Gene regulatory network inference from sparsely sampled noisy data

in Nature Communications (2020), 11

The complexity of biological systems is encoded in gene regulatory networks. Unravelling this intricate web is a fundamental step in understanding the mechanisms of life and eventually developing ... [more ▼]

The complexity of biological systems is encoded in gene regulatory networks. Unravelling this intricate web is a fundamental step in understanding the mechanisms of life and eventually developing efficient therapies to treat and cure diseases. The major obstacle in inferring gene regulatory networks is the lack of data. While time series data are nowadays widely available, they are typically noisy, with low sampling frequency and overall small number of samples. This paper develops a method called BINGO to specifically deal with these issues. Benchmarked with both real and simulated time-series data covering many different gene regulatory networks, BINGO clearly and consistently outperforms state-of-the-art methods. The novelty of BINGO lies in a nonparametric approach featuring statistical sampling of continuous gene expression profiles. BINGO’s superior performance and ease of use, even by non-specialists, make gene regulatory network inference available to any researcher, helping to decipher the complex mechanisms of life. [less ▲]

Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind

in Statistical Inference for Stochastic Processes (2015), 18(3), 205227

Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model

E-print/Working paper (2014)

We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst ... [more ▼]

We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter H of the fractional part satisfies H∈(3/4,1), the central limit theorem holds. In the nonsemimartingale case, that is, where H∈(1/2,3/4], the convergence toward the normal distribution with a nonzero mean still holds if H=3/4, whereas for the other values, that is, H∈(1/2,3/4), the central convergence does not take place. We also provide Berry--Esseen estimates for the estimator. [less ▲]

Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion

in Journal of Theoretical Probability (2013)

In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, where $B_t$ denotes the fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2},1)$, for a ... [more ▼]

In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, where $B_t$ denotes the fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2},1)$, for a large class of convex functions $f$ is considered. In $\big[$\cite{a-m-v}, Statistics \& Decisions, \textbf{27}, 129-143$\big]$, for any convex function $f$, the almost sure convergence of uniform discretization to such stochastic integral is proved. Here we prove $L^r$- convergence of uniform discretization to stochastic integral. In addition, we obtain a rate of convergence. It turns out that the rate of convergence can be brought arbitrary close to $H - \frac{1}{2}$. [less ▲]