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Klaus Kähler Holst

Principal Scientist

A.P. Moller-Maersk

Biography

I am a principal scientist in the Research & Development organisation of A.P. Møller-Mærsk.

My primary research interests are general aspects of computational statistics, measurement error models, missing data and causal inference with applications in logistics.

Interests

  • Computational Statistics
  • Causal inference & statistical reinforcement learning
  • High-dimensional statistical learning and forecasting
  • Latent variable models

Education

  • PhD in Biostastics, 2011

    University of Copenhagen, Department of Biostatistics

  • MSc in Mathematics, 2006

    University of Copenhagen, Department of Mathematics

Selected Publications

Full publication list

A two-stage estimation procedure for non-linear structural equation models

Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood …

Modeling the cumulative incidence function of multivariate competing risks data allowing for within-cluster dependence of risk and timing

We propose to model the cause-specific cumulative incidence function of multivariate competing risks data using a random effects model …

Cox regression with missing covariate data using a modified partial likelihood method

Missing covariate values is a common problem in survival analysis. In this paper we propose a novel method for the Cox regression model …

The liability threshold model for censored twin data

Family studies provide an important tool for understanding etiology of diseases, with the key aim of discovering evidence of family …

Linear latent variable models: the lava-package

An R package for specifying and estimating linear latent variable models is presented. The philosophy of the implementation is to …

Measuring early or late dependence for bivariate lifetimes of twins

We consider data from the Danish twin registry and aim to study in detail how lifetimes for twin-pairs are correlated. We consider …

Convergence of Markov Chains in Information Divergence

Information theoretic methods are used to prove convergence in information divergence of reversible Markov chains. Also some ergodic …

Recent Posts

List of all posts

Logic gates

Logic gates are the building blocks of digital electronics. Simple logic gates are efficiently implemented in various IC packages such as the 74HCXX series. However, it is educational to have a look at the implementation using just NPN transistors.

… Read more

Shift register circuit board

The 74HC165 and 74HC495 are useful integrated circuits for dealing with multiple digital inputs and outputs. In a recent project, I used the following prototype based on a variant of the above simple circuit schema:

The four 74HC495 ICs gives access to 2 x 16 bits accessible through IDC connectors controllable using just three pins on the microcontroller (DATA, CLOCK, LATCH). Similarly, two 74HC165 ICs gives access to 16 input bits through another IDC connector.

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A simple ODE Class

A small illustration on using the armadillo C++ linear algebra library for solving an ordinary differential equation of the form \[ X’(t) = F(t,X(t),U(t)).\]

The abstract super class Solver defines the methods solve (for approximating the solution in user-defined time-points) and solveint (for interpolating user-defined input functions on finer grid). As an illustration a simple Runge-Kutta solver is derived in the class RK4.

The first step is to define the ODE, here a simple one-dimensional ODE \(X’(t) = \theta\cdot\{U(t)-X(t)\}\) with a single input \(U(t)\):

rowvec dX(const rowvec &input, // time (first element) and additional input variables
	 const rowvec &x,     // state variables
	 const rowvec &theta) {   // parameters
  rowvec res = { theta(0)*theta(1)*(input(1)-x(0)) };
  return( res );
}

The ODE may then be solved using the following syntax

odesolver::RK4 MyODE(dX);
arma::mat res = MyODE.solve(input, init, theta);

with the step size defined implicitly by input (first column is the time variable and the following columns the optional different input variables) and boundary conditions defined by init.

… Read more

A probability game

Assume that two positive numbers are given, \(X\) and \(Y\), with unknown joint probability distribution \(P\), and \(X\neq Y\) a.s.

A player draws randomly one of the numbers and has to guess if the number is smaller or larger than the other unrevealed number, i.e., let \(U\sim Bernoulli(\tfrac{1}{2})\) independent of \(X, Y\), then the player sees \(Z_{1} = UX + (1-U)Y,\) and \(Z_{2} = (1-U)X + UY\) remains unseen.

A random guess (coin-flip) would due to the sampling \(U\), indepedently of \(F\), have probability \(\tfrac{1}{2}\) of correct guessing. The question is if we can find a better strategy?

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Shift register (output)

The 74HC595: an 8-bit serial-in/serial or parallel-out shift register with a storage register and 3-state outputs.

If higher load is required there is also the TPIC6C595 (e.g., for driving LEDs), or it should be paired with for example ULN2803 or similar. For multiple inputs see the 74HC165.

Figure 1: Pin-out 74HC595.

The basic usage is to serially transfer a byte from a microcontroller to the IC. When latched the byte will then in parallel be available on output pins QA-QH (Q0-Q7).

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Regression models for the relative risk

\(\newcommand{\pr}{\mathbb{P}}\newcommand{\E}{\mathbb{E}}\) Relative risks (and risk differences) are collapsible and generally considered easier to interpret than odds-ratios. In a recent publication Richardson et al (JASA, 2017) proposed a new regression model for a binary exposure which solves the computational problems that are associated with using for example binomial regression with a log-link function (or identify link for the risk difference) to obtain such parameter estimates.

Let \(Y\) be the binary response, \(A\) binary exposure, and \(V\) a vector of covariates, then the target parameter is

\begin{align*} &\mathrm{RR}(v) = \frac{\pr(Y=1\mid A=1, V=v)}{\pr(Y=1\mid A=0, V=v)}. \end{align*}

Let \(p_a(V) = \pr(Y \mid A=a, V), a\in\{0,1\}\), then the idea is to posit a linear model for \[ \theta(v) = \log \big(RR(v)\big) \] and a nuisance model for the odds-product \[ \phi(v) = \log\left(\frac{p_{0}(v)p_{1}(v)}{(1-p_{0}(v))(1-p_{1}(v))}\right) \] noting that these two parameters are variation independent which can be from the below L’Abbé plot. Similarly, a model can be constructed for the risk-difference on the following scale \[\theta(v) = \mathrm{arctanh} \big(RD(v)\big).\]

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Shift register (input)

The 74HC165 is an 8-bit parallel-load or serial-in shift register.

Figure 1: Pin-out 74HC165.

Wiring:

  • Pin 8 (GND): GND
  • Pin 16 (VCC): Voltage 5V
  • Pin 11-14 & 3-6 (A-H): Input 1-8
  • Pin 1 (SH/LD): shift/load pin
  • Pin 2 (CLK): Clock pin
  • Pin 9 (QH): Data output pin
  • Pin 15 (CLK INH): Clock-inhibit pin (or GND)

Clocking is accomplished by a low-to-high transition of the clock (CLK) input while SH/LD is held high and CLK INH is held low. CLK INH can be wired to GND to save a pin on the microcontroller. Unused inputs pins should be grounded as well.

Multiple 74HC165 ICs can be daisy chained by wiring the serial-out pin 9 (QH) to pin 10 (SER) of the succeeding IC allowing us to tie multiple 74165 ICs together that can be controlled using only 3 pins.

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