Markov chain

Mathematical Finance: Core Theory, Problems and Statistical Algorithms

by Nikolai Dokuchaev  · 24 Apr 2007

evolves as where and where is some Wiener process; • (a(t), σ(t))=f(ξ(t)), where f is a deterministic function, ξ is a Markov chain process; • σ(t)=CS(t)p, where • the volatility σ(t) is an Ito process that evolves as where and where is some Wiener process

Natural Language Annotation for Machine Learning

by James Pustejovsky and Amber Stubbs  · 14 Oct 2012  · 502pp  · 107,510 words

and TRIOS (UzZaman and Allen 2010) TRIPS and TRIOS were two different programs submitted by the same team of researchers, though both used combinations of Markov chains and CRF models trained on various syntactic and attribute features. The systems returned the same results for task A: .85 precision, .85 recall, .85 F

Silence on the Wire: A Field Guide to Passive Reconnaissance and Indirect Attacks

by Michal Zalewski  · 4 Apr 2005  · 412pp  · 104,864 words

is a method for describing a discrete system in which the next value depends only on its current state, and not on the previous values (Markov chain). The Hidden Markov Model is a variant that provides a method for describing a system for which each internal state generates an observation, but for

The Elements of Statistical Learning (Springer Series in Statistics)

by Trevor Hastie, Robert Tibshirani and Jerome Friedman  · 25 Aug 2009  · 764pp  · 261,694 words

, in order to make inferences about the parameters. Except for simple models, this is often a difficult computational problem. In this section we discuss the Markov chain Monte Carlo (MCMC) approach to posterior sampling. We will see that Gibbs sampling, an MCMC procedure, is closely related to the EM algorithm: the main

…

) that the samples (U1 , U2 , . . . , UK ) are clearly not independent for different t. More formally, Gibbs sampling produces a Markov chain whose stationary distribution is the true joint distribution, and hence the term “Markov chain Monte Carlo.” It is not surprising that the true joint distribution is stationary under this process, as the successive

…

statistical application of Gibbs sampling is due to Geman and Geman (1984), and Gelfand and Smith (1990), with related work by Tanner and Wong (1987). Markov chain Monte Carlo methods, including Gibbs sampling and the Metropolis– Hastings algorithm, are discussed in Spiegelhalter et al. (1996). The EM algorithm is due to Dempster

…

) = Pr(Ynew |Xnew , θ)Pr(θ|Xtr , ytr )dθ (11.20) (c.f. equation 8.24). Since the integral in (11.20) is intractable, sophisticated Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior distribution Pr(Ynew |Xnew , Xtr , ytr ). A few hundred values θ are generated and

…

p = (1 − d)eeT /N + dLD−1 c = Ap (14.109) where the matrix A is the expression in square braces. Exploiting a connection with Markov chains (see below), it can be shown that the matrix A has a real eigenvalue equal to one, and one is its largest eigenvalue. This means

…

with the random surfer interpretation. Then the page rank solution (divided by N ) is the stationary distribution of an irreducible, aperiodic Markov chain over the N webpages. Definition (14.107) also corresponds to an irreducible, aperiodic Markov chain, with different transition probabilities than those from he (1 − d)/N version. Viewing PageRank as a

…

Markov chain makes clear why the matrix A has a maximal real eigenvalue of 1. Since A has positive entries with 578 14. Unsupervised

…

Learning Page 2 Page 1 Page 4 Page 3 FIGURE 14.46. PageRank algorithm: example of a small network each column summing to one, Markov chain theory tells us that it has a unique eigenvector with eigenvalue one, corresponding to the stationary distribution of the chain (Bremaud, 1999). A small network

…

get the unconditional estimates. Hinton (2002) noticed empirically that learning still works well if we estimate the second expectation in (17.37) by starting the Markov chain at the data and only running for a few steps (instead of to convergence). He calls this contrastive divergence: we sample H given V1 , V2

…

Statistical Review 60: 291–319. Breiman, L., Friedman, J., Olshen, R. and Stone, C. (1984). Classification and Regression Trees, Wadsworth, New York. Bremaud, P. (1999). Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues, Springer, New York. Brown, P., Spiegelman, C. and Denham, M. (1991). Chemometrics and spectral frequency selection, Transactions of

