Motivated by the concept of degeneracy in biology [3], we establish a first connection between the Multiplicity Principle [4, 5] and mathematical statistics. Specifically, we exhibit two families of tests that satisfy this principle to achieve the detection of a signal in noise.
In this work, we propose a new algorithm for sequential non-parametric hypothesis testing based on Random Distortion Testing (RDT). The data based approach is nonparametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. Our previously proposed non-truncated sequential algorithm, SeqRDT, was shown to achieve desired error probabilities under a few assumptions on the signal model. In this work, we show that the proposed truncated sequential algorithm, T-SeqRDT, requires even fewer assumptions on the signal model, while guaranteeing the error probabilities to be below pre-specified levels and at the same time makes a decision faster compared to its optimal fixedsample-size (FSS) counterpart, BlockRDT. We derive bounds on the error probabilities and the average stopping times of the algorithm. Via numerical simulations, we compare the performance of T-SeqRDT to SeqRDT, BlockRDT, sequential probability ratio test (SPRT) and composite sequential probability ratio tests. We also show the robustness of the proposed approach compared to standard likelihood ratio based approaches.
In this work, we propose a non-parametric sequential hypothesis test based on random distortion testing (RDT). RDT addresses the problem of testing whether or not a random signal, Ξ, observed in independent and identically distributed (i.i.d) additive noise deviates by more than a specified tolerance, τ , from a fixed model, ξ0. The test is non-parametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. The need to control the probabilities of false alarm (PFA) and missed detection (PMD), while reducing the number of samples required to make a decision, leads to a novel sequential algorithm, SeqRDT. We show that under mild assumptions on the signal, SeqRDT follows the properties desired by a sequential test. We introduce the concept of a buffer and derive bounds on PFA and PMD, from which we choose the buffer size. Simulations show that SeqRDT leads to faster decisionmaking on an average compared to its fixed-sample-size (FSS) counterpart, BlockRDT. These simulations also show that the proposed algorithm is robust to model mismatches compared to the sequential probability ratio test (SPRT).
Communicating living systems detect and process a multiplicity of events with degeneracy, to continuously cope with environmental aleatoric incertitude. The concept of holon, communicating at various scales of living organizations, is hereafter formalized through dynamical systems driven by the multiplicity of statistical models. Then, the stimulus-response of elementary biological holons can be modeled by memoryless Boolean automata with different signal processing methods, in presence of noise and stochastic interference. Detection of a specified signal, to update the automaton state, can be performed via multiple families of update functions, with differentiated balances between sensitivity and specificity in presence of interference: (i) Neyman-Pearson update functions provide the best possible sensitivity to detect the signal of interest in absence of interference, but cannot guarantee a desired specificity; (ii) by detecting large amplitudes of any signal in noise, update functions based on Random Distortion Testing yield a suboptimal sensitivity to detect the signal in noise, but guarantee a wanted specificity even in presence of interference. Thus, statistical inference theories offer functional and structural redundancy and open prospects to model fractal-like holarchies, via networks of communicating degenerated automata, to feature properties of the immune system.
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