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Enrico Bibbona

Publications and source records attributed to Enrico Bibbona.

15 recordsLinked to original sources
arXiv2025

BayVel: A Bayesian Framework for RNA Velocity Estimation in Single-Cell Transcriptomics

RNA velocity is a model of gene expression dynamics designed to analyze single-cell RNA sequencing (scRNA-seq) data, and it has recently gained significant attention. However, despite its popularity, the model has raised several concerns, primarily related to three issues: its heavy dependence on data preprocessing, the need for post-processing of the results, and the limitations of the underlying statistical methodology. Current approaches, such as scVelo, suffer from notable statistical shortcomings. These include identifiability problems, reliance on heuristic preprocessing steps, and the absence of uncertainty quantification. To address these limitations, we propose BayVel, a Bayesian hierarchical model that directly models raw count data. BayVel resolves identifiability issues and provides posterior distributions for all parameters, including the RNA velocities themselves, without the need for any post processing. We evaluate BayVel's performance using simulated datasets. While scVelo fails to accurately reconstruct parameters, even when data are simulated directly from the model assumptions, BayVel demonstrates strong accuracy and robustness. This highlights BayVel as a statistically rigorous and reliable framework for studying transcriptional dynamics in the context of RNA velocity modeling. When applied to a real dataset of pancreatic epithelial cells previously analyzed with scVelo, BayVel does not replicate their findings, which appears to be strongly influenced by the postprocessing, supporting concerns raised in other studies about the reliability of scVelo.

stat.AP↗
arXiv2024

Bayesian inference of Latent Spectral Shapes

This paper proposes a hierarchical spatial-temporal model for modelling the spectrograms of animal calls. The motivation stems from analyzing recordings of the so-called grunt calls emitted by various lemur species. Our goal is to identify a latent spectral shape that characterizes each species and facilitates measuring dissimilarities between them. The model addresses the synchronization of animal vocalizations, due to varying time-lengths and speeds, with non-stationary temporal patterns and accounts for periodic sampling artifacts produced by the time discretization of analog signals. The former is achieved through a synchronization function, and the latter is modeled using a circular representation of time. To overcome the curse of dimensionality inherent in the model's implementation, we employ the Nearest Neighbor Gaussian Process, and posterior samples are obtained using the Markov Chain Monte Carlo method. We apply the model to a real dataset comprising sounds from 8 different species. We define a representative sound for each species and compare them using a simple distance measure. Cross-validation is used to evaluate the predictive capability of our proposal and explore special cases. Additionally, a simulation example is provided to demonstrate that the algorithm is capable of retrieving the true parameters.

stat.AP↗
arXiv2020

Stationary distributions of systems with Discreteness Induced Transitions

We provide a theoretical analysis of some autocatalytic reaction networks exhibiting the phenomenon of discretely induced transitions (DITs). The family of networks that we address includes the celebrated Togashi and Kaneko model. We prove positive recurrence, finiteness of all moments, and geometric ergodicity of the models in the family. For some parameter values, we find the analytic expression for the stationary distribution, and discuss the effect of volume scaling on the stationary behavior of the chain. We find the exact critical value of the volume for which DITs disappear.

math.PR↗
arXiv2019

New formulation of the Logistic-Gaussian process to analyze trajectory tracking data

Improved communication systems, shrinking battery sizes and the price drop of tracking devices have led to an increasing availability of trajectory tracking data. These data are often analyzed to understand animal behavior. In this work, we propose a new model for interpreting the animal movent as a mixture of characteristic patterns, that we interpret as different behaviors. The probability that the animal is behaving according to a specific pattern, at each time instant, is non-parametrically estimated using the Logistic-Gaussian process. Owing to a new formalization and the way we specify the coregionalization matrix of the associated multivariate Gaussian process, our model is invariant with respect to the choice of the reference element and of the ordering of the probability vector components. We fit the model under a Bayesian framework, and show that the Markov chain Monte Carlo algorithm we propose is straightforward to implement. We perform a simulation study with the aim of showing the ability of the estimation procedure to retrieve the model parameters. We also test the performance of the information criterion we used to select the number of behaviors. The model is then applied to a real dataset where a wolf has been observed before and after procreation. The results are easy to interpret, and clear differences emerge in the two phases.

stat.AP↗
arXiv2018

A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena, such as a deficiency and a bistability. It is advocated that the diffusion approximation can be considered as an alternative theoretical approach to study the reaction networks rather than a simulation shortcut. We discuss two examples in which the diffusion approximation is able to catch qualitative properties of reaction networks that the deterministic model misses. We provide an explicit construction of the original process and the diffusion approximation such that the distance between their trajectories is controlled and demonstrate this construction for the examples. We also discuss the limitations and potential directions of the developments.

math.PR↗
arXiv2017

Strong approximation of density dependent Markov chains on bounded domains

Density dependent families of Markov chains, such as the stochastic models of mass-action chemical kinetics, converge for large values of the indexing parameter $N$ to deterministic systems of differential equations (Kurtz, 1970). Moreover for moderate $N$ they can be strongly approximated by paths of a diffusion process (Kurtz, 1976). Such an approximation however fails if the state space is bounded (at zero or at a constant maximum level due to conservation of mass) and if the process visits the boundaries with non negligible probability. We present a strong approximation by a jump-diffusion process which is robust to this event. The result is illustrated with a particularly hard case study.

math.PR↗
arXiv2015

A copula-based method to build diffusion models with prescribed marginal and serial dependence