…

., Best, N., Gilks, W. and Inskip, H. (1996). Hepatitis B: a case study in MCMC methods, in W. Gilks, S. Richardson and D. Spegelhalter (eds), Markov Chain Monte Carlo in Practice, Interdisciplinary Statistics, Chapman and Hall, London, pp. 21–43. Spielman, D. A. and Teng, S.-H. (1996). Spectral partitioning works: Planar

…

, 441 Majority vote, 337 Majorization, 294, 553 Majorize-Minimize algorithm, 294, 584 MAP (maximum aposteriori) estimate, 270 Margin, 134, 418 Market basket analysis, 488, 499 Markov chain Monte Carlo (MCMC) methods, 279 Markov graph, 627 Markov networks, 638–648 MARS, see Multivariate adaptive regression splines MART, see Multiple additive regression trees Maximum

…

likelihood estimation, 31, 261, 265 MCMC, see Markov Chain Monte Carlo Methods MDL, see Minimum description length Mean field approximation, 641 Mean squared error, 24, 285 Memory-based method, 463 Metropolis-Hastings algorithm, 282

The Creativity Code: How AI Is Learning to Write, Paint and Think

by Marcus Du Sautoy  · 7 Mar 2019  · 337pp  · 103,522 words

learning in AI could help him compose music. He created the first AI jazz improviser using a mathematical formula from probability theory known as the Markov chain. Markov chains have been bubbling under many of the algorithms we have been considering thus far. They are fundamental tools for a slew of applications: from modelling

…

arrived at the current event. A series of events where the probability of each event depends only on the previous event became known as a Markov chain. Predicting the weather is a possible example. Tomorrow’s weather is certainly dependent on today’s but not particularly dependent on what happened last week

…

vowels. The chance of a vowel following a vowel, he calculated, was only 13 per cent. Eugene Onegin therefore provided a perfect example of a Markov chain to help him explain his ideas. Models of this sort are sometimes called models with amnesia: they forget what has happened and depend on the

…

was pushing the limits of the genre in more interesting ways. The Continuator has broken down boundaries and done remarkable things, but systems based on Markov chains have certain inbuilt limitations. Although it produced musical riffs that locally made sense and were even quite surprising, its compositions were ultimately unsatisfying because they

…

(AI) Macintosh computer 117 Malevich, Kasimir 11 Mandelbrot, Benoit: The Fractal Geometry of Nature 114 Mandelbrot set 113 Mankoff, Bob 284 Markov, Andrey 214–18 Markov chain 214–18, 216, 217, 221, 222, 223 Maros caves, Sulawesi 103–4 Martin, George R. R.: A Song of Ice and Fire/Game of Thrones

…

–8; Flow Machine and 221–4, 222; Hello World (AI album) 224; jazz/improvisation and 213–14, 218–24, 298, 299; Jukedeck and 225–6; Markov chain and 214–18, 216, 217; Sigur Rós: ‘Óveður and 228–9; Spotify and fake artists 224–5; why we make music 230–1 Sony 116

Analysis of Financial Time Series

by Ruey S. Tsay  · 14 Oct 2001

Factor-Volatility Models, 383 9.5 Application, 385 9.6 Multivariate t Distribution, 387 Appendix A. Some Remarks on Estimation, 388 357 x CONTENTS 10. Markov Chain Monte Carlo Methods with Applications 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10

…

Index 395 Markov Chain Simulation, 396 Gibbs Sampling, 397 Bayesian Inference, 399 Alternative Algorithms, 403 Linear Regression with Time-Series Errors, 406 Missing Values and Outliers, 410 Stochastic Volatility

…

in financial econometrics in the econometric and statistical literature. The developments discussed include the timely topics of Value at Risk (VaR), highfrequency data analysis, and Markov Chain Monte Carlo (MCMC) methods. In particular, the book covers some recent results that are yet to appear in academic journals; see Chapter 6 on derivative

…

covariance matrix to satisfy the positiveness constraint and reduce the complexity in volatility modeling. Finally, in Chapter 10, we introduce some newly developed Monte Carlo Markov Chain (MCMC) methods in the statistical literature and apply the methods to various financial research problems, such as the estimation of stochastic volatility and Markov switching

