Questions tagged [continuous-time]

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What is the calculation behind norm.dist function in Excel?

For example, I will enter in norm.dist(89,100,50,0) for x, mean,sd, cumulative or no. Do I use the pdf of normal distribution and integrate? Any help would be appreciated and please also explain isn't ...
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42 views

nested random effect - Can I nest continuous (time) and categorical variable (condition)?

Apologies for another stupid question within such a short period of time. I am struggling to include "Time" (continuous variable) in my model where I test the effects of 3 "Periods" (conditions) in a ...
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16 views

Issues with switching between discrete and continuous time in a linear mixed model

I'm confused why switching from discrete time to continuous time is not more of an issue. While talking about animal survival data from day 1, day 2, & day 3 in an exposure experiment, the ...
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431 views

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) ...
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many datasets with multivariable continuous time series

I have many data-sets, each one have many variables (Time, X1, X2,..,Xn, Y) and Time variable is continuous [0-1]. the number of observation in each data-set is not equal and not synchronized in time: ...
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20 views

Modeling unequally spaced time series as OU process

I have a time series wherein the data points are unevenly spaced. I read this can be modeled as discrete time observation from a continuous time process. So I am trying to model it as an Ornstein-...
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19 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 ...
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92 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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147 views

Continuous time Fourier representation

I have learned that the Fourier transform of a continuous-time unit-periodic stochastic process is: $$x(t) = \sum\limits_{k=-\infty}^{\infty} a_k e^{i2\pi kt} \quad \quad \text{ where } \quad \quad ...
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117 views

Simulating a (discretized) Cox process via binomial sampling

Let X be a Cox process (doubly-stochastic Poisson process) driven by a Poisson process with fixed intensity(rate) $\lambda=50$ , and choose some small time interval $dt=0.01$ . Is the proper way to ...
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93 views

Infill likelihood for a continuously observed continuous-time process

Consider a continuous-time stochastic process $y(t)$ having the following linear (Gaussian) state-space representation for $t \geq 0$ $$ \left\{ \begin{array}{c c l} \text{d}{\boldsymbol{\...
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55 views

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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57 views

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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70 views

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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991 views

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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67 views

Correlation of continuous-time series

I have two continuous time series of discrete events. The data from them are timestamps of occurences, e.g. ...