# Questions tagged [continuous-time]

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### Bayesian Inference of a Gaussian Process with a Continuous-time Obervations

In many books about Bayesian inference based on Gaussian process, it is assumed that one can only observe a set of data/signals at discrete points. This is a very realistic assumption. However, in ...
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### How to train a continuous-time normalizing flow model?

I'm confused on how we can actually train a continuous-time normalizing flow model. There are two use cases for the discrete-time (original) normalizing flows, and I've tried to outline how I would do ...
21 views

### Meta-analysis of odds ratio for continuous variables, how to interpret the decrease or increase per unit?

So, I am doing a meta-analysis of odds ratios to find out the risk factors for a certain medical outcome. One of those risk factors would be (simplified) the time spent in the operation room. My ...
42 views

### What is the natural progression from discrete AR models into continuous time?

Lets say we want to predict a single target variable and we have 10 regressors/features. Assume we would like to predict 30 days ahead (daily predictions up to 30 days ahead) and our data is a daily ...
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### Define Multi-Rate Network Model state space and transition rates between the states

Assume there's a network with audio and video call classes. Audio call requires 1 channel (b1) and video call classes requires different channels based on the video call type (V_low=2(b2), V_med=3(b3),...
35 views

### Combination of a discrete and a continuous Markov Chain in a MCMC

Recently, I've been questioning myself on the possibility of combining a discrete update and a continuous update on a single MCMC. Stephens (2000) in Algorithm 3.2 runs the process for a fixed amount ...
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### what type of machine learning or neural net algorithm would i use for predictions about the shape of a plot

if a data set is set up such that it has 5 independent variables and an array of 201 elements of "smooth continuous" data as the dependent variable. I was wondering if there was a model ...
1 vote
69 views

### When are continuous-time models important?

In Econometrics, majority of the models are in discrete-time setting, whereas when you move on to quantitative finance, continuous-time models are most prevalent. I get the theory and idea behind ...
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### Variance estimate in a gillespie simulation

Lets say I simulate a immigration-death process: $P(X(t + \delta t) = x+ 1 | X(t) = x) = \lambda \delta t$ $P(X(t + \delta t) = x-1 | X(t) =x) = v x \delta t$ using a Gillespie simulation - I pick a ...
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1 vote
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### What would be a continuous-time version of a VAR process?

It is often said that a AR(1) process can be viewed as a discretized version of the continuous-time Ornstein-Uhlenbeck process. Can we really claim this to be valid considering that the Ornstein-...
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### Continuously occurring true negatives

How can I handle discrete events in a continuous time stream in the context of an F1 metric? To give an example, let's say the Earthquake Forecasting Bureau would report the following for their ...
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### Is there a way to calculate the riskiest places to be infected by COVID-19?

Is there a way to calculate the riskiest places to be infected by COVID-19? My friends and I are having an argument of whether being in a "high traffic-short contact time" situation (public transport) ...
1 vote
54 views

### Can the interarrival times of a continuous time markov chain be distributed with 2 parameter (scale,location) exponential distributions?

I'm trying to model data with a time-homogenous CTMC with a number of states with corresponding constant transition rates $\lambda_{i}$ when I notice that much of the transition times from one state ...
1 vote
226 views

### Correspondence between time series models in continuous vs. discrete time

I am interested in an overview over the connection and correspondence between time series models in continuous vs. discrete time in finance. E.g. take ARMA(p,q) or GARCH(s,r) or ARMA(p,q)-GARCH(s,r) ...
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### Generate PDF from CTMC

I have an irreducible continuous-time Markov chain (CTMC) with a finite state space. The CTMC also does not have any one-step transitions from any state to itself. I have the transition rate matrix $Q$...
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### Modeling by means of a negative binomial process

The negative binomial distribution with parameters $p\in(0,1)$ and $t>0$ is sometimes defined as the distribution of the number of failures before the $t$th success. This is supported on the set \$\{...
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1 vote
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### Derivation Harvey (1984) Logistic Curve

Given a logistic function of the form. \begin{align*} f(t) = \frac{\alpha}{1 + \beta e^{\gamma t}} \end{align*} Harvey (1984) differentiates this and takes logs to yield: \begin{align*} \ln f' = 2 ...
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### Linear mixed model: Time as continuous or discrete variable?

I am analysing a dataset from a randomised controlled trial (2 treatment groups) with measurements at 3 time points (weeks 0, 1 and 8). I am struggling with whether to analyse this with the three time ...
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