…

via Kalman filtering or a Monte Carlo method. Jacquier, Polson, and Rossi (1994) provide some comparison of estimation results between quasi-likelihood and Monte Carlo Markov Chain (MCMC) methods. The difficulty in estimating a SV model is understandable because for each shock at the model uses two innovations t and vt . We

…

between various states of an economy, Hamilton (1989) considers the Markov switching autoregressive (MSA) model. Here the transition is driven by a hidden two-state Markov chain. A time series xt follows an MSA model if it satisfies xt = c1 + c2 + p i=1 φ1,i x t−i + a1t if st

…

=1 φ2,i x t−i + a2t if st = 2, p (4.16) where st assumes values in {1, 2} and is a first-order Markov chain with transition probabilities P(st = 2 | st−1 = 1) = w1 , P(st = 1 | st−1 = 2) = w2 . The innovational series {a1t } and {a2t } are sequences

…

is the expected duration of the process to stay in State i. From the definition, an MSA model uses a hidden 136 NONLINEAR TIME SERIES Markov chain to govern the transition from one conditional mean function to another. This is different from that of a SETAR model for which the transition is

…

directly observable. Hamilton (1990) uses the EM algorithm, which is a statistical method iterating between taking expectation and maximization. McCulloch and Tsay (1994) consider a Markov Chain Monte Carlo (MCMC) method to estimate a general MSA model. We discuss MCMC methods in Chapter 10. McCulloch and Tsay (1993) generalize the MSA model

…

Hamilton (1989) and McCulloch and Tsay (1994) employ Markov switching models. Employing the MSA model in Eq. (4.16) with p = 4 and using a Markov Chain Monte Carlo method, which is discussed in Chapter 10, McCulloch and Tsay (1994) obtain the estimates shown in Table 4.1. The results have several

…

xt should be short. This implies that the contraction phases in the U.S. economy tend to be shorter than the expansion phases. Applying a Markov Chain Monte Carlo method, Montgomery et al. (1998) obtain the following Markov switching model for xt : xt = −0.07 + 0.38xt−1 − 0.05xt

…

, . . . , k − 1), and those in the conditional variance function σi (wi ) in Eq. (5.16). These parameters can be estimated by the maximum likelihood or Markov Chain Monte Carlo methods. Example 5.1. Hauseman, Lo, and MacKinlay (1992) apply the ordered probit model to the 1988 transactions data of more than 100

…

is a price change. The specified models in Eqs. (5.48)–(5.53) can be estimated jointly by either the maximum likelihood method or the Markov Chain Monte Carlo methods. Based on Eq. (5.47), the models consist of six conditional models that can be estimated separately. Example 5.5. Consider the

…

change of more than 1 tick; as a matter of fact, there were seven changes with two ticks and one change with three ticks. Using Markov Chain Monte Carlo (MCMC) methods (see Chapter 10), we obtained the following models for the data. The reported estimates and their standard deviations are the posterior

…

(1996, 1997). The fourth approach uses semiparametric and reprojection methods; see Gallant and Long (1997) and Gallant and Tauchen (1997). Recently, many researchers have applied Markov Chain Monte Carlo methods to estimate the diffusion equation; see Eraker (2001) and Elerian, Chib, and Shephard (2001). APPENDIX A. INTEGRATION OF BLACK–SCHOLES FORMULA In

…

and a positive definite covariance matrix, and we have a simple multivariate stochastic volatility model. In a recent manuscript, Chib, Nardari, and Shephard (1999) use Markov Chain Monte Carlo (MCMC) methods to study high-dimensional stochastic volatility models. The model FACTOR - VOLATILITY MODELS 383 considered there allows for time-varying correlations, but

…

Financial Time Series. Ruey S. Tsay Copyright  2002 John Wiley & Sons, Inc. ISBN: 0-471-41544-8 C H A P T E R 10 Markov Chain Monte Carlo Methods with Applications Advances in computing facilities and computational methods have dramatically increased our ability to solve complicated problems. The advances also extend

…

the applicability of many existing econometric and statistical methods. Examples of such achievements in statistics include the Markov Chain Monte Carlo (MCMC) method and data augmentation. These techniques enable us to make some statistical inference that was not feasible just a few years ago

