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In statistics, sequential estimation refers to estimation methods in sequential analysis where the sample size is not fixed in advance. Instead, data is
Sequential_estimation
Statistical analysis where the sample size is not fixed in advance
classical hypothesis testing or estimation, at consequently lower financial and/or human cost. The method of sequential analysis is first attributed to
Sequential_analysis
Process of controlling orientation of an aerospace vehicle
Junkins.. Chapman and Hall/CRC, 2004. Kalman filtering can be used to sequentially estimate the attitude, as well as the angular rate. Because attitude
Spacecraft attitude determination and control
Spacecraft_attitude_determination_and_control
Method of data analysis
useful to make an estimate of the PCA projection that can be updated sequentially. This can be done efficiently, but requires different algorithms. In
Principal_component_analysis
American mathematician and statistician (1919–2010)
Blackwell published the paper "Conditional Expectation and Unbiased Sequential Estimation", which outlined a technique that later became known as the Rao–Blackwell
David_Blackwell
Algorithm that estimates unknowns from a series of measurements over time
"Factorization Methods for Discrete Sequential Estimation". Factorization Methods for Discrete Sequential Estimation. Bibcode:1977fmds.book.....B. Bar-Shalom
Kalman_filter
Branch of mathematics concerning probability
partial knowledge of their state, as in statistical mechanics or sequential estimation. A great discovery of twentieth-century physics was the probabilistic
Probability_theory
Nonparametric measure of rank correlation
estimators. These estimators, based on Hermite polynomials, allow sequential estimation of the probability density function and cumulative distribution
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Process for estimating a probability density function
PDF into a deterministic discrete grid Sequential Bayesian filtering is the extension of the Bayesian estimation for the case when the observed value changes
Recursive_Bayesian_estimation
Type of Monte Carlo algorithms for signal processing and statistical inference
localization Moving horizon estimation Recursive Bayesian estimation Wills, Adrian G.; Schön, Thomas B. (3 May 2023). "Sequential Monte Carlo: A Unified Review"
Particle_filter
Estimation method that minimizes the mean square error
estimates. One crucial difference between batch estimation and sequential estimation is that sequential estimation requires an additional Markov assumption.
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Mathematical decision rule
for sequential estimation, where the posterior of the current measurement is used as the prior in the next measurement. In sequential estimation, unless
Bayes_estimator
British statistician (c. 1701 – 1761)
the core of almost every modern estimation approach that includes conditioned probabilities, such as sequential estimation, probabilistic machine learning
Thomas_Bayes
Digital circuit design abstraction
A synchronous circuit consists of two kinds of elements: registers (sequential logic) and combinational logic. Registers (usually implemented as D flip-flops)
Register-transfer_level
Hypothesis test in mathematics
The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald and later proven to be optimal by Wald
Sequential probability ratio test
Sequential_probability_ratio_test
index Separation test Sequential analysis Sequential estimation Sequential Monte Carlo methods – redirects to Particle filter Sequential probability ratio
List_of_statistics_articles
In econometrics, structural estimation is a technique for estimating deep "structural" parameters of theoretical economic models. The term is inherited
Structural_estimation
although sequential versions were later developed, specifically the SNPHAP method. The most accurate and widely used methods for haplotype estimation utilize
Haplotype_estimation
Statistical experiment designs
GB; Chen, H; Vasudeva, RB (1966). "Sequential estimation of quantal response curves: a new method of estimation". Biometrika. 53 (3–4): 439–454. doi:10
Up-and-down_design
process has a finite state space. Magiera, R. (1998). "Optimal Sequential Estimation for Markov-Additive Processes". Advances in Stochastic Models for
Markov_additive_process
Statistical theorem
statistics Blackwell, D. (1947). "Conditional expectation and unbiased sequential estimation". Annals of Mathematical Statistics. 18 (1): 105–110. doi:10.1214/aoms/1177730497
Rao–Blackwell_theorem
Theorem in statistics
(1955) Ghosh, Malay; Mukhopadhyay, Nitis; Sen, Pranab Kumar (2011), Sequential Estimation, Wiley Series in Probability and Statistics, vol. 904, John Wiley
Basu's_theorem
Sequential model-based optimization of expensive black-box functions
Bayesian optimization is a sequential model-based strategy for global optimization of black-box objective functions whose evaluations are costly. It is
Bayesian_optimization
Creation and maintenance of software
customized and emergent for the development effort. The process may be sequential, in which each major phase (i.e., design, implement, and test) is completed
Software_development
Polish mathematician and statistician (1932–2008)
Doktoraty". www.impan.pl. Retrieved 2025-02-24. Trybuła, Stanisław. "Sequential estimation in processes with independent increments". Dissertationes Mathematicae
