Markov chain

A simple two-state Markov chain A Markov chain (discrete-time Markov chain or DTMC[1]), named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another on a state space. It is a random process usually characterized as memoryless: the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property. Markov chains have many applications as statistical models of real-world processes. Introduction A Markov chain is a stochastic process with the Markov property. In literature, different Markov processes are designated as "Markov chains". The changes of state of the system are called transitions. A discrete-time random process involves a system which is in a certain state at each step, with the state changing randomly between steps. Many other examples of Markov chains exist. Formal definition . . of states as input, where is defined, while and Related:  Art & Technology

Blog » Blog Archive » Pimp up your camera with Arduino timelapse video tutorial – auch auf Deutsch Pimp up your camera with Arduino timelapse video tutorial – auch auf Deutsch Zoe Romano — May 25th, 2013 Last month we launched the first of a series of tutorials hosted on our Youtube Channel and created by Max of MaxTechTV in german language. Today we are publishing the second video called “Pimp-up your camera with an Arduino timelapse“. The video explains how to connect an Arduino UNO with you camera and shoot pictures, for example, every 1, 5, 10 seconds to create wonderful videos of slow processes that would normally appear subtle to the human eye. Enjoy the tutorial below and share with us the results of your experimentations! Letzten Monat haben wir das erste einer Reihe von Video-Tutorials auf unserem YouTube Kanal veröffentlicht. Heute veröffentlichen wir das zweite Video mit dem Titel “Erstelle tolle Zeitrafferaufnahmen mit deiner Kamera & Arduino”.

Markov chains don’t converge I often hear people often say they’re using a burn-in period in MCMC to run a Markov chain until it converges. But Markov chains don’t converge, at least not the Markov chains that are useful in MCMC. These Markov chains wander around forever exploring the domain they’re sampling from. Any point that makes a “bad” starting point for MCMC is a point you might reach by burn-in. Not only that, Markov chains can’t remember how they got where they are. That’s their defining property. When someone says a Markov chain has converged, they may mean that the chain has entered a high-probability region. Burn-in may be ineffective. Why use burn-in? So why does it matter whether you start your Markov chain in a high-probability region? Samples from Markov chains don’t converge, but averages of functions applied to these samples may converge. It’s not just a matter of imprecise language when people say a Markov chain has converged.

Normative ethics Branch of philosophical ethics that examines standards for morality Normative ethics is the study of ethical behaviour and is the branch of philosophical ethics that investigates questions regarding how one ought to act, in a moral sense. Normative ethics is distinct from meta-ethics in that the former examines standards for the rightness and wrongness of actions, whereas the latter studies the meaning of moral language and the metaphysics of moral facts. Likewise, normative ethics is distinct from applied ethics in that the former is more concerned with 'who ought one be' rather than the ethics of a specific issue (e.g. if, or when, abortion is acceptable). Normative ethics is also distinct from descriptive ethics, as the latter is an empirical investigation of people's moral beliefs. In this context normative ethics is sometimes called prescriptive, as opposed to descriptive ethics. An adequate justification for a group of principles needs an explanation of those principles.

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Predator takes visual object tracking to new heights – Computer Chips & Hardware Technology Cameras have slowly made their way into the portable gadgets we all carry around with us and not having a camera in a new device is viewed as a missing feature. It’s got to the point now where the latest smartphones even have two cameras so as to make for better video chat. But while the prevalence and quality of the cameras has gone up, the software still lags behind in terms of being able to identify and track objects in any real-time or captured footage. That is about to change due to the work of Czech student Zdeneki Kalai. This algorithm not only tracks, it learns the more it gets used. Kalai believes what he has created, a combination of tracking, learning, and detection is completely unique and allows for a whole new set of functionality to be applied when looking at video feeds. In the video he gives examples of a new interface that can detect your fingers and use them to draw, learning to get better at trakcing those fingers as it is used more. Read more at GottaBeMobile

Random walk Example of eight random walks in one dimension starting at 0. The plot shows the current position on the line (vertical axis) versus the time steps (horizontal axis). A random walk is a mathematical formalization of a path that consists of a succession of random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be modeled as random walks, although they may not be truly random in reality. Various different types of random walks are of interest. . is defined for the continuum of times . Lattice random walk A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. One-dimensional random walk An elementary example of a random walk is the random walk on the integer number line, This walk can be illustrated as follows. .

Independent and identically distributed random variables The abbreviation i.i.d. is particularly common in statistics (often as iid, sometimes written IID), where observations in a sample are often assumed to be effectively i.i.d. for the purposes of statistical inference. The assumption (or requirement) that observations be i.i.d. tends to simplify the underlying mathematics of many statistical methods (see mathematical statistics and statistical theory). However, in practical applications of statistical modeling the assumption may or may not be realistic. To test how realistic the assumption is on a given data set the autocorrelation can be computed, lag plots drawn or turning point test performed.[2] The generalization of exchangeable random variables is often sufficient and more easily met. The assumption is important in the classical form of the central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution. Examples

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