…

the Markov process. If the transition probability depends on h − t, but not on t, then the process has a stationary transition distribution. 10.1 MARKOV CHAIN SIMULATION Consider an inference problem with parameter vector θ and data X, where θ ∈ Θ. To make inference, we need to know the distribution P

…

(θ | X). The idea of Markov chain simulation is to simulate a Markov process on Θ, which converges to a stationary transition distribution that is P(θ | X). The key to

…

Markov chain simulation is to create a Markov process whose stationary transition distribution is a specified P(θ | X) and run the simulation sufficiently long so that

…

stationary transition distribution. It turns out that, for a given P(θ | X), many Markov chains with the desired property can be constructed. We refer to methods that use Markov chain simulation to obtain the distribution P(θ | X) as Markov Chain Monte Carlo (MCMC) methods. The development of MCMC methods took place in various forms

…

,0 , θ2,0 , θ3,0 ), the prior Gibbs iterations have a chance to visit the full parameter space. The actual convergence theorem involves using the Markov Chain theory; see Tierney (1994). In practice, we use a sufficiently large n and discard the first m random draws of the Gibbs iterations to form

…

, 39, 1–38. Elerian, O., Chib, S., and Shephard, N. (2001), “Likelihood inference for discretely observed nonlinear diffusions,” Econometrica, 69, 959–993. Eraker, B. (2001), “Markov Chain Monte Carlo analysis of diffusion models with application to finance,” Journal of Business & Economic Statistics 19, 177–191. Gelfand, A. E., and Smith, A. F

…

the Bayesian restoration of images,” IEEE transactions on Pattern Analysis and Machine Intelligence, 6, 721–741. Hasting, W. K. (1970), “Monte Carlo sampling methods using Markov chains and their applications,” Biometrika, 57, 97–109. Jacquier, E., Polson, N. G., and Rossi, P. E. (1994), “Bayesian analysis of stochastic volatility models” (with discussion

…

, W. H. (1987), “The calculation of posterior distributions by data augmentation” (with discussion), Journal of the American Statistical Association, 82, 528– 550. Tierney, L. (1994), “Markov chains for exploring posterior distributions” (with discussion), Annals of Statistics, 22, 1701–1762. Tsay, R. S. (1988), “Outliers, level shifts, and variance changes in time series

The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World

by Pedro Domingos  · 21 Sep 2015  · 396pp  · 117,149 words

probability to, of all things, poetry. In it, he modeled a classic of Russian literature, Pushkin’s Eugene Onegin, using what we now call a Markov chain. Rather than assume that each letter was generated at random independently of the rest, he introduced a bare minimum of sequential structure: he let the

…

in English (or almost), regardless of the language the pages were originally written in. PageRank, the algorithm that gave rise to Google, is itself a Markov chain. Larry Page’s idea was that web pages with many incoming links are probably more important than pages with few, and links from important pages

…

themselves count for more. This sets up an infinite regress, but we can handle it with a Markov chain. Imagine a web surfer going from page to page by randomly following links: the states of this Markov chain are web pages instead of characters, making it a vastly larger problem, but the math is

…

fraction of the time the surfer spends on it, or equivalently, his probability of landing on the page after wandering around for a long time. Markov chains turn up everywhere and are one of the most intensively studied topics in mathematics, but they’re still a very limited kind of probabilistic model

…

. We can go one step further with a model like this: The states form a Markov chain, as before, but we don’t get to see them; we have to infer them from the observations. This is called a hidden Markov model

…

to infer the words from the sounds. The model has two components: the probability of the next word given the current one, as in a Markov chain, and the probability of hearing various sounds given the word being pronounced. (How exactly to do the inference is a fascinating problem that we’ll

…

variables, provided each variable depends directly on only a few others. We can represent these dependencies with a graph like the ones we saw for Markov chains and HMMs, except now the graph can have any structure (as long as the arrows don’t form closed loops). One of Pearl’s favorite

…

events, or “black swans,” as Nassim Taleb calls them. In retrospect, we can see that Naïve Bayes, Markov chains, and HMMs are all special cases of Bayesian networks. The structure of Naïve Bayes is: Markov chains encode the assumption that the future is conditionally independent of the past given the present. HMMs assume in