Stanisław_Trybuła
Probabilistic problem-solving algorithm
and MCMC methodologies, these mean-field particle techniques rely on sequential interacting samples. The terminology mean field reflects the fact that
Monte_Carlo_method
Problem in statistical estimation
In the statistical theory of estimation, the German tank problem consists of estimating the maximum of a discrete uniform distribution from sampling without
German_tank_problem
Procedure to estimate standard deviation from a sample
In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Form of dyadic relationship
Serial monogamy is a mating practice in which individuals may engage in sequential monogamous pairings, or in terms of humans, when men or women can marry
Monogamy
Image-based positioning and orientation of a robot
odometry is the process of determining equivalent odometry information using sequential camera images to estimate the distance traveled. Visual odometry allows
Visual_odometry
Resource problem in machine learning
constructed convergent population selection strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published
Multi-armed_bandit
Hungarian-American mathematician (1902–1950)
decision theory, geometry and econometrics, and founded the field of sequential analysis. One of his well-known statistical works was written during World
Abraham_Wald
Statistical method of dividing data into equal-sized intervals for analysis
a random process. These are statistics derived methods, sequential nonparametric estimation algorithms in particular. There are a number of such algorithms
Quantile
Computational method in Bayesian statistics
wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years
Approximate Bayesian computation
Approximate_Bayesian_computation
Process by which software is developed
difference between methodologies is the degree to which the phases are sequential vs. iterative. Agile methodologies, such as XP and scrum, focus on lightweight
Software_development_process
Statistical technique correcting sampling bias
ISBN 0-674-00560-0. Cameron, A. Colin; Trivedi, Pravin K. (2005). "Sequential Two-Step m-Estimation". Microeconometrics: Methods and Applications. New York: Cambridge
Heckman_correction
German academic working in photogrammetry and geodesy
studies and blunder detection in bundle systems Algorithms for sequential estimation in bundle systems (on-line triangulation) Geometrically constrained
Armin_Gruen
Rule for estimating the mean of a dataset
{\displaystyle {\boldsymbol {Y}}:=(Y_{1},Y_{2},\dots Y_{m})} . It arose sequentially in two main published papers. The earlier version of the estimator was
James–Stein_estimator
Branch of statistics focusing on spatial data sets
random variable) theory to model the uncertainty associated with spatial estimation and simulation. A number of simpler interpolation methods/algorithms,
Geostatistics
Sub-field of reinforcement learning
explored using classic matrix games such as prisoner's dilemma, more complex sequential social dilemmas, and recreational games such as Among Us, Diplomacy and
Multi-agent reinforcement learning
Multi-agent_reinforcement_learning
Distribution estimation technique
to sample from a different distribution to lower the variance of the estimation of 𝔼P[X], or when sampling directly from P is difficult. This is accomplished
Importance_sampling
Israeli-American academic
interplay between estimation theory and information theory, entropy, noise reduction (denoising), filtering, prediction, sequential decision making, learning
Tsachy_Weissman
foundations of statistics. Included earlier results of Wald on sequential analysis and the sequential probability ratio test and on Wald's complete class theorem
List of publications in statistics
List_of_publications_in_statistics
Perception concept
subsystem, or an elementary component of the system (e.g. a neuron). In sequential ideal observer analysis, the goal is to measure a real system's performance
Ideal_observer_analysis
Statistical Markov model
at t=t0 given X at time t=t0. Estimation of the parameters in an HMM can be performed using maximum likelihood estimation. For linear chain HMMs, the Baum–Welch
Hidden_Markov_model
Class of reinforcement learning algorithm
algorithms include Monte Carlo (MC) RL, SARSA, and Q-learning. Monte Carlo estimation is a central component of many model-free RL algorithms. The MC learning
Model-free (reinforcement learning)
Model-free_(reinforcement_learning)
Overview of and topical guide to statistics
(statistics) Survival analysis Density estimation Kernel density estimation Multivariate kernel density estimation Time series Time series analysis Box–Jenkins
Outline_of_statistics
Mathematical problem involving optimal stopping theory
ranked from best to worst unambiguously. The applicants are interviewed sequentially in random order, with each order being equally likely. Immediately after
Secretary_problem
Collection of statistical models
planned to satisfy the goals of the experiment. Experimentation is often sequential. Early experiments are often designed to provide mean-unbiased estimates
Analysis_of_variance
Method of statistical inference
interesting information. Also, this technique can hardly be avoided in sequential analysis." "A useful fact is that any Bayes decision rule obtained by
Bayesian_inference
Relationship between items in a set
an Internet search engine may rank the pages it finds according to an estimation of their relevance, making it possible for the user quickly to select
