scholarly journals NON-STATIONARY HYDROLOGIC FREQUENCY ANALYSIS USING TIME DEPENDENT PARAMETERS AND ITS MODEL SELECTION

2015 ◽  
Vol 71 (1) ◽  
pp. 28-42
Author(s):  
Hiromasa HAYASHI ◽  
Yasuto TACHIKAWA ◽  
Michiharu SHIIBA
Keyword(s):  
Model Selection ◽  
Frequency Analysis ◽  
Time Dependent ◽  
Hydrologic Frequency Analysis

scholarly journals Detecting Lineage-Specific Shifts in Diversification: A Proper Likelihood Approach

2020 ◽  
Author(s):  
Giovanni Laudanno ◽  
Bart Haegeman ◽  
Daniel L Rabosky ◽  
Rampal S Etienne
Keyword(s):  
Model Selection ◽  
Phylogenetic Tree ◽  
Time Dependent ◽  
Parameter Estimates ◽  
Time Varying ◽  
Diversification Rates ◽  
Branching Patterns ◽  
Recent Debate ◽  
Likelihood Approach ◽  
New Framework

Abstract The branching patterns of molecular phylogenies are generally assumed to contain information on rates of the underlying speciation and extinction processes. Simple birth–death models with constant, time-varying, or diversity-dependent rates have been invoked to explain these patterns. They have one assumption in common: all lineages have the same set of diversification rates at a given point in time. It seems likely, however, that there is variability in diversification rates across subclades in a phylogenetic tree. This has inspired the construction of models that allow multiple rate regimes across the phylogeny, with instantaneous shifts between these regimes. Several methods exist for calculating the likelihood of a phylogeny under a specified mapping of diversification regimes and for performing inference on the most likely diversification history that gave rise to a particular phylogenetic tree. Here, we show that the likelihood computation of these methods is not correct. We provide a new framework to compute the likelihood correctly and show, with simulations of a single shift, that the correct likelihood indeed leads to parameter estimates that are on average in much better agreement with the generating parameters than the incorrect likelihood. Moreover, we show that our corrected likelihood can be extended to multiple rate shifts in time-dependent and diversity-dependent models. We argue that identifying shifts in diversification rates is a nontrivial model selection exercise where one has to choose whether shifts in now-extinct lineages are taken into account or not. Hence, our framework also resolves the recent debate on such unobserved shifts. [Diversification; macroevolution; phylogeny; speciation]

scholarly journals Model selection techniques for the frequency analysis of hydrological extremes

2009 ◽  
Vol 45 (7) ◽  
Author(s):  
Francesco Laio ◽  
Giuliano Di Baldassarre ◽  
Alberto Montanari
Keyword(s):  
Model Selection ◽  
Frequency Analysis ◽  
Hydrological Extremes

scholarly journals Accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

2018 ◽  
Author(s):  
Yen Ting Lin ◽  
Nicolas E. Buchler
Keyword(s):  
Gene Expression ◽  
Monte Carlo ◽  
Bayesian Inference ◽  
Model Selection ◽  
Single Cell ◽  
Kinetic Parameters ◽  
Information Criterion ◽  
Time Dependent ◽  
Data Sets ◽  
Bayesian Evidence

Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to statistical inference is the most complete method for model selection and uncertainty quantification of kinetic parameters from single-cell data. This approach is impractical because current numerical algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piece-wise deterministic Markov process. We combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We validated our method of accelerated Bayesian inference on several synthetic data sets. Our results show that kinetic parameters can be reasonably constrained for modestly sampled data sets, if the model is known a priori. If the model is unknown,the Bayesian evidence can be used to rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics, e.g., Bayesian Information Criterion (BIC) or Akaike Information Criterion (AIC), often used for model selection.

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