…

most popular option, however, is to drown our sorrows in alcohol, get punch drunk, and stumble around all night. The technical term for this is Markov chain Monte Carlo, or MCMC for short. The “Monte Carlo” part is because the method involves chance, like a visit to the eponymous casino, and the

…

“Markov chain” part is because it involves taking a sequence of steps, each of which depends only on the previous one. The idea in MCMC is to

…

then estimate the probability of a burglary, say, as the fraction of times we visited a state where there was a burglary. A “well-behaved” Markov chain converges to a stable distribution, so after a while it always gives approximately the same answers. For example, when you shuffle a deck of cards

…

you know that if there are n possible orders, the probability of each one is 1/n. The trick in MCMC is to design a Markov chain that converges to the distribution of our Bayesian network. One easy option is to repeatedly cycle through the variables, sampling each one according to its

…

conditional probability given the state of its neighbors. People often talk about MCMC as a kind of simulation, but it’s not: the Markov chain does not simulate any real process; rather, we concocted it to efficiently generate samples from a Bayesian network, which is itself not a sequential model

…

it’s converged when it hasn’t. Real probability distributions are usually very peaked, with vast wastelands of minuscule probability punctuated by sudden Everests. The Markov chain then converges to the nearest peak and stays there, leading to very biased probability estimates. It’s as if the drunkard followed the scent of

…

stayed there all night, instead of wandering all around the city like we wanted him to. On the other hand, if instead of using a Markov chain we just generated independent samples, like simpler Monte Carlo methods do, we’d have no scent to follow and probably wouldn’t even find that

…

of luck. We have to resort to, for example, doing MCMC over the space of networks, jumping from one possible network to another as the Markov chain progresses. Combine all this complexity and computational cost with Bayesians’ controversial notion that there’s really no such thing as objective reality, and it’s

…

Jones (Journal of the American Society for Information Science, 1976), explains the use of Naïve Bayes–like methods in information retrieval. “First links in the Markov chain,” by Brian Hayes (American Scientist, 2013), recounts Markov’s invention of the eponymous chains. “Large language models in machine translation,”* by Thorsten Brants et al

…

hidden Markov model, 154–155 If . . . then . . . rules and, 155–156 inference problem, 161–166 learning and, 166–170 logic and probability and, 173–175 Markov chain, 153–155 Markov networks, 170–173 Master Algorithm and, 240–241, 242 medical diagnosis and, 149–150 models and, 149–153 nature and, 141 probabilistic

…

Institute of Biotechnology, 16 Mandelbrot set, 30, 300 Margins, 192–194, 196, 241, 242, 243, 307 Markov, Andrei, 153 Markov chain Monte Carlo (MCMC), 164–165, 167, 170, 231, 241, 242, 253, 256 Markov chains, 153–155, 159, 304–305 Markov logic. See Markov logic networks (MLNs) Markov logic networks (MLNs), 246–259, 309

…

Matrix factorization for recommendation systems, 215 Maximum likelihood principle, 166–167, 168 Maxwell, James Clerk, 235 McCulloch, Warren, 96 McKinsey Global Institute, 9 MCMC. See Markov chain Monte Carlo (MCMC) Means-ends analysis, 225 Mechanical Turk, 14 Medical data, sharing of, 272–273 Medical diagnosis, 23, 147, 149–150, 160, 169, 228

Hands-On Machine Learning With Scikit-Learn and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems

by Aurélien Géron  · 13 Mar 2017  · 1,331pp  · 163,200 words

first introduce Markov decision processes (MDP). Markov Decision Processes In the early 20th century, the mathematician Andrey Markov studied stochastic processes with no memory, called Markov chains. Such a process has a fixed number of states, and it randomly evolves from one state to another at each step. The probability for it

…

it depends only on the pair (s,s′), not on past states (the system has no memory). Figure 16-7 shows an example of a Markov chain with four states. Suppose that the process starts in state s0, and there is a 70% chance that it will remain in that state at

…

a number of times between these two states, but eventually it will fall into state s3 and remain there forever (this is a terminal state). Markov chains can have very different dynamics, and they are heavily used in thermodynamics, chemistry, statistics, and much more. Figure 16-7. Example of a

