Related papers: On the Generalized Birth-Death Process and its Lin…
Gradient boosted decision trees (GBDTs) are widely used in machine learning, and the output of current GBDT implementations is a single variable. When there are multiple outputs, GBDT constructs multiple trees corresponding to the output…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…
The multivariate generalized Pareto distribution (mGPD) is a common method for modeling extreme threshold exceedance probabilities in environmental and financial risk management. Despite its broad applicability, mGPD faces challenges due to…
We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the Bolker-Pacala-Dieckmann-Law model. Under the…
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates.…
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
Spatial birth-and-death processes with a finite number of particles are obtained as unique solutions to certain stochastic equations. Conditions are given for existence and uniqueness of such solutions, as well as for continuous dependence…
Continuous-time linear birth-death-immigration (BDI) processes are frequently used in ecology and epidemiology to model stochastic dynamics of the population of interest. In clinical settings, multiple birth-death processes can describe…
Motivated by a range of biological applications related to the transport of molecules in cells, we present a modular framework to treat first-passage problems for diffusion in partitioned spaces. The spatial domains can differ with respect…
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…
We survey the 'generalized fractional Poisson process' (GFPP). The GFPP is a renewal process generalizing Laskin's fractional Poisson counting process and was first introduced by Cahoy and Polito. The GFPP contains two index parameters with…
We study two families of QBD processes with linear rates: (A) the multiserver retrial queue and its easier relative; and (B) the multiserver M/M/infinity Markov modulated queue. The linear rates imply that the stationary probabilities…
Consider the batch-arrival $GI^X/M/c/N$ model with $c$ servers, general inter-arrival batch times, finite buffer, and exponential service times. Inter-arrival batch times, batch sizes, and service times are $i.i.d.$ and independent of each…
This paper proposes simple perfect samplers using monotone birth-and-death processes (BD-processes), which draw samples from an arbitrary finite discrete target distribution. We first construct a monotone BD-process whose stationary…
We study large deviations of the time-averaged size of stochastic populations described by a continuous-time Markov jump process. When the expected population size $N$ in the steady state is large, the large deviation function (LDF) of the…
In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described.…
The birth-death process is a special type of continuous-time Markov chain with index set $\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(\gamma, \beta, \nu)$, where $\gamma$ and $\beta$ are…
Gaussian Processes (GPs) provide powerful probabilistic frameworks for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we investigate data sampled on one dimension (e.g., a scalar or…
Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the…