Ranking
Business process modeling tool
and IDEF. A control-flow diagram can consist of a subdivision to show sequential steps, with if-then-else conditions, repetition, and/or case conditions
Control-flow_diagram
the two-factor interaction BC has an effect on the response, then the estimation of factor A's effect on the response is contaminated because factor A's
Robust_parameter_design
3D reconstruction technique
orientation, often through some combination of SLAM, GPS, or inertial estimation. Researchers often use synthetic data to evaluate NeRF and related techniques
Neural_radiance_field
American statistician
November 15, 1941) is an American statistician who has worked extensively on sequential analysis. Siegmund grew up in Webster Groves, Missouri. He received his
David_Siegmund
Statistical model for a binary dependent variable
mortgage. Conditional random fields, an extension of logistic regression to sequential data, are used in natural language processing. Disaster planners and engineers
Logistic_regression
Design of tasks
experimenting, is within the scope of sequential analysis, a field that was pioneered by Abraham Wald in the context of sequential tests of statistical hypotheses
Design_of_experiments
Type of degradation in signal transmission
receive antennas. The ML estimation for the fractional CFO is quite popular in MIMO-OFDM systems. Another fractional CFO estimation algorithm for MIMO-OFDM
Carrier_frequency_offset
Theory in microeconomics
Jae Hyen; Chintagunta, Pradeep K.; Misra, Sanjog (2019-05-06). "Estimation of Sequential Search Model". SSRN. Rochester, NY. SSRN 3203973. Ursu, Raluca;
Search_theory
Statistical concept
clustering, under the name model-based clustering, and also for density estimation. Mixture models should not be confused with models for compositional data
Mixture_model
Model to simulate Li-ion cells electrical dynamics
real-time Battery Management System (BMS) tasks like State of Charge (SoC) estimation, State of Health (SoH) monitoring and battery thermal management. The
Equivalent circuit model for Li-ion cells
Equivalent_circuit_model_for_Li-ion_cells
Study of mathematical algorithms for optimization problems
(or approximate Hessians, using finite differences): Newton's method Sequential quadratic programming: A Newton-based method for small-medium scale constrained
Mathematical_optimization
Experimental design that is optimal with respect to some statistical criterion
design of sequential experiments. Sequential analysis was pioneered by Abraham Wald. In 1972, Herman Chernoff wrote an overview of optimal sequential designs
Optimal_experimental_design
Indian statistician
in 1995. Most notable areas of his research include, sequential analysis, statistical estimation in diffusion processes, the law of large numbers and
Arup_Bose
Selection of data points in statistics
counts within the size variable. This method is sometimes called PPS-sequential or monetary unit sampling in the case of audits or forensic sampling.
Sampling_(statistics)
Discrete probability distribution
Paszek, Ewa. "Maximum likelihood estimation – examples". cnx.org. Van Trees, Harry L. (2013). Detection estimation and modulation theory. Kristine L
Poisson_distribution
Indian statistician (1937–2017)
K. Nandi. He started his research career in the early 1960s, studying sequential analysis as a graduate student in the department of statistics at the
Jayanta_Kumar_Ghosh
Graphical tool in probability
copulas and enable extensions to arbitrary dimensions. Sampling theory and estimation theory for regular vines are well developed and model inference has left
Vine_copula
Statistical tool used in project management
CPM are complementary tools, because "CPM employs one time estimation and one cost estimation for each activity; PERT may utilize three time estimates (optimistic
Program evaluation and review technique
Program_evaluation_and_review_technique
Statistical algorithm
Zili; Zhang, Peng; Qi, Wenjuan; Liu, Jinfang; Gao, Yuan (2012-04-15). "Sequential covariance intersection fusion Kalman filter". Information Sciences. 189:
Covariance_intersection
Feature to efficiently execute queries efficiently in DBMS software
results by scanning the disk, for example by performing an index scan or a sequential scan. The performance of a query plan is determined largely by the order
Query_optimization
Calculation of complex statistical distributions
expanded the MCMC toolkit, including particle filters (Sequential Monte Carlo) for sequential problems, Perfect sampling aiming for exact simulation (Jim
Markov_chain_Monte_Carlo
Bayesian-optimal mechanism Bayesian-optimal pricing Bayesian optimization – Sequential model-based optimization of expensive black-box functions Bayesian poisoning –
List of things named after Thomas Bayes
List_of_things_named_after_Thomas_Bayes
Statistical test
advantage of the Wald test over the other two is that it only requires the estimation of the unrestricted model, which lowers the computational burden as compared
Wald_test
Theory and paradigm of statistics
includes a concept called 'influence of prior beliefs'. This approach uses sequential analysis techniques to include the outcome of earlier experiments in the
Bayesian_statistics
Statistical measure of the magnitude of a phenomenon
group of data-analysis methods concerning effect sizes is referred to as estimation statistics. Effect size is an essential component in the evaluation of