…

Markov chain Markov decision processes were first described in the 1950s by Richard Bellman.11 They resemble Markov chains but with a twist: at each step, an agent can choose one of several possible actions, and the

…

manifold assumption/hypothesis, Manifold Learning Manifold Learning, Manifold Learning, LLE(see also LLE (Locally Linear Embedding) MapReduce, Frame the Problem margin violations, Soft Margin Classification Markov chains, Markov Decision Processes Markov decision processes, Markov Decision Processes-Markov Decision Processes master service, The Master and Worker Services Matplotlib, Create the Workspace, Take a

Model Thinker: What You Need to Know to Make Data Work for You

by Scott E. Page  · 27 Nov 2018  · 543pp  · 153,550 words

in Evolution. Oxford: Oxford University Press. Kennedy, John F. 1956. Profiles in Courage. New York: Harper & Brothers. Khmelev, Dmitri, and F. J. Tweedie. 2001. “Using Markov Chains for Identification of Writers.” Literary and Linguistic Computing 16, no. 4: 299–307. Kleinberg, Jon, and M. Raghu. 2015. “Team Performance with Test Scores.” Working

…

Pooled Cross-Sectional Analysis.” American Journal of Political Science 32: 137–154. Martin, Andrew D., and Kevin M. Quinn. 2002. “Dynamic Ideal Point Estimation via Markov Chain Monte Carlo for the U.S. Supreme Court, 1953–1999.” Political Analysis 10: 134–153. Martin, Francis, et al. 2008. “The Genome of Laccaria bicolor

Life After Google: The Fall of Big Data and the Rise of the Blockchain Economy

by George Gilder  · 16 Jul 2018  · 332pp  · 93,672 words

only in Silicon Valley but also in finance. CHAPTER 8 Markov and Midas One of the supremely seminal ideas of the twentieth century is the Markov chain. Introduced by the Russian mathematician and information theorist Andrey Markov in 1913, it became a set of statistical tools for predicting the future from the

…

throws of a single die and a thousand dice each thrown once.”2 Addressing the temporal dependencies between events, how one thing leads to another, Markov chains trace the probabilistic transitions from one state or condition to another, step by step through time. Markov followed the lead of the nineteenth-century intellectual

…

rocket or airplane trajectories during World War II, using Markov math to predict the future location of moving objects by observing their current positions. Bringing Markov chains to big data, the mathematician Leonard E. Baum of the Institute for Defense Analyses (IDA) demonstrated how a sufficiently long chain of observations can be

…

the predictive use of the chains “hidden Markov models” at a 1980 conference in Princeton. By every measure, the most widespread, immense, and influential of Markov chains today is Google’s foundational algorithm, PageRank, which encompasses the petabyte reaches of the entire World Wide Web. Treating the Web as a

…

Markov chain enables Google’s search engine to gauge the probability that a particular Web page satisfies your search.5 To construct his uncanny search engine, Larry

…

is consistent with what we know about statistics: they predict group behavior without accounting for individual decisions or free will. A defining property of a Markov chain is that it is memoryless. The history is assumed to be summed up by the current state and not by any past history of the

…

is famous for his political role funding Republicans (Simons and Brown finance Democrats), he and his associates remain obdurately obscure with their unique achievements, hidden Markov chains of gold. Unlike its West Coast counterpart Google, the Renaissance group completely escaped the perils of the Great Recession, which humbled so many hedge funds

…

dimensions. With more than $65 billion currently under management, Mercer’s team relies on racks of Renaissance workstations linked to form supercomputers. They parse immense Markov chains of ordered data to find filigree “ghosts” of tradable correlation. Like Google’s PageRank and its Deep Learning successes with language translation and games, like

…

amazing performance in 2007 and 2008. Without relying on the outsized leverage that brought down other funds, Renaissance thrives by processing more data, building larger Markov chains, ferreting out more correlations and probabilities, and executing more trades than anyone else. A venture capitalist on Sand Hill Road in Palo Alto investing in

…

pure sounds or colors. In finance, a Fourier model would move from the time domain of the record of trades, one after another in a Markov chain, to the frequency domain depicting the pure frequency components of the trading pattern. Converting from the time domain of all Medallion’s trades, for example

