In this tutorial we demonstrate how one can use TKRISK to analyze vaccine response to COVID19. We create a simple model of contamination and show how vaccine and exposition can jointly affect the probability of being infected.
We review with this example the logic and applicability of Bayesian networks. We are able to closely match the analytical solution thanks to efficient sampling methods including low discrepancy sequences. This is the first of a three parts demo.
In this tutorial we demonstrate how one can use TKRISK to analyze vaccine response to COVID19. We create a simple model of contamination and show how vaccine and exposition can jointly affect the probability of being infected.
We review with this example the logic and applicability of Bayesian networks. We are able to closely match the analytical solution thanks to efficient sampling methods including low discrepancy sequences. This is the first of a three parts demo.
SCENARIO ENGINE
Tenokonda Scenario Engine allows for random variables and processes modeling and simuLation. Its role is fundamental in risk analysis as joint risk factors simulation allows in turn estimating tail metrics such as value at risk or expected shortfall.
Features

Time series preprocessing: aligning dates and filling gaps

Probability distributions sampling

Stochastic processes simulation

External random number generation

Distribution lower and/or upper bound truncation

Joint distribution/process sampling through variancecovariance

Joint distribution/process sampling through copulas
Distributions covered

Discrete
categorical, binomial, geometric, hypergeometric, logseries, multinomial, negative binomial, Poisson, zipf 
Continuous
beta, Cauchy, chi square, Dirichlet, exponential, f, gamma, Gumbel, Laplace, logistic, lognormal, non central chi square, non central f, normal, normal multivariate, Pareto, power, Rayleigh, t, triangular, uniform, Von Mises, Wald, Weibull
Stochastic Processes covered

Black Karazinski

Brownian Motion

Exponential Brownian Motion

Geometric Brownian Motion

Hybrid

Normal Increments

Ornstein Uhlenbeck
References
[1] Drake, A. Fundamentals of Applied Probability Theory. New York, NY: McGrawHill, 1988.
[2] Rice, John A. Mathematical Statistics and Data Analysis. Duxbury Press, 2006.
[3] Karatzas, Ioannis and Steven, Shreve. Brownian Motion and Stochastic Calculus. 2nd ed. SpringerVerlag, 1991.
[4] Øksendal, B. Stochastic Differential Equations: An Introduction with Applications. Springer, 2010.
[5] Roger B. Nelsen (1999), "An Introduction to Copulas", Springer.
[6] Abe Sklar (1997): "Random variables, distribution functions, and copulas – a personal look backward and forward" in Rüschendorf, L., Schweizer, B. und Taylor, M. (eds) Distributions With Fixed Marginals & Related Topics
[7] Kiyosi Itô (1951). On stochastic differential equations. Memoirs, American Mathematical Society 4, 1–51.
[8] Black, F.; Karasinski, P. (July–August 1991). "Bond and Option pricing when Short rates are Lognormal". Financial Analysts Journal: 52–59.
[9] Uhlenbeck, G. E.; Ornstein, L. S. (1930). "On the theory of Brownian Motion". Phys. Rev. 36 (5): 823–841.