed strategy, we use the organic materials database () to identify organic candidates for sensors: the narrow band gap semiconductors BNQ-TTF and DEBTTT with gaps of 40 and 38 meV, and the Dirac-line semimetal (BEDT-TTF)center dot Br which exhibits a tiny gap of approximate to 50 meV when spin-orbit coupling is included. We outline a novel and powerful approach to search for dark matter detection sensor materials by means of a rapid assay of materials using informatics tools.

Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific independence. However, parameter estimation is often simpler under a direct parameterization, provided that the model enjoys certain decomposability properties. Here we introduce a cyclical projection algorithm for obtaining maximum likelihood estimates of log-linear parameters under an arbitrary context-specific graphical log-linear model, which needs not satisfy criteria of decomposability. We illustrate that lifting the restriction of decomposability makes the models more expressive, such that additional context-specific independencies embedded in real data can be identified. It is also shown how a context-specific graphical model can correspond to a non-hierarchical log-linear parameterization with a concise interpretation. This observation can pave way to further development of non-hierarchical log-linear models, which have been largely neglected due to their believed lack of interpretability.

Gaussian distribution has for several decades been ubiquitous in the theory and practice of statistical classification. Despite the early proposals motivating the use of predictive inference to design a classifier, this approach has gained relatively little attention apart from certain specific applications, such as speech recognition where its optimality has been widely acknowledged. Here we examine statistical properties of different inductive classification rules under a generic Gaussian model and demonstrate the optimality of considering simultaneous classification of multiple samples under an attractive loss function. It is shown that the simpler independent classification of samples leads asymptotically to the same optimal rule as the simultaneous classifier when the amount of training data increases, if the dimensionality of the feature space is bounded in an appropriate manner. Numerical investigations suggest that the simultaneous predictive classifier can lead to higher classification accuracy than the independent rule in the low-dimensional case, whereas the simultaneous approach suffers more from noise when the dimensionality increases.

Measures of research productivity (e.g. peer reviewed papers per researcher) is a fundamental part of bibliometric studies, but is often restricted by the properties of the data available. This paper addresses that fundamental issue and presents a detailed method for estimation of productivity (peer reviewed papers per researcher) based on data available in bibliographic databases (e.g. Web of Science and Scopus). The method can, for example, be used to estimate average productivity in different fields, and such field reference values can be used to produce field adjusted production values. Being able to produce such field adjusted production values could dramatically increase the relevance of bibliometric rankings and other bibliometric performance indicators. The results indicate that the estimations are reasonably stable given a sufficiently large data set.