…

sees randomness everywhere, from a random walk on Wall Street or on Main Street or down the Vegas Strip with gambler’s ruin wrapped in Markov chains, or through geological time in evolution, or through the history of “inevitable” invention, or across the wastes and wealth of the World Wide Web. Happenstance

…

of individual companies to find the pure tones of true technology advance. Since Einstein used the concept to calculate the spontaneous gigahertz jiggling of molecules, Markov chains accelerated to gigahertz frequencies have enabled scientists to dominate a world economy ruled by chaotic money creation from central banks. Now, in the Google system

…

a high-entropy era of human creativity and accomplishment. The new era will move beyond Markov chains of disconnected probabilistic states to blockchain hashes of history and futurity, trust and truth. The opposite of memoryless Markov chains is blockchains. While Markov chains gain efficiency and speed by rigorously eclipsing the past, blockchains elaborately perpetuate the past

…

in every block with a mathematical hash. Perhaps ten thousand times slower to compute than Markov chains, every hash contains an indelible signature of all transactions

…

going back to the original block. Markov chains tell you the statistically likely future without knowing the past; blockchains enable the real-life future by

…

indelibly recording the past. Blockchains thus preserve and extend information, while Markov chains risk destroying it with the assumption of randomness. Removing the specific intentions and plans, histories and identities from their calculus, Markov models represent a flight

…

become the sixth-most-cited in the entire corpus of computer science. 2. Philipp von Hilgers and Amy N. Langville, “The Five Greatest Applications of Markov Chains,” in Amy N. Langville and William J. Stewart, eds., Proceedings of the Markov Anniversary Meeting (Altadena, Calif.: Boson Books, 2006), 156–57. 3. Claude Elwood

…

and Brion Shimamoto, “Embedded Systems and the Microprocessor,” Microprocessor Report (Cahners) April 24, 2000. von Hilgers, Philipp and Amy Langville, “The Five Greatest Applications of Markov Chains”, Proceedings of the Markov Anniversary Meeting. Boson Press, 2006. Index A note about the index: The pages referenced in this index refer to the page

Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else

by Jordan Ellenberg  · 14 May 2021  · 665pp  · 159,350 words

Artificial Intelligence: A Modern Approach

by Stuart Russell and Peter Norvig  · 14 Jul 2019  · 2,466pp  · 668,761 words

Programming in Lua, Fourth Edition

by Roberto Ierusalimschy  · 14 Jul 2016  · 489pp  · 117,470 words

The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy

by Sharon Bertsch McGrayne  · 16 May 2011  · 561pp  · 120,899 words

The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling

by Adam Kucharski  · 23 Feb 2016  · 360pp  · 85,321 words

Monte Carlo Simulation and Finance

by Don L. McLeish  · 1 Apr 2005

Web Scraping With Python: Collecting Data From the Modern Web

by Ryan Mitchell  · 14 Jun 2015  · 255pp  · 78,207 words

The Singularity Is Near: When Humans Transcend Biology

by Ray Kurzweil  · 14 Jul 2005  · 761pp  · 231,902 words

Literary Theory for Robots: How Computers Learned to Write

by Dennis Yi Tenen  · 6 Feb 2024  · 169pp  · 41,887 words

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution

by Gregory Zuckerman  · 5 Nov 2019  · 407pp  · 104,622 words

Data Mining: Concepts and Techniques: Concepts and Techniques

by Jiawei Han, Micheline Kamber and Jian Pei  · 21 Jun 2011

Mastering Pandas

by Femi Anthony  · 21 Jun 2015  · 589pp  · 69,193 words

Understanding search engines: mathematical modeling and text retrieval

by Michael W. Berry and Murray Browne  · 15 Jan 2005

Tools for Computational Finance

by Rüdiger Seydel  · 2 Jan 2002  · 313pp  · 34,042 words

The Art of R Programming

by Norman Matloff  · 404pp  · 43,442 words

Finding Alphas: A Quantitative Approach to Building Trading Strategies

by Igor Tulchinsky  · 30 Sep 2019  · 321pp

NumPy Cookbook

by Ivan Idris  · 30 Sep 2012  · 197pp  · 35,256 words

Mapmatics: How We Navigate the World Through Numbers

by Paulina Rowinska  · 5 Jun 2024  · 361pp  · 100,834 words

The Art of Computer Programming: Fundamental Algorithms

by Donald E. Knuth  · 1 Jan 1974

Handbook of Modeling High-Frequency Data in Finance

by Frederi G. Viens, Maria C. Mariani and Ionut Florescu  · 20 Dec 2011  · 443pp  · 51,804 words