Effect_size
Statistical method for handling multiple comparisons
Bonferroni adjustment. This stepwise algorithm sorts the p-values and sequentially rejects the hypotheses starting from the smallest p-values. Benjamini
False_discovery_rate
Polynomial sequence
Herrmann, J. (1981). "Cross coupling and aliasing in modal wave-front estimation". J. Opt. Soc. Am. 71 (8): 989. Bibcode:1981JOSA...71..989H. doi:10.1364/JOSA
Zernike_polynomials
AI's tendency to abruptly and drastically forget old info after learning new info
then the network readily learned all of the associations correctly. In sequential training the A-B list was trained first, followed by the A-C list. After
Catastrophic_interference
Indian-American mathematician (1920–2023)
Sample. 1996. Bootstrap by Sequential Resampling. PN 1993. Applications of Multivariate Analysis. PN 1992. Signal Estimation, Multitarget Tracking and
C._R._Rao
Optimization method
differentiation as an option to solve maximum likelihood estimation and maximum a posteriori estimation problems. Notable proprietary implementations include:
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Concept in econometrics
from those that are predetermined (exogenous). Ignoring simultaneity in estimation leads to biased and inconsistent estimators, as it violates the exogeneity
Endogeneity_(econometrics)
Signal processing technique
{\textstyle [B]} are M × M {\textstyle M\times M} diagonal matrices with sequentially-placed z i {\textstyle z_{i}} and R i {\textstyle R_{i}} values, respectively
Generalized pencil-of-function method
Generalized_pencil-of-function_method
Mathematical model for sequential decision making under uncertainty
decision theory, a Markov decision process (MDP) is a mathematical model for sequential decision making when outcomes are uncertain. It is a type of stochastic
Markov_decision_process
Computational navigational technique used by robots and autonomous vehicles
x_{t+1}|o_{1:t+1},u_{1:t})} Applying Bayes' rule gives a framework for sequentially updating the location posteriors, given a map and a transition function
Simultaneous localization and mapping
Simultaneous_localization_and_mapping
Reconstructing an historical ocean state
climatological monthly estimates. The second approach is that of the sequential data assimilation analyses, which move forward in time from a previous
Ocean_reanalysis
Mathematical optimization algorithm
methods include: Successive linear programming (SLP) Sequential quadratic programming (SQP) Sequential linear-quadratic programming (SLQP) Reduced gradient
Active-set_method
Procedure for comparing multivariate sample means
life satisfactions scores measured at sequential time points and p job satisfaction scores measured at sequential time points. In this case there are k+p
Multivariate analysis of variance
Multivariate_analysis_of_variance
Class of artificial neural network
networks, recurrent neural networks (RNNs) are designed for processing sequential data, such as text, speech, and time series, where the order of elements
Recurrent_neural_network
Algorithm for modelling sequential data
until the 2017 publication of transformers. However, LSTM still used sequential processing, like most other RNNs. Specifically, RNNs operate one token
Transformer_(deep_learning)
Statistical method
intervals, prediction error, etc.) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling
Bootstrapping_(statistics)
Optimization algorithm
Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association rules Semantic analysis
Gradient_descent
Nonparametric spectral estimation method
analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series analysis, multivariate
Singular_spectrum_analysis
Statistic measuring inter-rater agreement for categorical items
R.; Gottman, J.M. (1997). Observing interaction: An introduction to sequential analysis (2nd ed.). Cambridge, UK: Cambridge University Press. ISBN 978-0-521-27593-4
Cohen's_kappa
Mathematical model for state estimation
to attack the infinite dimensional filtering problem and are based on sequential Monte Carlo methods. In general, if the separation principle applies,
Filtering problem (stochastic processes)
Filtering_problem_(stochastic_processes)
Computer simulation of chemical systems
theorem. The phase estimation algorithm can be enhanced or altered in several ways, such as using a single ancilla qubit for sequential measurements, increasing
Quantum computational chemistry
Quantum_computational_chemistry
Statistician and professor
research in nonparametric inference, sequential analysis, decision theory, Bayesian statistics and small-area estimation. As a recognition of his seminal
Malay_Ghosh
Algorithms for matrix decomposition
one by one (sequentially), i.e., learn the (n+1)-th component with the first n components constructed. The contribution of the sequential NMF components
Non-negative matrix factorization
Non-negative_matrix_factorization
Machine learning technique
but a more recent design, namely the transformer, removed the slower sequential RNN and relied more heavily on the faster parallel attention scheme, which
Attention_(machine_learning)
Model selection principle
other forms of inductive inference and learning, for example to estimation and sequential prediction, without explicitly identifying a single model of the
Minimum_description_length
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