This paper investigates the probabilistic properties that determine the existence of space-time transformations between diffusion processes. We prove that two diffusions are related by a monotone space-time transformation if and only if they share the same serial dependence. The serial dependence of a diffusion process is studied by means of its copula density and the effect of monotone and non-monotone space-time transformations on the copula density is discussed. This provides us a methodology to build diffusion models by freely combining prescribed marginal behaviors and temporal dependence structures. Explicit expressions of copula densities are provided for tractable models. A possible application in neuroscience is sketched as a proof of concept.

math.PR↗
arXiv2015

Approximate analysis of biological systems by hybrid switching jump diffusion

In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has proposed two kinds of approximations. One is based on ordinary differential equations, while the other uses a diffusion process. The computational cost of the deterministic approximation is significantly lower, but the diffusion approximation retains stochasticity and is able to reproduce relevant random features like variance, bimodality, and tail behavior. In a recent paper, for particular stochastic Petri net models, we proposed a jump diffusion approximation that aims at being applicable beyond the limits of Kurtz's diffusion approximation, namely when the process reaches the boundary with non-negligible probability. Other limitations of the diffusion approximation in its original form are that it can provide inaccurate results when the number of objects in some groups is often or constantly low and that it can be applied only to pure density dependent Markov chains. In order to overcome these drawbacks, in this paper we propose to apply the jump-diffusion approximation only to those components of the model that are in density dependent form and are associated with high population levels. The remaining components are treated as discrete quantities. The resulting process is a hybrid switching jump diffusion. We show that the stochastic differential equations that characterize this process can be derived automatically both from the description of the original Markov chains or starting from a higher level description language, like stochastic Petri nets. The proposed approach is illustrated on three models: one modeling the so called crazy clock reaction, one describing viral infection kinetics and the last considering transcription regulation.

cs.PF↗
arXiv2014

Higher Moments and Prediction Based Estimation for the COGARCH(1,1) model

COGARCH models are continuous time version of the well known GARCH models of financial returns. They are solution of a stochastic differential equation driven by a Lévy process. The first aim of this paper is to show how the method of Prediction-Based Estimating Functions (PBEFs) can be applied to draw statistical inference from a discrete sample of observations of a COGARCH(1,1) model as far as the higher order structure of the process is clarified. Motivated by the search for an optimal PBEF, a second aim of the paper is to provide recursive expressions for the joint moments of any fixed order of the process, whenever they exist. Asymptotic results are given and a simulation study shows that the method of PBEF outperforms the other available estimation methods.

math.PR↗
arXiv2014

Analysis of Petri Net Models through Stochastic Differential Equations

It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODEs) when their indexing parameter grows very large. This approximation cannot capture the stochastic nature of the process and, consequently, it can provide an erroneous view of the behavior of the Markov chain if the indexing parameter is not sufficiently high. Important phenomena that cannot be revealed include non-negligible variance and bi-modal population distributions. A less-known approximation proposed by Kurtz applies stochastic differential equations (SDEs) and provides information about the stochastic nature of the process. In this paper we apply and extend this diffusion approximation to study stochastic Petri nets. We identify a class of nets whose underlying stochastic process is a density dependent Markov chain whose indexing parameter is a multiplicative constant which identifies the population level expressed by the initial marking and we provide means to automatically construct the associated set of SDEs. Since the diffusion approximation of Kurtz considers the process only up to the time when it first exits an open interval, we extend the approximation by a machinery that mimics the behavior of the Markov chain at the boundary and allows thus to apply the approach to a wider set of problems. The resulting process is of the jump-diffusion type. We illustrate by examples that the jump-diffusion approximation which extends to bounded domains can be much more informative than that based on ODEs as it can provide accurate quantity distributions even when they are multi-modal and even for relatively small population levels. Moreover, we show that the method is faster than simulating the original Markov chain.

cs.PF↗
arXiv2012

Estimation in discretely observed diffusions killed at a threshold

Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modeled as discretely observed diffusions which are killed when the threshold is reached. Statistical inference is often based on the misspecified likelihood ignoring the presence of the threshold causing severe bias, e.g. the bias incurred in the drift parameters of the Ornstein-Uhlenbeck model for biological relevant parameters can be up to 25-100%. We calculate or approximate the likelihood function of the killed process. When estimating from a single trajectory, considerable bias may still be present, and the distribution of the estimates can be heavily skewed and with a huge variance. Parametric bootstrap is effective in correcting the bias. Standard asymptotic results do not apply, but consistency and asymptotic normality may be recovered when multiple trajectories are observed, if the mean first-passage time through the threshold is finite. Numerical examples illustrate the results and an experimental data set of intracellular recordings of the membrane potential of a motoneuron is analyzed.

math.PR↗
arXiv2011

Boundary crossing Random Walks, clinical trials and multinomial sequential estimation

A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or multinomial Random Walks which are observed until they reach a boundary. An application to clinical trials is presented.

math.ST↗
arXiv2006

Gauge-natural parameterized variational problems, vakonomic field theories and relativistic hydrodynamics of a charged fluid

Variational principles for field theories where variations of fields are restricted along a parametrization are considered. In particular, gauge-natural parametrized variational problems are defined as those in which both the Lagrangian and the parametrization are gauge covariant and some further conditions is satisfied in order to formulate a Nöther theorem that links horizontal and gauge symmetries to the relative conservation laws (generalizing what Fern{á}ndez, Garc{\'ı}a and Rodrigo did in some recent papers). The case of vakonomic constraints in field theory is also studied within the framework of parametrized variational problems, defining and comparing two different concepts of criticality of a section, one arising directly from the vakonomic schema, the other making use of an adapted parametrization. The general theory is then applied to the case of hydrodynamics of a charged fluid coupled with its gravitational and electromagnetic field. A variational formulation including conserved currents and superpotentials is given that turns out to be computationally much easier than the standard one.

math-ph↗