Seeking SRE: Conversations About Running Production Systems at Scale

by David N. Blank-Edelman  · 16 Sep 2018

We Are All Completely Beside Ourselves

by Karen Joy Fowler  · 29 May 2013  · 298pp  · 84,394 words

SciPy and NumPy

by Eli Bressert  · 14 Oct 2012  · 62pp  · 14,996 words

Machine Learning for Hackers

by Drew Conway and John Myles White  · 10 Feb 2012  · 451pp  · 103,606 words

The Cultural Logic of Computation

by David Golumbia  · 31 Mar 2009  · 268pp  · 109,447 words

A Mathematician Plays the Stock Market

by John Allen Paulos  · 1 Jan 2003  · 295pp  · 66,824 words

The Art of SEO

by Eric Enge, Stephan Spencer, Jessie Stricchiola and Rand Fishkin  · 7 Mar 2012

Algorithms to Live By: The Computer Science of Human Decisions

by Brian Christian and Tom Griffiths  · 4 Apr 2016  · 523pp  · 143,139 words

Co-Intelligence: Living and Working With AI

by Ethan Mollick  · 2 Apr 2024  · 189pp  · 58,076 words

From Bacteria to Bach and Back: The Evolution of Minds

by Daniel C. Dennett  · 7 Feb 2017  · 573pp  · 157,767 words

Principles of Protocol Design

by Robin Sharp  · 13 Feb 2008

Six Degrees: The Science of a Connected Age

by Duncan J. Watts  · 1 Feb 2003  · 379pp  · 113,656 words

The Big Nine: How the Tech Titans and Their Thinking Machines Could Warp Humanity

by Amy Webb  · 5 Mar 2019  · 340pp  · 97,723 words

The Most Human Human: What Talking With Computers Teaches Us About What It Means to Be Alive

by Brian Christian  · 1 Mar 2011  · 370pp  · 94,968 words

Track Changes

by Matthew G. Kirschenbaum  · 1 May 2016  · 519pp  · 142,646 words

A Brief History of Everyone Who Ever Lived

by Adam Rutherford  · 7 Sep 2016

Transport for Humans: Are We Nearly There Yet?

by Pete Dyson and Rory Sutherland  · 15 Jan 2021  · 342pp  · 72,927 words

With a Little Help

by Cory Efram Doctorow, Jonathan Coulton and Russell Galen  · 7 Dec 2010  · 549pp  · 116,200 words

Skin in the Game: Hidden Asymmetries in Daily Life

by Nassim Nicholas Taleb  · 20 Feb 2018  · 306pp  · 82,765 words

The Rapture of the Nerds

by Cory Doctorow and Charles Stross  · 3 Sep 2012  · 311pp  · 94,732 words

Creative Selection: Inside Apple's Design Process During the Golden Age of Steve Jobs

by Ken Kocienda  · 3 Sep 2018  · 255pp  · 76,834 words

The Patient Will See You Now: The Future of Medicine Is in Your Hands

by Eric Topol  · 6 Jan 2015  · 588pp  · 131,025 words

Bleeding Edge: A Novel

by Thomas Pynchon  · 16 Sep 2013  · 532pp  · 141,574 words

Gnomon

by Nick Harkaway  · 18 Oct 2017  · 778pp  · 239,744 words

Networks, Crowds, and Markets: Reasoning About a Highly Connected World

by David Easley and Jon Kleinberg  · 15 Nov 2010  · 1,535pp  · 337,071 words

The Road to Ruin: The Global Elites' Secret Plan for the Next Financial Crisis

by James Rickards  · 15 Nov 2016  · 354pp  · 105,322 words

The Year's Best Science Fiction: Twenty-Sixth Annual Collection

by Gardner Dozois  · 23 Jun 2009  · 1,263pp  · 371,402 words

The Data Warehouse Toolkit: The Definitive Guide to Dimensional Modeling

by Ralph Kimball and Margy Ross  · 30 Jun 2013