Unit root tests for panel data

The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (i.e., double-exponential) priors. Gibbs sampling from this posterior is possible using an expanded hierarchy with conjugate normal priors for the regression parameters and independent exponential priors on their variances. A connection with the inverse-Gaussian distribution provides tractable full conditional distributions. The Bayesian Lasso provides interval estimates (Bayesian credible intervals) that can guide variable selection. Moreover, the structure of the hierarchical model provides both Bayesian and likelihood methods for selecting the Lasso parameter. Slight modifications lead to Bayesian versions of other Lasso-related estimation methods, including bridge regression and a robust variant.

The Bayesian Lasso

GPS-equipped taxis can be regarded as mobile sensors probing traffic flows on road surfaces, and taxi drivers are usually experienced in finding the fastest (quickest) route to a destination based on their knowledge. In this paper, we mine smart driving directions from the historical GPS trajectories of a large number of taxis, and provide a user with the practically fastest route to a given destination at a given departure time. In our approach, we propose a time-dependent landmark graph, where a node (landmark) is a road segment frequently traversed by taxis, to model the intelligence of taxi drivers and the properties of dynamic road networks. Then, a Variance-Entropy-Based Clustering approach is devised to estimate the distribution of travel time between two landmarks in different time slots. Based on this graph, we design a two-stage routing algorithm to compute the practically fastest route. We build our system based on a real-world trajectory dataset generated by over 33,000 taxis in a period of 3 months, and evaluate the system by conducting both synthetic experiments and in-the-field evaluations. As a result, 60-70% of the routes suggested by our method are faster than the competing methods, and 20% of the routes share the same results. On average, 50% of our routes are at least 20% faster than the competing approaches.

/pdf/t-drive-driving-directions-based-on-taxi-trajectories-1xb3zuw0ip.pdf

T-drive: driving directions based on taxi trajectories

The integrate-and-fire neuron model is one of the most widely used models for analyzing the behavior of neural systems. It describes the membrane potential of a neuron in terms of the synaptic inputs and the injected current that it receives. An action potential (spike) is generated when the membrane potential reaches a threshold, but the actual changes associated with the membrane voltage and conductances driving the action potential do not form part of the model. The synaptic inputs to the neuron are considered to be stochastic and are described as a temporally homogeneous Poisson process. Methods and results for both current synapses and conductance synapses are examined in the diffusion approximation, where the individual contributions to the postsynaptic potential are small. The focus of this review is upon the mathematical techniques that give the time distribution of output spikes, namely stochastic differential equations and the Fokker–Planck equation. The integrate-and-fire neuron model has become established as a canonical model for the description of spiking neurons because it is capable of being analyzed mathematically while at the same time being sufficiently complex to capture many of the essential features of neural processing. A number of variations of the model are discussed, together with the relationship with the Hodgkin–Huxley neuron model and the comparison with electrophysiological data. A brief overview is given of two issues in neural information processing that the integrate-and-fire neuron model has contributed to – the irregular nature of spiking in cortical neurons and neural gain modulation.

https://link.springer.com/content/pdf/10.1007%2Fs00422-006-0068-6.pdf

A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input

MicroRNAs (miRNAs) are small endogenous RNA molecules that regulate gene expression through mRNA degradation and/or translation repression, affecting many biological processes. DIANA-microT web server (http://www.microrna.gr/webServer) is dedicated to miRNA target prediction/functional analysis, and it is being widely used from the scientific community, since its initial launch in 2009. DIANA-microT v5.0, the new version of the microT server, has been significantly enhanced with an improved target prediction algorithm, DIANAmicroT-CDS. It has been updated to incorporate miRBase version 18 and Ensembl version 69. The in silico-predicted miRNA–gene interactions in Homo sapiens, Mus musculus, Drosophila melanogaster and Caenorhabditis elegans exceed 11 million in total. The web server was completely redesigned, to host a series of sophisticated workflows, which can be used directly from the on-line web interface, enabling users without the necessary bioinformatics infrastructure to perform advanced multi-step functional miRNA analyses. For instance, one available pipeline performs miRNA target prediction using different thresholds and meta-analysis statistics, followed by pathway enrichment analysis. DIANAmicroT web server v5.0 also supports a complete integration with the Taverna Workflow Management System (WMS), using the in-house developed DIANA-Taverna Plug-in. This plug-in provides ready-to-use modules for miRNA target prediction and functional analysis, which can be used to form advanced high-throughput analysis pipelines.

/pdf/diana-microt-web-server-v5-0-service-integration-into-mirna-50ia8mgp0u.pdf

DIANA-microT web server v5.0: service integration into miRNA functional analysis workflows

1. Introduction 2. Properties of the Inverse Gaussian Distribution 3. Genesis 4. Certain Useful Transformations and Characterizations 5. Sampling and Estimation of Parameters 6. Significance Tests 7. Bayesian Inference 8. Regression Analysis 9. Life Testing and Reliability 10. Applications 11. Additional Topics

The inverse gaussian distribution: theory, methodology, and applications

Four methods of combining independent tests of hypothesis are compared via exact Bahadur relative efficiency. The methods considered are Fisher's method, the mean of the normal transforms of the significance levels, the maximum significance level, and the minimum significance level. None of these is uniformly more powerful than the others, but, according to Bahadur efficiency, Fisher's method is the most efficient of the four. In some cases, Fisher's method is most efficient of all tests based on the data, but this is not generally true.

Asymptotic Optimality of Fisher's Method of Combining Independent Tests

It does not appear to be widely known that the moment-generating function Mx (t) contains information about negative as well as positive integer moments. Proofs of this are provided, extensions are indicated, and earlier literature deriving and using this type of result is briefly noted. Some examples are given.

https://www.jstor.org/stable/pdfplus/2683982.pdf

The Moment-Generating Function and Negative Integer Moments

Minimum variance unbiased estimates of the inverse Gaussian distribution function for all possible cases are given. A direct relationship is established between its density function and the normal density function, which throws more light on its salient features and possibly on its application in statistical inference. It is shown that the estimates are very similar in nature to those of the normal distribution and can be evaluated from the normal and Student's t distribution tables.

Estimation of the Inverse Gaussian Distribution Function

Peirce (1839-1914) was one of the greatest of American philosophers and wrote on a wide range of scientific and other topics. He wrote on randomness and the need for experimental randomization, and on scientific method, statistical inference and hypothesis testing.


Keywords:

randomization;
inference;
hypothesis test;
scientific method

J. Leroy Folks

Papers

The inverse gaussian distribution: theory, methodology, and applications

Asymptotic Optimality of Fisher's Method of Combining Independent Tests

The Moment-Generating Function and Negative Integer Moments

Estimation of the Inverse Gaussian Distribution Function

Peirce, Charles Sanders †